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OpenFst Advanced Usage

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.

Arc Iterators

An arc iterator doc 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;  
  // Advance to next arc (when !Done)  
  void Next();  
  // Return current position 
  size_t Position();  
  // Return to initial position          
  void Reset();  
  // Arc access by position              
  void Seek(size_t pos);
};

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 doc is similar to an ArcIterator except its constructor takes a pointer to a MutableFst and it additionally has a SetValue() method.

Arc Filters

Arc filters are accepted by various operations to control which arcs are transitioned. An arc filter has the form:

template <class Arc>
class ArcFilter {
public: 
  // Return true iff arc is to be transitioned. 
  bool operator()(const Arc &arc) const;
};

Pre-defined arc filters include:

Name Description
AnyArcFilter Accept all arcs doc
EpsilonArcFilter Accept only arcs with input and output epsilons doc
InputEpsilonArcFilter Accept only arcs with input epsilons doc
OutputEpsilonArcFilter Accept only arcs with output epsilons doc

Arcs

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 Arc {
   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
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 DONE
MinMaxArc int int MinMaxWeight  
ProductArc<W1, W2> int int ProductWeight<W1, W2>  
StdArc int int TropicalWeight DONE
StringArc<S> int int StringWeight<int, S>  

Additional arc information:

Base Fsts

Every Fst doc 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 inteface:

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.

Caching Work in progress, under construction

Command Line Flags

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_pair_parentheses string "" Characters enclosing the first weight of a printed pair weight (and derived classes) to ensure proper I/O of nested pair weights; must have size 0 (none) or 2 (open and close parenthesis)
FLAGS_fst_pair_separator string "," Character separator between printed pair weights; must be a single character
FLAGS_fst_verify_properties bool false Verify Fst properites are correctly set when queried

The first ensures the arguments of binary FST operations (e.g. ComposeDoc) 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 of the on-the-fly Fst classes; the default values should normally be satisfactory. The next two are used to control the text formating of ProductWeight and other weight pairs. The last is used to ensure that the properties of an FST have been correctly set; is 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_pair_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 user-defined 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.

Composition Filters Work in progress, under construction

Expanded Fsts

An ExpandedFst doc 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 doc and ConstFst doc

FST Input/Output

The following code:

VectorFst<A> ifst;
...
ifst.Write("a.fst");
VectorFst<A> *ofst = VectorFst<A>::Read("a.fst");

writes and reads a defined Fst type (VectorFst) and arc type (A) to and from a file in a straight-forward way.

Library Registration

The call:

Fst<Arc> *fst = Fst<A>::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 library-registered. Some arc types (see here) are already registered for all the Fst types defined in the OpenFst library. Other arc type A and Fst type F pairs can be registered with the following call:

REGISTER_FST(F, A);

To avoid code bloat in a given program, registering arc types, in particular, should be used sparingly.

Main Registration

In the above examples, the user provided the arc type as a template parameter. However, the call:

$ fstinfo a.fst

works e.g. for both StdArc and LogArc arcs. This is accomplished by calling in main(argc, argv):

return CALL_FST_MAIN(InfoMain, argc, argv);

where:

template <class Arc>
int InfoMain(int argc; char **argv, istream &strm, const FstReadOptions &opts) {
    Fst<Arc> *fst = Fst<Arc>::Read(strm, opts);
    ...
    return 0;
}

is a templated `main' function that does the arc-specific work. CALL_FST_MAIN passes to InfoMain the command line arguments and an opened stream to an Fst (opened from the first argument or standard input if no arguments). CALL_FST_MAIN does the type dispatch by examining the Fst's header and then passing on the (partially-read) input stream, which can be used by InfoMain to read in the actual Fst. This dispatch works only with arc and main function pairs that have been main-registered. Each OpenFst distribution binary registers its templated main function with the arc types marked registered here. An arc type A and main function M pair can be registered with the following call:

REGISTER_FST_MAIN(M, A);

To avoid code bloat in a given program, registering arc types should be used sparingly.

To use main registration in your own program, you need to include additionally <fst/main.h> and link additionally to libfstmain.so.

FST Dynamic Shared Objects

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:

extern "C" {
void my_fst_init() { 
  // 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:

extern "C" {
void my_arc_init() { 
  // Register some Fst types with this arc type 
  REGISTER_FST(VectorFst, MyArc);
  REGISTER_FST(ConstFst, MyArc);

  // Register the OpenFst binaries with this arc type 
  REGISTER_FST_MAINS(MyArc); 
  // Register some other main with this arc type 
  REGISTER_FST_MAIN(SomeMain, MyArc);
}
}

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.

Mappers Work in progress, under construction

Matchers Work in progress, under construction

Mutable Fsts

A MutableFst doc 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 doc .

The companion mutable arc iterator class provides access to and modification of the transitions of the FST

Natural Orders

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 10.

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 Shortest-Distance Problems", Journal of Automata, Languages and Combinatorics 7(3):321-350, 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.

Properties

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
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 Non-trivial 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. 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.

State Iterators

A state iterator doc 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 Queues

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 Queue {
 public: 
   // Ctr: may need args (e.g., Fst, comparator) for some queues 
   Queue(...); 
   // 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();
};

Pre-defined state queues include:

Queue Description
AutoQueue Automatically-selected from Fst properties doc
FifoQueue First-In, first-Out doc
LifoQueue Last-In, first-Out doc
SccQueue Component graph top-ordered meta-queue doc
ShortestFirstQueue Priority (least weight) doc
StateOrderQueue State-ID ordered doc
TopOrderQueue Topologically ordered doc

Some queues accept arc filters to control which transitions are explored.

State Tables Work in progress, under construction

Symbol Tables Work in progress, under construction

User-defined Fst Arcs and Weights

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.

User-defined Fst Classes Work in progress, under construction

Visitors

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); doc [bad link?]

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 Visitor {
public:
   typedef typename Arc::StateId StateId;

   Visitor(T *return_data); 
   // Invoked before visit 
   void InitVisit(const Fst &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 depth-first search can be implemented using Visit() with the LifoQueue(), it is often better to use the more specialized DFSVisit()doc [bad link?] in <fst/dfs-visit.h> since it is somewhat more space-efficient and the specialized visitor interface described there has additional funcitionality for a DFS.

Pre-defined FST visitors include:

Visitor Type Description
CopyVisitor Visit Copies in a queue-specified order doc
SccVisitor DfsVisit Finds strongly-connected components, accessibility and coaccessibility doc
TopOrderVisitor DfsVisit Finds topological order doc

The visit operations optionally accept arc filters to control which transitions are explored.

Weights

A Weight is a type that represents an FST transition's cost.

The following basic weight templates are defined in the OpenFst library:

Semiring Name Set
(Plus)

(Times)
0
(Zero)
1
(One)
Notes
Lexicographic LexicographicWeight<W1, W2> W1 X W2 min W1 X ⊗W2 (0W1,0W2) (1W1,1W2) min: lexicographic order w.r.t.
W1 and W2 natural orders
doc
Log LogWeightTpl<T> [-∞, ∞] -log(e-x + e-y) + 0 T: floating point doc
MinMax MinMaxWeightTpl<T> [-∞, ∞] min max -∞ T: floating point doc
Product ProductWeight<W1, W2> W1 X W2 W1 X ⊕W2 W1 X ⊗W2 (0W1,0W2) (1W1,1W2)   doc
String StringWeight<L, STRING_LEFT> L* ∪ {∞} longest com. prefix ε L: signed integral doc
  StringWeight<L, STRING_RIGHT> L* ∪ {∞} longest com. suffix ε L: signed integral doc
Tropical TropicalWeightTpl<T> [-∞, ∞] min + 0 T: floating point doc

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>
MinMaxWeight MinMaxWeightTpl<float>
TropicalWeight TropicalWeightTpl<float>

Weight pairs, such as ProductWeight and LexicographicWeight, can use command line flags to control their textual formatting. FLAGS_fst_product_weight_separator is printed between the weights (default: ","). FLAGS_fst_parentheses (default: "") brackets the pair; if you create complex nested pairs (i.e., tuples), they may need to be printed with non-empty brackets (e.g. "()") to ensure correct parsing if read back in.

Additional weight information:

-- MichaelRiley - 27 Feb 2009

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Topic revision: r9 - 2009-03-04 - MichaelRiley
 
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