Below are a variety of topics covered in greater depth or of more specialized interest than found in the Quick Tour. Reading the Quick Tour first is recommended.
An arc iterator is used to access the transitions leaving an FST state. It has the form:
template <class F> class ArcIterator { typedef typename F::Arc Arc; typedef typename Arc::StateId StateId; public: ArcIterator(const &F fst, StateId s); // End of iterator? bool Done() const; // Current arc (when !Done) const Arc& Value() const; // Advances to next arc (when !Done) void Next(); // Returns current position size_t Position(); // Returns to initial position void Reset(); // Arc access by position void Seek(size_t pos); // Returns arc flags uint32 Flags() const; // Sets arc flags void SetFlags(uint32 flags, uint32 mask); };
It is templated on the Fst class F
to allow efficient specializations but defaults to a generic version on the abstract
base Fst class.
See here for conventions that arc iterator use must respect.
All current OpenFst library Seek()
methods are constant time.
An example use of an arc iterator is shown here.
A MutableArcIterator
is similar to an ArcIterator
except its
constructor takes a pointer to a MutableFst
and it additionally has a SetValue()
method.
Arc filters are accepted by various operations to control which arcs are transitioned. An arc filter has the form:
template <class Arc>
class SomeArcFilter {
public:
// Return true iff arc is to be transitioned.
bool operator()(const Arc &arc) const;
};
Predefined arc filters include:
Name  Description  

AnyArcFilter 
Accept all arcs  
EpsilonArcFilter 
Accept only arcs with input and output epsilons  
InputEpsilonArcFilter 
Accept only arcs with input epsilons  
OutputEpsilonArcFilter 
Accept only arcs with output epsilons 
Arc mappers are function objects used by the ArcMap operation to transform arcs and/or final states. An arc mapper has the form:
// This determines how final weights are mapped. enum MapFinalAction { // A final weight is mapped into a final weight. An error // is raised if this is not possible. MAP_NO_SUPERFINAL, // A final weight is mapped to an arc to the superfinal state // when the result cannot be represented as a final weight. // The superfinal state will be added only if it is needed. MAP_ALLOW_SUPERFINAL, // A final weight is mapped to an arc to the superfinal state // unless the result can be represented as a final weight of weight // Zero(). The superfinal state is always added (if the input is // not the empty Fst). MAP_REQUIRE_SUPERFINAL }; // This determines how symbol tables are mapped. enum MapSymbolsAction { // Symbols should be cleared in the result by the map. MAP_CLEAR_SYMBOLS, // Symbols should be copied from the input FST by the map. MAP_COPY_SYMBOLS, // Symbols should not be modified in the result by the map itself. // (They may set by the mapper). MAP_NOOP_SYMBOLS }; class SomeArcMapper { public: // Assumes input arc type is A and result arc type is B typedef A FromArc; typedef B ToArc; // Maps an arc type A to arc type B. B operator()(const A &arc); // Specifies final action the mapper requires (see above). // The mapper will be passed final weights as arcs of the // form A(0, 0, weight, kNoStateId). MapFinalAction FinalAction() const; // Specifies input symbol table action the mapper requires (see above). MapSymbolsAction InputSymbolsAction() const; // Specifies output symbol table action the mapper requires (see above). MapSymbolsAction OutputSymbolsAction() const; // This specifies the known properties of an Fst mapped by this // mapper. It takes as argument the input Fst's known properties uint64 Properties(uint64 props) const; };
The following arc mappers are defined in the OpenFst library:
Name  Description  

FromGallicMapper 
Extracts output label from gallic weight  
IdentityArcMapper 
Maps to self  
InvertWeightMapper 
Reciprocate all non0 weights  
PlusMapper 
Adds (⊕) a constant to all weights  
QuantizeMapper 
Quantize all weights  
ReverseWeightMapper 
Reverse all weights  
RmWeightMapper 
Map all non0 weights to 1  
SuperFinalMapper 
Redirects final states to new superfinal state  
TimesMapper 
(Right) multiplies (⊗) a constant to all weights  
ToGallicMapper 
Combines output label and weight into gallic weight  
WeightConvertMapper 
Converts arc weight types (assuming appropriate WeightConvert class specialization), leaving labels and nextstates the same. 
ToGallicMapper
and FromGallicMapper
are used, for example, to implement transducer determinization and
minimization using weighted acceptor versions of these algorithms. Other specialized arc mappers are used to implement Decode, Encode, Invert, and Project.
An Arc
is a type that represents an FST transition from a given source state. It specifies an input label, an output label, a weight, and a destination state ID and it has a type name. In particular, it has the following form:
struct SomeArc { typedef W Weight; typedef L Label; typedef S StateId; static const string &Type(); Label ilabel; Label olabel; Weight weight; StateId nextstate; };
where W
is a valid weight type, and L
and S
are signed integral types.
The following arc types are defined in the OpenFst library:
Name  Label Type  State ID Type  Weight Type  Registered 

ExpectationArc<A, W> 
int 
int 
ExpectationWeight<A::Weight, W> 

GallicArc<A, S> 
A::Label 
A::StateId 
GallicWeight<A::Label, A::Weight, S> 

LexicographicArc<W1, W2> 
int 
int 
LexicographicWeight<W1, W2> 

LogArc 
int 
int 
LogWeight 

Log64Arc 
int 
int 
Log64Weight 

MinMaxArc 
int 
int 
MinMaxWeight 

PowerArc<A, n> 
int 
int 
PowerWeight<A::Weight, n> 

ProductArc<W1, W2> 
int 
int 
ProductWeight<W1, W2> 

SignedLogArc 
int 
int 
SignedLogWeight 

SignedLog64Arc 
int 
int 
SignedLog64Weight 

SparsePowerArc<A> 
int 
int 
SparsePowerWeight<A::Weight> 

StdArc 
int 
int 
TropicalWeight 

StringArc<S> 
int 
int 
StringWeight<int, S> 
Additional arc information:
Every Fst
must specify an initial state, the final weights, arc and epsilon counts per states, an Fst type name, the Fst's properties, how to copy, read and write the Fst, and the input and output symbol tables (if any). In particular, the base Fst
class has the interface:
template <class A> class Fst { public: typedef A Arc; typedef typename A::Weight Weight; typedef typename A::StateId StateId; // Initial state virtual StateId Start() const = 0; // States's final weight virtual Final(StateId) const = 0: // State's arc count virtual NumArcs(StateId) const = 0; // States's input epsilon count virtual NumInputEpsilons(StateId) const = 0; // State's output epsilon count virtual NumOutputEpsilons(StateId) const = 0; // If test=false, return stored properties bits for mask (some poss. unknown) // If test=true, return property bits for mask (computing o.w. unknown) virtual Properties(uint64 mask, bool test) const = 0; // Fst type name virtual const string& Type() const = 0; // Get a copy of this Fst virtual Fst<A> *Copy() const = 0; // Read an Fst from an input stream; returns NULL on error static Fst<A> *Read(istream &strm, const FstReadOptions &opts); // Read an Fst from a file; return NULL on error // Empty filename reads from standard input static Fst<A> *Read(const string &filename); // Write an Fst to an output stream; return false on error virtual bool Write(ostream &strm, const FstWriteOptions &opts); // Write an Fst to a file; return false on error // Empty filename writes to standard output virtual bool Write(const string &filename); // Return input label symbol table; return NULL if not specified virtual const SymbolTable* InputSymbols() const = 0; // Return output label symbol table; return NULL if not specified virtual const SymbolTable* OutputSymbols() const = 0; };
Fst
is an abstract class (note the pure virtual methods). All OpenFst FSTs must meet this interface.
The companion state iterator and arc iterator classes provide access to the states and transitions of the FST.
Most of the delayed Fst classes use internal caching to save expanded states and arcs. This caching is controlled by this struct:
struct CacheOptions { // enable GC bool gc; // # of bytes allowed before GC size_t gc_limit; CacheOptions(bool g, size_t l) : gc(g), gc_limit(l) {} CacheOptions() : gc(FLAGS_fst_default_cache_gc), gc_limit(FLAGS_fst_default_cache_gc_limit) {} };
All OpenFst cached Fsts have constructors that accept this (or a class derived from it) as an argument. The member defaults are controlled by global flags. These options can be used for:
gc
is false
, then any expanded state will be cached for the extent of the FST. This case is useful when states are revisited and memory is not a concern.
gc
is true
, then the cache will be garbagecollected when it grows past gc_limit
. This case is useful when states are revisited and memory is a concern. This is the default case (based on the global flags).
gc
is true
, (2) gc_limit
is 0, and (3) arcs iterators have been created (and then destroyed) only one state at a time, then only information for that state is cached and this case is especially optimized. This case is useful when states are not revisited (e.g. when a cached FST is simply being copied to a mutable FST).
OpenFst has several global options in the library proper that most users can ignore, leaving them with their default values:
Option  Type  Default  Description 

FLAGS_fst_compat_symbols 
bool  true  Require symbol tables to match when appropriate 
FLAGS_fst_default_cache_gc 
bool  true  Enable garbage collection of cached Fsts 
FLAGS_fst_default_cache_gc_limit 
int64  1048576  Byte size that triggers garbage collection of cached Fsts 
FLAGS_fst_error_fatal 
bool  true  FST errors are fatal; o.w. return objects flagged as bad: e.g., FSTs  kError prop. true, FST weights  not a Member() 
FLAGS_fst_field_separator 
string  " \t"  Set of characters used as a separator between printed fields 
FLAGS_fst_weight_parentheses 
string  ""  Characters enclosing the first weight of a printed composite weight (and derived classes) to ensure proper I/O of nested composite weights; must have size 0 (none) or 2 (open and close parenthesis) 
FLAGS_fst_weight_separator 
string  ","  Character separator between printed composite weights; must be a single character 
FLAGS_fst_verify_properties 
bool  false  Verify Fst properties are correctly set when queried 
The first ensures the arguments of binary FST operations (e.g. composition) have compatible symbol tables (e..g output symbol table matches input symbol table for composition). The second two are used to control the caching of expanded state and arc information found in most delayed Fst classes; the default values should normally be satisfactory. The next determines how errors are handled. The next is used in the textual representation of FSTs and symbol tables. The next two are used to control the text formating of ProductWeight and other weight tuples. The last is used to ensure that the properties of an FST have been correctly set; it is used for debugging only since it incurs considerable computational cost.
In each of the Fst distribution installed binaries, the above options, as well as any of those defined specific to the binary, can be set from the command line using e.g.
fst_default_cache_gc=false
or fst_weight_parenthesis="("
. Additionally, the option help
and v=N
(where N = 0,1,2,..) will print out usage information and
set the verbosity level of logging, respectively. The flag processing is modeled after the Google gflags package.
In a userdefined binary, the command line options processing will all also work if the user calls:
SetFlags(usage, &argc, &argv, true);
In that case, the user can set his own flags as well, following the conventions in <fst/flags.h>.
Alternatively, the user can process options in his own way and directly assign to any of the above global options if he wishes to modify their defaults.
A composition filter determines which matches are allowed to proceed in composition. The basic filters handle correct epsilon matching. In particular, they ensure that redundant epsilon paths, which would be incorrect with nonidempotent weights, are not created. More generally, composition filters can be used to block or modify composition paths for efficiency or other purposes usually working in tandem with specialized matchers. Their interface is:
template <class M1, M2> class SomeComposeFilter { public: typedef typename M1::FST1 FST1; typedef typename M1::FST2 FST2; typedef typename FST1::Arc Arc; typedef ... FilterState; typedef ... Matcher1; typedef ... Matcher2; typedef ... FilterState; typedef typename Arc::StateId StateId; typedef typename Arc::Weight Weight; // Required constructor. The filter is either passed composition matchers or constructs // them internally. This is done so the filter can possibly modify the result (useful e.g. with lookahead). SomeComposeFilter(const FST1 &fst1, const FST2 &fst2, M1 *matcher1 = 0, M2 *matcher2); // Return start state of filter. FilterState Start() const; // Specifies current composition state. void SetState(StateId s1, StateId s2, const FilterState &f); Matcher2 *GetMatcher2(); // Apply filter at current composition state to these transitions. // If an arc label to be matched is kNolabel, then that side does not consume a symbol. // Returns the new filter state or, if disallowed, FilterState::NoState(). // The filter is permitted to modify its inputs, e.g. for optimizations. FilterState FilterArc(A *arc1, A *arc2) const; // Apply filter at current composition state to these final weights // (cf. superfinal transitions). The filter may modify its inputs, // e.g. for optimizations. void FilterFinal(Weight *final1, Weight *final2) const; // Return resp matchers. Ownership stays with the filter. These // methods allow the filter to access and possibly modify // the composition matchers (useful e.g. with lookahead). Matcher1 *GetMatcher1(); };The filter's state is represented by the type
SomeComposeFilter::FilterState
and is stored in the composition
state table tuple. It has the form:
class SomeFilterState { public: // Required constructors SomeFilterState(); SomeFilterState(const SomeFilterState &f); // An invalid filter state. static const SomeFilterState NoState(); // Maps state to integer for hashing. size_t Hash() const; // Equality of filter states. bool operator==(const SomeFilterState &f) const; // Inequality of filter states. bool operator!=(const SomeFilterState &f) const; // Assignment to filter states. SomeFilterState& operator=(const SomeFilterState& f); };
The following composition filters are defined in the OpenFst library:
Name  Description  

SequenceComposeFilter 
Requires epsilons on FST1 to be read before epsilons on FST2  
AltSequenceComposeFilter 
Requires epsilons on FST2 to be read before epsilons on FST1  
MatchComposeFilter 
Requires epsilons on FST1 to be matched with epsilons on FST2 whenever possible  
LookAheadComposeFilter 
Used with a lookahead matcher to block noncoaccessible paths  
PushWeightsComposeFilter 
Adds weightpushing to a lookahead composition filter  
PushLabelsComposeFilter 
Adds labelpushing to a lookahead composition filter 
SequenceComposeFilter
is the default composition filter. It can be changed by using the version of ComposeFst
that accepts
ComposeFstOptions
.
See lookahead matchers for more information about composition with lookahead.
FLAGS_fst_error_fatal
is true (the default), then most serious errors cause program exit. The exception are most functions and methods that return NULL, a boolean, or NoWeight()
on error  typically I/O and weight operations.
If FLAGS_fst_error_fatal
is false, then no operation is fatal. In that case, operations that return FSTs set the kError
property bit. Otherwise classes have an Error() method that should be checked and functions return a boolean. It is intended
that a sequence of operations preserve the kError
property bit and the NoWeight()
, so that it should suffice to check for error at the end of the sequence.
An ExpandedFst
is an Fst that has an additional method that specifies the state count as well as methods to copy and read the expanded FST. In particular, an ExpandedFst
class has the interface:
template <class A> class ExpandedFst : public Fst<class A> { public: typedef A Arc; typedef typename A::StateId StateId; // State count StateId NumStates(); // Get a copy of this ExpandedFst virtual ExpandedFst<A> *Copy() const = 0; // Read an ExpandedFst from an input stream; returns NULL on error static ExpandedFst<A> *Read(istream &strm, const FstReadOptions &opts); // Read an ExpandedFst from a file; return NULL on error // Empty filename reads from standard input static ExpandedFst<A> *Read(const string &filename); };
ExpandedFst
is an abstract class (note the pure virtual methods). Examples are VectorFst
and
ConstFst
The following describes methods for reading and writing binary file representations of FSTS. Note these binary file representations are machine architecture dependent; use the textual file format crossplatform independence.
The code:
VectorFst<Arc> ifst; ... ifst.Write("a.fst"); VectorFst<Arc> *ofst = VectorFst<Arc>::Read("a.fst");
writes and reads a defined Fst type (VectorFst
) and arc type (Arc
) to and from a file in a straightforward way.
The call:
Fst<Arc> *fst = Fst<Arc>::Read("a.fst");
reads the same VectorFst
from the file as above, but returns a base Fst
. This form, useful for code that works generically for different Fst types,
can not work unless the Fst and arc type are appropriately registered. Some arc types (see here) are already registered
for common Fst types defined in the OpenFst library. Other arc type Arc
and Fst type F
pairs can be registered with the following call:
REGISTER_FST(F, Arc);
To avoid code bloat in a given program, registering arc types, in particular, should be used sparingly.
In the above examples, the user provided the arc type as a template parameter. However, the call:
$ fstdeterminize in.fst >out.fst
works e.g. for both StdArc
and LogArc
arcs. This is accomplished by calling in main(argc, argv)
:
namespace script { FstClass *ifst = FstClass::Read(in_name); VectorFstClass ofst(ifst>ArcType()); Determinize(*ifst, &ofst); ofst.Write(out_name); }
where:
class VectorFstClass; void Determinize(const FstClass &ifst, MutableFstClass *ofst);
are a class and function in the fst:script namespace that do not depend on the Arc
template parameter.
These forms, useful for code that works generically for different Arc types,
can not work unless the arc type is appropriately registered. Some arc types (see here) are already registered.
Other arc types Arc
can be registered with the following calls:
REGISTER_FST_CLASS(VectorFstClass, Arc); REGISTER_FST_OPERATION(Determinize, Arc, DeterminizeArgs);
If Arc
defines a new weight type, it can be registered at the script level (enabling WeightClass support) with the call:
REGISTER_FST_WEIGHT(Arc::Weight);
To avoid code bloat in a given program, registering arc types should be used sparingly.
The examples above show how users can modify programs to be able to read new arc and Fst types. However, it would not be ideal to have to do so for all the distribution binaries or other existing programs. Instead, this can be done more easily with dynamic shared objects (DSOs).
To add a new Fst type, MyFst
with MyFst::Type()
= "my_fst"
, use the code:
// Register some arc types with this Fst type REGISTER_FST(MyFst, StdArc); REGISTER_FST(MyFst, LogArc);
compiled into a dynamic shared object my_fst.so
. If my_fst.so
can be found in the LD_LIBRARY_PATH
(or equivalent), you should
be able to read the new Fst type with existing programs.
To add a new arc type, MyArc
with MyArc::Type()
= "my_arc"
, use the code:
// Register some Fst types with this arc type REGISTER_FST(VectorFst, MyArc); REGISTER_FST(ConstFst, MyArc); // Register the fst::script operations with this arc type REGISTER_FST_OPERATIONS(MyArc); // Register some other operation with this arc type REGISTER_FST_OPERATION(Operations, MyArc, Args);
compiled into a dynamic shared object my_arc.so
. If can be found in LD_LIBRARY_PATH
(or equivalent), you should
be able to read the new arc type with existing programs.
fst::script
namespace, is somewhat less efficient, due to indirection, and in general exposes fewer methods and options. It is used principally to implement the shelllevel FST commands and Python bindings. From C++, users are encouraged in most circumstances to use the lowerlevel templated classes and operations for their efficiency and completeness. However, for simple 'glue' code that will work seamlessly with different arc types (esp. I/O), this higherlevel might be appropriate. To use the scripting layer, include <fst/fstscript.h>
in the installation include directory and link to libfstscript.{a,so}
in the installation library directory. The extension libraries work similarly; e.g. for the FAR extension,
include <fst/extension/farscript.h>
and link to lib/libfstfarscript.{a,so}
.
In the following, all classes and methods mentioned are in the namespace fst::script.
Fst<Arc>
class template hierarchy is partially mirrored with a templatefree FstClass
hierarchy. For example, these classes are defined:
class FstClass { public: // Construct an FstClass from a templated Fst, hiding its arc type. template<class Arc> explicit FstClass(const Fst<Arc> &fst); // Copy constructor explicit FstClass(const FstClass &other); // Read an arctemplated Fst from disk, and return as an FstClass static FstClass *Read(const string &fname); // String representation of the arc type virtual const string &ArcType() const; // String representation of the underlying Fst type (e.g. 'vector') virtual const string &FstType() const; // String representation of the arc's weight type virtual const string &WeightType() const; // A pointer to this Fst's input symbol table virtual const SymbolTable *InputSymbols() const; // A pointer to this Fst's output symbol table virtual const SymbolTable *OutputSymbols() const; // Write the underlying arctemplated Fst to disk virtual void Write(const string &fname); // Return an integer representing all the properties (see Fst::Properties) virtual uint64 Properties(uint64 mask, bool test) const; // Call to get the underlying FST, if you know the concrete arc type // e.g. for an FstClass fc, // const Fst<StdArc> &f = *(fc.GetFst<StdArc>()); // Returns NULL if the given arc type doesn't match the underlying FST. template<class Arc> const Fst<Arc> *GetFst() const; virtual ~FstClass(); }
Unlike its lowerlevel analogue Fst<Arc>, FstClass is not abstract; it is a container which can be constructed from an arbitrary Fst<Arc>.
class MutableFstClass : public FstClass { public: // Construct a MutableFstClass from some kind of MutableFst<> template<class Arc> explicit MutableFstClass(const MutableFst<Arc> &fst); // If your code knows the arc type of the underlying MutableFst<>, it // can use this method to extract a pointer to it. This pointer can be used // to change the underlying MutableFst<> template<class Arc> MutableFst<Arc> *GetMutableFst(); // Set the input symbol table of the underlying MutableFst virtual void SetInputSymbols(SymbolTable *is); // Set the output symbol table of the underlying MutableFst virtual void SetOutputSymbols(SymbolTable *os); };
class VectorFstClass : public MutableFstClass { public: // Construct a copy of "other" as a VectorFstClass explicit VectorFstClass(const FstClass &other); // Construct a blank VectorFstClass with the given arc type explicit VectorFstClass(const string &arc_type); // Wrap the given VectorFst<Arc> template<class Arc> explicit VectorFstClass(VectorFst<Arc> *fst); };
class WeightClass { public: // Construct a Zero WeightClass(); // Wrap a weight of the given type template<class W> explicit WeightClass(const W &weight); // Construct a weight given the string representation of its type // (e.g. "tropical") and a string representation of the weight // itself. WeightClass(const string &weight_type, const string &weight_str); // Copy constructor and assign WeightClass(const WeightClass &other); WeightClass &operator = (const WeightClass &other); // If you know the correct weight type, you can get it with this method. Will return NULL if an incorrect type is attempted. template<class W> W *GetWeight() const; // Constants representing zero and one in all possible weight types static const WeightClass &Zero(); static const WeightClass &One(); ~WeightClass(); };
In general, many of the operations that are implemented for the underlying templated FSTs are implemented for instances of
FstClass, sometimes with modified option lists. Check <fst/fstscript.h>
.
// Reads in an input FST. FstClass *input = FstClass::Read("input.fst"); // Reads in the transduction model. FstClass *model = FstClass::Read("model.fst"); // The FSTs must be sorted along the dimensions they will be joined. // In fact, only one needs to be so sorted. // This could have instead been done for "model.fst" when it was created. ArcSort(input, OLABEL_COMPARE); ArcSort(model, ILABEL_COMPARE); // Container for composition result. VectorFstClass result(input>ArcType()); // Create the composed FST. Compose(*input, *model, &result); // Just keeps the output labels. Project(&result, PROJECT_OUTPUT);
The following nonabstract FST types with file representations are defined in the OpenFst library:
Name  Usage  Description  Registered  

vector  VectorFst<A> 
Generalpurpose mutable FST  libfst.{a,so} 

const  ConstFst<A> 
Generalpurpose expanded, immutable FST (# arcs < 2^{32})  libfst.{a,so} 

constN, N=8,16,64  ConstFst<A, uintN> 
Generalpurpose expanded, immutable FST (# arcs < 2^{N})  fst/libfstconst.{a,so} , fst/constNfst.so 

compact_string  CompactFst<A, StringCompactor<A>> 
Compact, immutable, unweighted, string FST (# arcs < 2^{32})  libfst.{a,so} 

compactN_string, N=8,16,64  CompactFst<A, StringCompactor<A>, uintN> 
Compact, immutable, unweighted string FST (# arcs < 2^{N})  fst/libfstcompact.{a,so} , fst/compactNfst.{a,so} 

compact_weighted_string  CompactFst<A, WeightedStringCompactor<A>> 
Compact, immutable, weighted, string FST (# arcs < 2^{32})  libfst.{a,so} 

compactN_weighted_string, N=8,16,64  CompactFst<A, WeightedStringCompactor<A>, uintN> 
Compact, immutable, weighted, string FST (# arcs < 2^{N})  fst/libfstcompact.{a,so} , fst/compactN_weightedfst.{a,so} 

compact_acceptor  CompactFst<A, AcceptorCompactor<A>> 
Compact, immutable, weighted FSA (# arcs < 2^{32})  libfst.{a,so} 

compactN_acceptor, N=8,16,64  CompactFst<A, AcceptorCompactor<A>, uintN> 
Compact, immutable, weighted FSA (# arcs < 2^{N})  fst/libfstcompact.{a,so} , fst/compactN_acceptorfst.{a,so} 

compact_unweighted  CompactFst<A, UnweightedCompactor<A>> 
Compact, immutable, unweighted FST (# arcs < 2^{32})  libfst.{a,so} 

compactN_unweighted N=8,16,64  CompactFst<A, UnweightedCompactor<A>, uintN> 
Compact, immutable, unweighted FST (# arcs < 2^{N})  fst/libfstcompact.{a,so} , fst/compactN_unweightedfst.{a,so} 

compact_unweighted_acceptor  CompactFst<A, UnweightedAcceptorCompactor<A>> 
Compact, immutable, unweighted FSA (# arcs < 2^{32})  libfst.{a,so} 

compactN_unweighted_acceptor, N=8,16,64  CompactFst<A, UnweightedAcceptorCompactor<A>, uintN> 
Compact, immutable, unweighted FSA (# arcs < 2^{N})  fst/libfstcompact.{a,so} , fst/compactN_unweighted_acceptorfst.{a,so} 

ilabel_lookahead  {Std,Log}ILabelLookAheadFst 
Immutable FST with input label lookahead matcher  fst/libfstlookahead.{a,so} , fst/ilabel_lookaheadfst.{a,so} 

olabel_lookahead  {Std,Log}OLabelLookAheadFst 
Immutable FST with output label lookahead matcher  fst/libfstllookahead.{a,so} , fst/olabel_lookaheadfst.{a,so} 

arc_lookahead  {Std,Log}ArcLookAheadFst 
Immutable FST with arc lookahead matcher  fst/libfstllookahead.{a,so} , fst/arc_lookaheadfst.{a,so} 

ngram  NGramFst<A> 
Immutable FST for ngram language models  fst/libfstngram.{a,so} 
These FST types are registered for StdArc
and LogArc
in the indicated libraries.
The user must register other types themselves for general FST I/O.
Note the libraries other than libfst.{a,so}
are extensions that must be built and linked separately (to avoid code bloat). For each of these, there is a version that contains all
variants of that extension (e.g., lib/libfstconst.{a,so}
) that should be specified at compile time . Alternatively, there are per variant libraries (e.g. lib/constNfst.so
) that will be dynamically loaded into any binary compiled with OpenFst when the LD_LIBRARY_PATH
(or equivalent) includes e.g. /usr/local/lib/fst
.
Note Std{I,O}LabelLookAheadFst
, despite its name, uses the LogWeight::Plus()
during weightpushing in composition (only). This choice was made for reasons of efficiency and convenience; it can
circumvented by changing the accumulator used.
Nonabstract FST types without file representations include the onthefly Fst operations and the following:
Name  Description  

EditFst<A> 
Wraps an ExpandedFst as a MutableFst , sharing nonmutated components. 
F<A>
by calling its F<A>(const Fst<A> &)
constructor from C++ or the fstconvert fst_type=Fname
shelllevel command (when there is a file representation).
Lookahead matchers are matchers that implement additional functionality to allow lookingahead along paths. When used in combination with a lookahead filter in composition, this can result in considerable efficiency improvements. See Cyril Allauzen, Michael Riley and Johan Schalkwyk, "Filters for Efficient Composition of Weighted FiniteState Transducers", Proceedings of the Fifteenth International Conference on Implementation and Application of Automata, (CIAA 2010), Winnipeg, MB.
The matcher interface is augmented with the following methods:
template <class F> class SomeLookAheadMatcher { public: typedef F FST; typedef F::Arc Arc; typedef typename Arc::StateId StateId; typedef typename Arc::Label Label; typedef typename Arc::Weight Weight; // Required constructors. LookAheadMatcher(const F &fst, MatchType match_type); LookAheadMatcher(const LookAheadMatcher &matcher); Below are methods for looking ahead for a match to a label and more generally, to a rational set. Each returns false if there is definitely not a match and returns true if there possibly is a match // LABEL LOOKAHEAD: Can 'label' be read from the current matcher state // after possibly following epsilon transitions? bool LookAheadLabel(Label label) const; // RATIONAL LOOKAHEAD: The next methods allow looking ahead for an // arbitrary rational set of strings, specified by an FST and a state // from which to begin the matching. If the lookahead FST is a // transducer, this looks on the side different from the matcher // 'match_type' (cf. composition). // Are there paths P from 's' in the lookahead FST that can be read from // the cur. matcher state? bool LookAheadFst(const Fst<Arc>& fst, StateId s); // Gives an estimate of the combined weight of the paths P in the // lookahead and matcher FSTs for the last call to LookAheadFst. // A trivial implementation returns Weight::One(). Nontrivial // implementations are useful for weightpushing in composition. Weight LookAheadWeight() const; // Is there is a single nonepsilon arc found in the lookahead FST // that begins P (after possibly following any epsilons) in the last // call LookAheadFst? If so, return true and copy it to '*arc', o.w. // return false. A trivial implementation returns false. Nontrivial // implementations are useful for labelpushing in composition. bool LookAheadPrefix(Arc *arc); // Optionally prespecifies the lookahead FST that will be passed // to LookAheadFst() for possible precomputation. If copy is true, // then 'fst' is a copy of the FST used in the previous call to // this method (useful to avoid unnecessary updates). void InitLookAheadFst(const Fst<Arc>& fst, bool copy = false); };
The following lookahead matchers are defined in the OpenFst library:
Name  Description  

ILabelLookAheadMatcher 
Lookahead to first nonepsilon input label on a path  
OLabelLookAheadMatcher 
Lookahead to first nonepsilon output label on a path  
ArcLookAheadMatcher 
Lookahead to first transition on a path 
There are FST types that are provided with these matchers. When these are used in composition, no special options need to be passed; the appropriate matcher and filter are selected automatically.
The ilabel (olabel) lookahead matcher has some special properties. It currently requires that there are no input (output) epsilon cycles. Further, it may relabel the input (output) alphabet in order to efficiently lookahead. The class LabelLookAheadRelabeler
(in <fst/lookaheadmatcher.h>
) can be used to obtain the mapping between the old and new alphabet (LabelLookAheadRelabeler::RelabelPairs
) and to relabel and sort other FSTs with the new labeling to make them suitable for composition (LabelLookAheadRelabeler::Relabel
). Alternatively, the flag save_relabel_ipairs
(save_relabel_opairs
) can be used to send the relabeling information to a file when the lookahead matcher is constructed (useful when fstconvert
is used to create a lookahead FST from the command line).
Matchers can find and iterate through requested labels at FST states; their principal use is in composition matching. In the simplest form, these are just a search or hash keyed on labels. More generally, they may implement matching special symbols that represent sets of labels such as ρ (rest), σ (all) or φ (fail), which can be used for more compact automata representations and faster matching.
The Matcher interface is:
// Specifies matcher action. enum MatchType { MATCH_INPUT, // Match input label. MATCH_OUTPUT, // Match output label. MATCH_NONE, // Match nothing. MATCH_UNKNOWN, // Match type unknown. };
template <class F> class SomeMatcher { public: typedef F FST; typedef F::Arc Arc; typedef typename Arc::StateId StateId; typedef typename Arc::Label Label; typedef typename Arc::Weight Weight; // Required constructors. SomeMatcher(const F &fst, MatchType type); SomeMatcher(const SomeMatcher &matcher); // Returns the match type that can be provided (depending on // compatibility of the input FST). It is either // the requested match type, MATCH_NONE, or MATCH_UNKNOWN. // If 'test' is false, a constant time test is performed, but // MATCH_UNKNOWN may be returned. If 'test' is true, // a definite answer is returned, but may involve more costly // computation (e.g., visiting the Fst). MatchType Type(bool test) const; // Specifies the current state. void SetState(StateId s); // This finds matches to a label at the current state. // Returns true if a match found. kNoLabel matches any // 'nonconsuming' transitions, e.g., epsilon transitions, // which do not require a matching symbol. bool Find(Label label); // These iterate through any matches found: // No more matches. bool Done() const; // Current arc (when !Done) const A& Value() const; // Advance to next arc (when !Done) void Next(); // Indicates preference for being the side used for matching // in composition/intersection. ssize_t Priority(StateId s); // Return matcher FST. const F& GetFst() const; // This specifies the known Fst properties as viewed from this // matcher. It takes as argument the input Fst's known properties. uint64 Properties(uint64 props) const; };
The following matchers are defined in the OpenFst library (see also the lookahead matcher topic).
Name  Description  

SortedMatcher 
Binary search on sorted input  
RhoMatcher<M> 
ρsymbol handling; templated on underlying matcher  
SigmaMatcher<M> 
σsymbol handling; templated on underlying matcher  
PhiMatcher<M> 
φsymbol handling; templated on underlying matcher  
MultiEpsMatcher<M> 
Treats specified non0 labels as nonconsuming labels (in addition to 0)  
ExplicitMatcher<M> 
Suppresses any implicit matches of nonconsuming labels 
SortedMatcher
expects the underlying FST be sorted on the appropriate side. Find(0)
matches any epsilons on the underlying FST explicitly (as if they were any other symbol) but also returns an
implicit selfloop (namely Arc(kNoLabel, 0, Weight::One(), current_state)
if the match_type
is MATCH_INPUT
and
Arc(0, kNoLabel, Weight::One(), current_state)
if the match_type
is MATCH_OUTPUT
); in other words, an epsilon matches at every state without moving forward on the matched FST, a natural interpretation. This behavior implements epsilontransition handling in composition, or, more generally, a 'nonconsuming' match as with the MultiEpsMatcher
(with kNoLabel
informing composition of such a match). A
composition filter determines which of these epsilon transitions are ultimately
accepted. Any matcher used in composition and related algorithms must implement these implicit matches for correct epsilon handling. In some other uses, the implicit matches may not be needed. In that case, an ExplicitMatcher
can be used to conveniently suppress them (or the user can recognize the kNoLabel
loop and skip them).
The special symbols referenced above behave as described in this table:
Consumes no symbol  Consumes symbol  

Matches all  ε  σ 
Matches rest  φ  ρ 
The ε symbol is assigned label 0
by convention. The numeric label of the other special symbols is determined by a constructor argument to their respective matchers.
The ρ, σ and φ matchers augment the functionality of their underlying template argument matcher. In this way, matchers can be cascaded (with special symbol precedence determined by the order).
A design choice for these matchers is whether to remove the special symbol in the result
(used for the ρ, σ, and φ matchers) or return it
(used for epsilonhandling). The first case is equivalent to (but more efficient than)
applying specialsymbol removal prior to composition (c.f., epsilon removal). This case requires that only
one of the FSTs in composition contain such symbols for any paired states.
The second case requires welldefined semantics and that composition proper identify and handle any nonconsuming
symbols on each FST. (The result of Find(kNoLabel)
identifies on one FST,
while the matcher's returning a kNolabel
loop handles the other, both described above.)
The template Matcher<F>
selects the predesignated matcher for Fst
type F
; it is typically SortedMatcher
.
Composition uses this matcher by default. It can be changed by using the version of ComposeFst
that accepts
ComposeFstOptions
. Note two matchers (usually of the same C++ type but different
MatchType
) are used in composition  one for each FST. Whether actual match queries are performed on one or both FSTs depends on the matcher constructor arguments, the matcher capabilities (queried by Type()
) and composition itself.
An example access of an FST's matcher is here. An example use of a ρ matcher in composition is here; σ and φ matcher usage is similar.
A MutableFst
is an ExpandedFst that has additional methods that specifiy
how to set the start state, final weights, properties and the input and output symbols, how to add and delete states and arcs, as well as methods to copy and read the mutable FST. In particular, a MutableFst
class has the interface:
template <class A> class MutableFst : public ExpandedFst<class A> { public: typedef A Arc; typedef typename A::StateId StateId; typedef typename A::Weight Weight; // Set the initial state virtual void SetStart(StateId) = 0; // Set the initial state virtual void SetFinal(StateId, Weight) = 0; // Set property bits wrt mask virtual void SetProperties(uint64 props, uint64 mask) = 0; // Add a state, return its ID virtual StateId AddState() = 0; // Add an arc to state virtual void AddArc(StateId, const A &arc) = 0; // Delete some states virtual void DeleteStates(const vector<StateId>&) = 0; // Delete all states virtual void DeleteStates() = 0; // Delete some arcs at state virtual void DeleteArcs(StateId, size_t n) = 0; // Delete all arcs at state virtual void DeleteArcs(StateId) = 0; // Get a copy of this MutableFst virtual MutableFst<A> *Copy() const = 0; // Read an MutableFst from an input stream; returns NULL on error static MutableFst<A> *Read(istream &strm, const FstReadOptions &opts); // Read an MutableFst from a file; return NULL on error // Empty filename reads from standard input static MutableFst<A> *Read(const string &filename); // Set input label symbol table; NULL signifies not unspecified virtual void SetInputSymbols(const SymbolTable* isyms) = 0; // Set output label symbol table; NULL signifies not unspecified virtual void SetOutputSymbols(const SymbolTable* osyms) = 0; };
MutableFst
is an abstract class (note the pure virtual methods). An example is VectorFst
.
The companion mutable arc iterator class provides access to and modification of the transitions of the FST
The natural order ≤ associated with a semiring is defined as a ≤ b iff a ⊕ b = a. In the OpenFst library, we define the strict version of this order as:
template <class W> NaturalLess() { bool operator()(const W &w1, const W &w2) const { return (Plus(w1, w2) == w1) && w1 != w2; } };
An order is left monotonic w.r.t a semring iff a ≤ b ⇒ ∀c, c ⊕ a ≤ c ⊕ b and c ⊗ a ≤ c ⊗ b; right monotonic is defined similarly. An order is negative iff 1 ≤ 0.
The natural order is a left (right) monotonic and negative partial order iff the semiring is idempotent and left (right) distributive. It is a total order iff the semiring has the path property. See Mohri, "Semiring Framework and Algorithms for ShortestDistance Problems", Journal of Automata, Languages and Combinatorics 7(3):321350, 2002.
This is the default total order (under the requirements above) that we use for the shortest path and pruning algorithms. This order is the natural one to use given that it generally needs to be total, monotonic and. negative: total so that all weights can be compared, monotonic so there is a practical algorithm, and negative so that the "free" weight 1 is preferred to the "disallowed" weight 0.
Many FST operations have versions that accept options, especially option structures, that have not been documented in this Wiki for brevity other than to mention some of the parameters that can be changed. For example, most of the delayed Fsts have constructors that accept options that control caching behavior.
Here is an example that selects minimal caching and the rho matcher (for fst2 ρ's) in composition::
typedef RhoMatcher< SortedMatcher<StdFst> > RM; ComposeFstOptions<StdArc, RM> opts; opts.gc_limit = 0; opts.matcher1 = new RM(fst1, MATCH_NONE, kNoLabel); opts.matcher2 = new RM(fst2, MATCH_INPUT, SomeRhoLabel); StdComposeFst cfst(fst1, fst2, opts);
Follow the links to the code under each operation's documentation for the specific details.
Each Fst
has associated with it a set of stored properties that assert facts about it. These are queried in an FST with the Properties()
method and set in a MutableFst
with the SetProperties()
method. OpenFst library operations use these properties to optimize their performance. OpenFst library operations and mutable FSTs attempt to preserve as much
property information in their results as possible without significant added computation.
Some properties are binary  they are either true or false. For each such property, there is a single stored bit that is set
if true and not set if false. The binary Fst
properties are:
Name  Description 

kError 
an error was detected while constructing/using the FST 
kExpanded 
Is an ExpandedFst 
kMutable 
Is a MutableFst 
Other properties are trinary  they are either true, false or unknown. For each such property, there are two stored bits; one is set if true, the other is set if false and neither is set if unknown.
Type  Name  Description 

Acceptor  kAcceptor 
Input and output label are equal for each arc 
kNotAcceptor 
Input and output label are not equal for some arc  
Accessible  kAccessible 
All states reachable from the initial state 
kNotAccessible 
Not all states reachable from the initial state  
kCoAccessible 
All states can reach a final state  
kNotCoAccessible 
Not all states can reach a final state  
Cyclic  kCyclic 
Has cycles 
kAcyclic 
Has no cycles  
kInitialCyclic 
Has cycles containing the initial state  
KInitialAcyclic 
Has no cycles containing the initial state  
Deterministic  kIDeterministic 
Input labels are unique leaving each state 
kNonIDeterministic 
Input labels are not unique leaving some state  
kODeterministic 
Output labels are unique leaving each state  
kNonODeterministic 
Output labels are not unique leaving some state  
Epsilons  kEpsilons 
Has input/output epsilons 
KNoEpsilons 
Has no input/output epsilons  
kIEpsilons 
Has input epsilons  
KNoIEpsilons 
Has no input epsilons  
kOEpsilons 
Has output epsilons  
KNoOEpsilons 
Has no output epsilons  
Sorted  kILabelSorted 
Input labels sorted for each state 
kNotILabelSorted 
Input labels not sorted for each state  
kOLabelSorted 
Output labels sorted for each state  
kNotOLabelSorted 
Output labels not sorted for each state  
kTopSorted 
States topologically sorted  
kNotTopSorted 
States not topologically sorted  
Weighted  kWeighted 
Nontrivial arc or final weights 
kNotWeighted 
Only trivial arc and final weights 
The call fst.Properties(mask, false)
returns the stored property bits set in the mask bits; some properties
may be unknown. it is a constanttime operation.
The call fst.Properties(mask, true)
returns the stored property bits set in the mask bits after
computing and updating any of those set in the mask that are unknown. It is a lineartime (O(V + E)) operation if any of the requested bits were unknown.
Note fstinfo test_properties=false
will show the stored properties bits, while fstinfo
or fstinfo test_properties=true
will compute unknown properties.
A state iterator is used to access the states of an FST. It has the form:
template <class F> class StateIterator { typedef typename F::Arc Arc; typedef typename Arc::StateId StateId; public: StateIterator(const &F fst); // End of iterator? bool Done() const; // Current state ID (when !Done) StateId Value() const; // Advance to next state (when !Done) void Next(); // Return to initial position void Reset(); };
It is templated on the Fst class F
to allow efficient specializations but defaults to a generic version on the abstract
base Fst class.
See here for conventions that state iterator use must respect.
An example use of a state iterator is shown here.
State mappers are function objects used by the StateMap operation to transform states. A state mapper has the form:
// This determines how symbol tables are mapped. enum MapSymbolsAction { // Symbols should be cleared in the result by the map. MAP_CLEAR_SYMBOLS, // Symbols should be copied from the input FST by the map. MAP_COPY_SYMBOLS, // Symbols should not be modified in the result by the map itself. // (They may set by the mapper). MAP_NOOP_SYMBOLS }; class SomeStateMapper { public: // Assumes input arc type is A and result arc type is B typedef A FromArc; typedef B ToArc; // Typical constructor. SomeStateMapper(const Fst<A> &fst); // Required copy constructor that allows updating Fst argument. SomeStateMapper(const SomStateMapper &mapper, const Fst<A&ft; *fst = 0); // Specifies initial state of result B::StateId Start() const; // Specifies state's final weight in result B::Weight Final(B::StateId s) const; // These methods iterate through a state's arcs in result // Specifies state to iterator over void SetState(B::StateId s); // End of arcs? bool Done() const; // Current arc const B &Value() const; // Advance to next arc (when !Done) void Next(); // Specifies input symbol table action the mapper requires (see above). MapSymbolsAction InputSymbolsAction() const; // Specifies output symbol table action the mapper requires (see above). MapSymbolsAction OutputSymbolsAction() const; // This specifies the known properties of an Fst mapped by this // mapper. It takes as argument the input Fst's known properties uint64 Properties(uint64 props) const; };
The following state mappers are defined in the OpenFst library:
Name  Description  

ArcSumMapper 
Sums weights of identically labeled multiarcs  
ArcUniqueMapper 
Keeps one of identically labelled and weighted multiarcs  
IdentityStateMapper 
Maps to self 
Another specialized state mapper is used to implement ArcSort.
State queues are used by, among others, the shortest path and shortest distance algorithms and by the Visit operation. A state queue
has the form:
template <class StateId> class SomeQueue { public: // Ctr: may need args (e.g., Fst, comparator) for some queues SomeQueue(...); // Returns the head of the queue StateId Head() const; // Inserts a state void Enqueue(StateId s); // Removes the head of the queue void Dequeue(); // Updates ordering of state s when weight changes, if necessary void Update(StateId s); // Does the queue contain no elements? bool Empty() const; // Remove all states from queue void Clear(); };
Predefined state queues include:
Queue  Description  

AutoQueue 
Automaticallyselected from Fst properties  
FifoQueue 
FirstIn, firstOut  
LifoQueue 
LastIn, firstOut  
NaturalAStarQueue 
A* (under natural order with provided estimate)  
NaturalPruneQueue 
Pruning metaqueue (within provided threshold under natural order)  
NaturalShortestFirstQueue 
Priority (least weight under natural order)  
SccQueue 
Component graph topordered metaqueue  
StateOrderQueue 
StateID ordered  
TopOrderQueue 
Topologically ordered 
Some queues accept arc filters to control which transitions are explored.
template <class T> class SomeStateTable { typedef typename T StateTuple; // Required constructors. SomeStateTable(); // Lookup state ID by tuple. If it doesn't exist, then add it. StateId FindState(const StateTuple &); // Lookup state tuple by state ID. const StateTuple<StateId> &Tuple(StateId) const; };
A state tuple has the form:
template <class S> struct SomeStateTuple { typedef typename S StateId; // Required constructor. SomeStateTuple(); // Data ... };
A specific state tuple is a ComposeStateTuple
that has data members StateId state_id1
, StateId state_id2
, and FilterState filter_state
.
The following state tables are defined in the OpenFst library:
Name  Description  

HashStateTable 
Hash map implementation  
CompactHashStateTable 
Hash set implementation  
VectorStateTable 
Vector implementation  
VectorHashStateTable 
Vector and hash set implementation  
ErasableStateTable 
Deque implementation  permits erasures 
Different state tables provide different time and space tradeoffs for applications.
Composition state tables are defined using state tables with ComposeStateTuple
. They are the principal data structure used by
composition other than the result cache.
The following composition state tables are defined in the OpenFst library:
Name  State Table  Description  

GenericComposeStateTable 
CompactHashStateTable 
Generalpurpose choice  
ProductComposeStateTable 
VectorStateTable 
Efficient when the composition state space is densely populated  
StringDetComposeStateTable 
VectorStateTable 
Efficient when FST1 is a string and FST2 is deterministic  
DetStringComposeStateTable 
VectorStateTable 
Efficient when FST1 is deterministic and FST2 is a string  
EraseableComposeStateTable 
ErasableStateTable 
Allows composition state tuple erasure 
GenericComposeStateTable
is the default composition state table. It can be changed by using the version of ComposeFst
that accepts
ComposeFstOptions
.
Symbol tables store the bijective mapping between textual labels, used in reading and printing an FST textual file, and their integer assignment, used in the FST's internal representation. Symbol tables are usually read in with fstcompile, can be stored by the FST, and used to print out the FST with fstprint,. Here are a examples of symbol table manipulation:
// Various ways to reading symbol tables StdFst *fst = StdFst::Read("some.fst"); SymbolTable *isyms = fst>InputSymbolTable(); SymbolTable *osyms = fst>OutputSymbolTable(); SymbolTable *syms = SymbolTable::ReadText("some.syms"); // Adding and accessing symbols and keys syms>AddSymbol("kumquat", 7); int64 key = syms>Find("kumquat"); string symbol = syms>Find(7); // Various ways of writing symbol tables fst>SetInputSymbols(isyms); fst>SetOutputSymbols(osyms); fst>Write("some.fst"): syms>WriteText("some.syms");
A user may define his own weight type so long as it meets the necessary requirements.
A user may define his own arc type so long as has the right form. Some Fst I/O with new arc types requires registration.
The simplest way to traverse an FST is in state order using a state iterator.
A very general traversal method is to use:
Visit(fst, visitor, queue);
where the visitor
object specfies the actions taken in the traversal while the state queue
object specifies the traversal order. A visitor
has the form:
// Visitor Interface  class determines actions taken during a visit. // If any of the boolean member functions return false, the visit is // aborted by first calling FinishState() on all unfinished (grey) // states and then calling FinishVisit(). template <class Arc> class SomeVisitor { public: typedef typename Arc::StateId StateId; SomeVisitor(T *return_data); // Invoked before visit void InitVisit(const Fst<Arc> &fst); // Invoked when state discovered (2nd arg is visitation root) bool InitState(StateId s, StateId root); // Invoked when arc to white/undiscovered state examined bool WhiteArc(StateId s, const Arc &a); // Invoked when arc to grey/unfinished state examined bool GreyArc(StateId s, const Arc &a); // Invoked when arc to black/finished state examined bool BlackArc(StateId s, const Arc &a); // Invoked when state finished void FinishState(StateId s); // Invoked after visit void FinishVisit(); };
While a depthfirst search can be implemented
using Visit()
with the LifoQueue()
, it is often better to use the more specialized
DFSVisit()
in <fst/dfsvisit.h> since it is somewhat more spaceefficient and the specialized visitor interface described there has additional funcitionality for a DFS.
Predefined FST visitors include:
Visitor  Type  Description  

CopyVisitor 
Visit  Copies in a queuespecified order  
SccVisitor 
DfsVisit  Finds stronglyconnected components, accessibility and coaccessibility  
TopOrderVisitor 
DfsVisit  Finds topological order 
The visit operations optionally accept arc filters to control which transitions are explored.
Weight
is a type that is used to represent the cost of taking transitions in an FST.
The following basic weight templates are defined in the OpenFst library:
Semiring  Name  Set  ⊕ (Plus) 
⊗ (Times) 
0 (Zero) 
1 (One) 
Notes  

Expectation  ExpectationWeight<W1, W2> 
W1 X W2  ⊕_{W1} X ⊕_{W2}  ⊗_{expectation}  (0_{W1},0_{W2})  (1_{W1},0_{W2})  
Lexicographic  LexicographicWeight<W1, W2> 
W1 X W2  min  ⊗_{W1} X ⊗_{W2}  (0_{W1},0_{W2})  (1_{W1},1_{W2})  min: lexicographic order w.r.t. W1 and W2 natural orders 

Log  LogWeightTpl<T> 
[∞, ∞]  log(e^{x} + e^{y})  +  ∞  0  T : floating point 

MinMax  MinMaxWeightTpl<T> 
[∞, ∞]  min  max  ∞  ∞  T : floating point 

Power  PowerWeight<W, n> 
W^{n}  ⊕_{W}^{n}  ⊗_{W}^{n}  0_{W}^{n}  1_{W}^{n}  
Product  ProductWeight<W1, W2> 
W1 X W2  ⊕_{W1} X ⊕_{W2}  ⊗_{W1} X ⊗_{W2}  (0_{W1},0_{W2})  (1_{W1},1_{W2})  
SignedLog  SignedLogWeightTpl<T> 
{1,1} X [∞, ∞]  ⊕_{signed_log}  (*,+)  (1, ∞)  (1, 0)  T : floating point 

SparsePower  SparsePowerWeight<W> 
W^{n}  ⊕_{W}^{n}  ⊗_{W}^{n}  0_{W}^{n}  1_{W}^{n}  n : arbitrary 

String  StringWeight<L, STRING_LEFT> 
L^{*} ∪ {∞}  longest com. prefix  ⋅  ∞  ε  L : signed integral 

StringWeight<L, STRING_RIGHT> 
L^{*} ∪ {∞}  longest com. suffix  ⋅  ∞  ε  L : signed integral 

Tropical  TropicalWeightTpl<T> 
[∞, ∞]  min  +  ∞  0  T : floating point 
The following weight types have been defined in the OpenFst library in terms of the above:
Name  Type 

GallicWeight<L, W, S> 
ProductWeight<StringWeight<L, S>, W> 
LogWeight 
LogWeightTpl<float> 
Log64Weight 
LogWeightTpl<double> 
MinMaxWeight 
MinMaxWeightTpl<float> 
SignedLogWeight 
SignedLogWeightTpl<float> 
SignedLog64Weight 
SignedLogWeightTpl<double> 
TropicalWeight 
TropicalWeightTpl<float> 
Composite weights, such as ProductWeight
and LexicographicWeight
, can use command line flags to control
their textual formatting. FLAGS_fst_weight_separator
is printed between the weights (default: ","
). FLAGS_fst_weight_parentheses
(default: ""
)
brackets the weight; if you create nested composite weights, they need to be printed with nonempty brackets (e.g. "()"
) to ensure correct parsing if read back in. These affect only textual (not binary) I/O.
Additional weight information: