OpenFst Python extension

This extension exposes the OpenFst scripting API to Python (3.6 or better). Like the scripting API, it supports arbitrary arcs and weights. The extension allows for rapid prototyping and interactive construction of FSTs using the Python REPL.

Note that this extension is unrelated to, and incompatible with, any other third-party Python extensions for OpenFst (e.g., pyfst).

To install this package, either:

• issue --enable-python during configuration of OpenFst
• Or, install OpenFst with FAR support (--enable-far) then install the PyPi package openfst using Pip: pip install openfst

NB: >>> indicates the Python interactive prompt; all other typewriter-text lines are print to stdout or stderr.

Module import

The Python module itself is called pywrapfst but in this tutorial, we will alias it to fst.

>>> import pywrapfst as fst

FST construction

FSTs can be compiled from arc-lists in the same format used by the fstcompile binary.

>>> compiler = fst.Compiler()
>>> print >> compiler, "0 1 97 120 .5"
>>> print >> compiler, "0 1 98 121 1.5"
>>> print >> compiler, "1 2 99 123 2.5"
>>> print >> compiler, "2 3.5"
>>> f = compiler.compile()   # Creates the FST and flushes the compiler buffer.
>>> f.num_states
3
>>> f.final(2)
<tropical Weight 3.5 at 0x1215ed0>

FSTs can be read in from disk using Fst.read, which takes a string argument specifying the input file's location.

>>> v = fst.Fst.read("vector.fst")

This class method takes an optional second argument, a string indicating the desired FST type. The FST is converted to this type if it the on-disk FST is not already of the desired type.

>>> c = fst.Fst.read("const.fst")
>>> c.fst_type
'const'
>>> v = fst.Fst.read("const.fst", fst_type="vector")
>>> v.fst_type
'vector'

This conversion can also be accomplished after instantiation using the convert function.

>>> v = fst.convert(c, fst_type="vector")
>>> v.fst_type
'vector'

Note that this conversion to the vector FST type is mandatory if one wishes to perform mutation operations on an const FST.

FSTs can be read in from FST Archives (FARs) using the FarReader object.

>>> reader = fst.FarReader.open("lattice.far")

Each FST stored within a FAR has a unique string ID which can be used to extract it from the reader object.

>>> f = reader["1best"]

Or, all FSTs stored within a FAR may be accessed via iteration over the reader object.

>>> for (name, f) in reader:
...     print name, f.num_states
('1best', 23)
('2best', 27)
('3best', 27)
...

Finally, an empty mutable vector FST can be created using VectorFst.

>>> f = fst.VectorFst()

By default, the resulting FST uses standard (tropical-weight) arcs, but users can specify other arc types (e.g., log) via an optional argument.

>>> f.arc_type
'standard'
>>> g = fst.VectorFst("log")
>>> g.arc_type
'log'

FST object attributes and properties

All FSTs have the following read-only attributes ("properties" in Python jargon):

arc_type	A string indicating the arc type
input_symbols	The input SymbolTable, or None if no input table is set
fst_type	A string indicating the FST (container) type
output_symbols	The output SymbolTable, or None if no output table is set
start	The state ID for the start state
weight_type	A string indicating the weight type

Mutable FSTs also provide the num_states attribute, which indicates the number of states in the FST.

To access FST properties (i.e., cyclicity, weightedness), use the properties method.

>>> print "Is f cyclic?", f.properties(fst.CYCLIC, True) == fst.CYCLIC
Is f cyclic? True

FST access and iteration

FST arcs and states can be accessed via the StateIterator, ArcIterator, and MutableArcIterator objects. These are most naturally constructed using the states and arcs methods, as follows.

>>> for state in f.states():
...     for arc in f.arcs(state):
...         print state, arc.ilabel, arc.olabel, arc.weight, arc.nextstate
0 97 120 1.5 1
0 98 121 2.5 1
1 99 123 2.5 2

The final weight of a state can be accessed using the final instance method.

>>> for state in f.states():
...     print state, f.final(state)
0 Infinity
1 Infinity
2 3.5

The following function can be used to count the number of arcs and states in an FST.

>>> def num_arcs_and_states(f):
...   return sum(1 + f.num_arcs(s) for s in f.states())

FST mutation

Mutable FSTs can be modified by adding states (add_state), adding arcs leaving existing states (add_arc), marking a existing state as the start state (set_start), or giving a non-infinite final weight to an existing state (set_final). Optionally, the user can reserve states before adding them using the reserve_states instance method, and reserve arcs leaving an existing state using the reserve_arcs method. The following snippet creates an acceptor which, when its arc labels are interpreted as bytes, accepts the well-known "sheep language" /baa+/.

>>> f = fst.VectorFst()
>>> one = fst.Weight.one(f.weight_type())
>>> f.reserve_states(3)  # Optional.
>>> s = f.add_state()
>>> f.set_start(s)
>>> n = f.add_state()
>>> f.reserve_arcs(s, 1)  # Optional.
>>> f.add_arc(s, fst.Arc(98, 98, one, n))
>>> s = n
>>> n = f.add_state()
>>> f.reserve_arcs(s, 1)  # Optional.
>>> f.add_arc(s, fst.Arc(97, 97, one, n))
>>> s = n
>>> n = f.add_state()
>>> f.reserve_arcs(s, 1)  # Optional.
>>> f.add_arc(s, fst.Arc(97, 97, one, n))
>>> f.reserve_arcs(n, 1)  # Optional.
>>> f.add_arc(n, fst.Arc(97, 97, one, n))
>>> f.set_final(n, one)
>>> f.verify()  # Checks FST's sanity.
True
>>> print f
0       1       98      98
1       2       97      97
2       3       97      97
3       3       97      97
3

While it is possible to add arcs whose destination state has not yet been added, any other references to states not yet created (by add_state) is forbidden and will raise an FstIndexError.

Existing arcs and states can also be deleted using delete_states, and arcs leaving an existing state can be deleted using delete_arcs. For example, the following function can be used to remove all arcs and states from an FST.

>>> def clear(f):
...   for state in f.states():
...       f.delete_arcs(state)
...   f.delete_states()

FST visualization

The instance method text returns a string representing the FST as an arc-list using the same format and options as the fstprint binary. If f is an FST, then print f is an alias for print f.text().

>>> print f
0       1       98      98
1       2       97      97
2       3       97      97
3       3       97      97
3

FSTs can also be written to a GraphViz file using the draw instance method.

>>> f.draw("f.gv")

FST operations

All FSTs support constructive operations such as composition (compose), intersection (intersect), and reversal (reverse), storing the result in a vector FST.

>>> cv = fst.compose(c, v)

FSTs also support tests for equality (equal), equivalence (equivalent), stochastic equivalence (randequivalent), and isomorphism (isomorphic).

>>> fst.isomorphic(c, v)
True

FSTs which are mutable (e.g., vector FSTs) also support destructive operations such as arc-sorting (arcsort), inversion (invert), projection (project), and union (union). These operations work in place, mutating the instance they are called on and returning nothing. These instance methods are not available for immutable FST types (e.g., const FSTs).

>>> v.arcsort(sort_type="olabel")
>>> v.invert()
>>> v.project()

A few operations (e.g., weight-pushing, epsilon-removal) are available in both constructive and destructive forms, albeit with slightly different options.

To read documentation on individual FST operations, use Python's built-in help function.

>>> help(fst.equal)
Help on built-in function equal in module pywrapfst:

equal(...)
    equal(ifst1, ifst2, delta=fst.kDelta)

Are two FSTs equal?
 
    This function tests whether two FSTS have the same states with the same
    numbering and the same transitions with the same labels and weights in the
    same order.

    Args:
      ifst1: The first input FST.
      ifst2: The second input FST.
      delta: Comparison/quantization delta.

    Returns:
      True if the two FSTs satisfy the above conditions, otherwise False.

    See also: `equivalent`, `isomorphic`, `randequivalent`.

FST output

FSTs can be written to disk using the write instance method.

>>> f.write("f.fst")

They also can be written into FARs using the FarWriter object. Once created, an FST can be written to the FarWriter object using dictionary-style assignment.

>>> writer = fst.FarWriter.create("lattice.far")
>>> writer["1best"] = 1best
>>> writer["2best] = 2best

Note that the FAR itself is not guaranteed to be flushed to disk until the FarWriter is garbage-collected. Under normal circumstances, calling del on the FarWriter variable will decrement the reference count to zero and trigger garbage collection on the next cycle.

>>> del writer

Worked example

Putting it all together, the following example, based on Mohri et al. 2002, 2008, shows the construction of an ASR recognition transducer from a pronunciation lexicon L, grammar G, a transducer from context-dependent phones to context-independent phones C, and an HMM set H (where we assume that the components are all determinizable and, preferably, in the log semiring).

>>> reader = fst.FarReader.open("hclg.far")
>>> LG = fst.determinize(fst.compose(reader["L"], reader["G"]))
>>> CLG = fst.determinize(fst.compose(reader["C"], LG))
>>> HCLG = fst.determinize(fst.compose(reader["H"], CLG))
>>> HCLG.minimize()
>>> HCLG.write("hclg.fst")