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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

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_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 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 second two are used to control the text formating of ProductWeight doc 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 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

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

User-defined Fst Arcs and Weights Work in progress, under construction

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.

-- MichaelRiley - 27 Feb 2009

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Topic revision: r6 - 2009-03-03 - MichaelRiley
 
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