fst/lib/synchronize.h

// synchronize.h
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//      http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
// Author: allauzen (at) cs.nyu.edu (Cyril Allauzen)
//
// \file
// Synchronize an FST with bounded delay.

#ifndef FST_LIB_SYNCHRONIZE_H__
#define FST_LIB_SYNCHRONIZE_H__

#include <algorithm>

#include <unordered_map>
#include <unordered_set>

#include "fst/lib/cache.h"
#include "fst/lib/test-properties.h"

namespace fst {

typedef CacheOptions SynchronizeFstOptions;


// Implementation class for SynchronizeFst
template <class A>
class SynchronizeFstImpl
    : public CacheImpl<A> {
 public:
  using FstImpl<A>::SetType;
  using FstImpl<A>::SetProperties;
  using FstImpl<A>::Properties;
  using FstImpl<A>::SetInputSymbols;
  using FstImpl<A>::SetOutputSymbols;

  using CacheBaseImpl< CacheState<A> >::HasStart;
  using CacheBaseImpl< CacheState<A> >::HasFinal;
  using CacheBaseImpl< CacheState<A> >::HasArcs;

  typedef A Arc;
  typedef typename A::Label Label;
  typedef typename A::Weight Weight;
  typedef typename A::StateId StateId;

  typedef basic_string<Label> String;

  struct Element {
    Element() {}

    Element(StateId s, const String *i, const String *o)
        : state(s), istring(i), ostring(o) {}

    StateId state;     // Input state Id
    const String *istring;     // Residual input labels
    const String *ostring;     // Residual output labels
    // Residual strings are represented by const pointers to
    // basic_string<Label> and are stored in a hash_set. The pointed
    // memory is owned by the hash_set string_set_.
  };

  SynchronizeFstImpl(const Fst<A> &fst, const SynchronizeFstOptions &opts)
      : CacheImpl<A>(opts), fst_(fst.Copy()) {
    SetType("synchronize");
    uint64 props = fst.Properties(kFstProperties, false);
    SetProperties(SynchronizeProperties(props), kCopyProperties);

    SetInputSymbols(fst.InputSymbols());
    SetOutputSymbols(fst.OutputSymbols());
  }

  ~SynchronizeFstImpl() {
    delete fst_;
    // Extract pointers from the hash set
    vector<const String*> strings;
    typename StringSet::iterator it = string_set_.begin();
    for (; it != string_set_.end(); ++it)
      strings.push_back(*it);
    // Free the extracted pointers
    for (size_t i = 0; i < strings.size(); ++i)
      delete strings[i];
  }

  StateId Start() {
    if (!HasStart()) {
      StateId s = fst_->Start();
      if (s == kNoStateId)
        return kNoStateId;
      const String *empty = FindString(new String());
      StateId start = FindState(Element(fst_->Start(), empty, empty));
      SetStart(start);
    }
    return CacheImpl<A>::Start();
  }

  Weight Final(StateId s) {
    if (!HasFinal(s)) {
      const Element &e = elements_[s];
      Weight w = e.state == kNoStateId ? Weight::One() : fst_->Final(e.state);
      if ((w != Weight::Zero()) && (e.istring)->empty() && (e.ostring)->empty())
        SetFinal(s, w);
      else
        SetFinal(s, Weight::Zero());
    }
    return CacheImpl<A>::Final(s);
  }

  size_t NumArcs(StateId s) {
    if (!HasArcs(s))
      Expand(s);
    return CacheImpl<A>::NumArcs(s);
  }

  size_t NumInputEpsilons(StateId s) {
    if (!HasArcs(s))
      Expand(s);
    return CacheImpl<A>::NumInputEpsilons(s);
  }

  size_t NumOutputEpsilons(StateId s) {
    if (!HasArcs(s))
      Expand(s);
    return CacheImpl<A>::NumOutputEpsilons(s);
  }

  void InitArcIterator(StateId s, ArcIteratorData<A> *data) {
    if (!HasArcs(s))
      Expand(s);
    CacheImpl<A>::InitArcIterator(s, data);
  }

  // Returns the first character of the string obtained by
  // concatenating s and l.
  Label Car(const String *s, Label l = 0) const {
    if (!s->empty())
      return (*s)[0];
    else
      return l;
  }

  // Computes the residual string obtained by removing the first
  // character in the concatenation of s and l.
  const String *Cdr(const String *s, Label l = 0) {
    String *r = new String();
    for (int i = 1; i < s->size(); ++i)
      r->push_back((*s)[i]);
    if (l && !(s->empty())) r->push_back(l);
    return FindString(r);
  }

  // Computes the concatenation of s and l.
  const String *Concat(const String *s, Label l = 0) {
    String *r = new String();
    for (int i = 0; i < s->size(); ++i)
      r->push_back((*s)[i]);
    if (l) r->push_back(l);
    return FindString(r);
  }

  // Tests if the concatenation of s and l is empty
  bool Empty(const String *s, Label l = 0) const {
    if (s->empty())
      return l == 0;
    else
      return false;
  }

  // Finds the string pointed by s in the hash set. Transfers the
  // pointer ownership to the hash set.
  const String *FindString(const String *s) {
    typename StringSet::iterator it = string_set_.find(s);
    if (it != string_set_.end()) {
      delete s;
      return (*it);
    } else {
      string_set_.insert(s);
      return s;
    }
  }

  // Finds state corresponding to an element. Creates new state
  // if element not found.
  StateId FindState(const Element &e) {
    typename ElementMap::iterator eit = element_map_.find(e);
    if (eit != element_map_.end()) {
      return (*eit).second;
    } else {
      StateId s = elements_.size();
      elements_.push_back(e);
      element_map_.insert(pair<const Element, StateId>(e, s));
      return s;
    }
  }


  // Computes the outgoing transitions from a state, creating new destination
  // states as needed.
  void Expand(StateId s) {
    Element e = elements_[s];

    if (e.state != kNoStateId)
      for (ArcIterator< Fst<A> > ait(*fst_, e.state);
           !ait.Done();
           ait.Next()) {
        const A &arc = ait.Value();
        if (!Empty(e.istring, arc.ilabel)  && !Empty(e.ostring, arc.olabel)) {
          const String *istring = Cdr(e.istring, arc.ilabel);
          const String *ostring = Cdr(e.ostring, arc.olabel);
          StateId d = FindState(Element(arc.nextstate, istring, ostring));
          AddArc(s, Arc(Car(e.istring, arc.ilabel),
                        Car(e.ostring, arc.olabel), arc.weight, d));
        } else {
          const String *istring = Concat(e.istring, arc.ilabel);
          const String *ostring = Concat(e.ostring, arc.olabel);
          StateId d = FindState(Element(arc.nextstate, istring, ostring));
          AddArc(s, Arc(0 , 0, arc.weight, d));
        }
      }

    Weight w = e.state == kNoStateId ? Weight::One() : fst_->Final(e.state);
    if ((w != Weight::Zero()) &&
        ((e.istring)->size() + (e.ostring)->size() > 0)) {
      const String *istring = Cdr(e.istring);
      const String *ostring = Cdr(e.ostring);
      StateId d = FindState(Element(kNoStateId, istring, ostring));
      AddArc(s, Arc(Car(e.istring), Car(e.ostring), w, d));
    }
    SetArcs(s);
  }

 private:
  // Equality function for Elements, assume strings have been hashed.
  class ElementEqual {
   public:
    bool operator()(const Element &x, const Element &y) const {
      return x.state == y.state &&
              x.istring == y.istring &&
              x.ostring == y.ostring;
    }
  };

  // Hash function for Elements to Fst states.
  class ElementKey {
   public:
    size_t operator()(const Element &x) const {
      size_t key = x.state;
      key = (key << 1) ^ (x.istring)->size();
      for (size_t i = 0; i < (x.istring)->size(); ++i)
        key = (key << 1) ^ (*x.istring)[i];
      key = (key << 1) ^ (x.ostring)->size();
      for (size_t i = 0; i < (x.ostring)->size(); ++i)
        key = (key << 1) ^ (*x.ostring)[i];
      return key;
    }
  };

  // Equality function for strings
  class StringEqual {
   public:
    bool operator()(const String * const &x, const String * const &y) const {
      if (x->size() != y->size()) return false;
      for (size_t i = 0; i < x->size(); ++i)
        if ((*x)[i] != (*y)[i]) return false;
      return true;
    }
  };

  // Hash function for set of strings
  class StringKey{
   public:
    size_t operator()(const String * const & x) const {
      size_t key = x->size();
      for (size_t i = 0; i < x->size(); ++i)
        key = (key << 1) ^ (*x)[i];
      return key;
    }
  };


  typedef std::unordered_map<Element, StateId, ElementKey, ElementEqual> ElementMap;
  typedef std::unordered_set<const String*, StringKey, StringEqual> StringSet;

  const Fst<A> *fst_;
  vector<Element> elements_;  // mapping Fst state to Elements
  ElementMap element_map_;    // mapping Elements to Fst state
  StringSet string_set_;

  DISALLOW_EVIL_CONSTRUCTORS(SynchronizeFstImpl);
};


// Synchronizes a transducer. This version is a delayed Fst.  The
// result will be an equivalent FST that has the property that during
// the traversal of a path, the delay is either zero or strictly
// increasing, where the delay is the difference between the number of
// non-epsilon output labels and input labels along the path.
//
// For the algorithm to terminate, the input transducer must have
// bounded delay, i.e., the delay of every cycle must be zero.
//
// Complexity:
// - A has bounded delay: exponential
// - A does not have bounded delay: does not terminate
//
// References:
// - Mehryar Mohri. Edit-Distance of Weighted Automata: General
//   Definitions and Algorithms, International Journal of Computer
//   Science, 14(6): 957-982 (2003).
template <class A>
class SynchronizeFst : public Fst<A> {
 public:
  friend class ArcIterator< SynchronizeFst<A> >;
  friend class CacheStateIterator< SynchronizeFst<A> >;
  friend class CacheArcIterator< SynchronizeFst<A> >;

  typedef A Arc;
  typedef typename A::Weight Weight;
  typedef typename A::StateId StateId;
  typedef CacheState<A> State;

  SynchronizeFst(const Fst<A> &fst)
      : impl_(new SynchronizeFstImpl<A>(fst, SynchronizeFstOptions())) {}

  SynchronizeFst(const Fst<A> &fst,  const SynchronizeFstOptions &opts)
      : impl_(new SynchronizeFstImpl<A>(fst, opts)) {}

  SynchronizeFst(const SynchronizeFst<A> &fst) : impl_(fst.impl_) {
    impl_->IncrRefCount();
  }

  virtual ~SynchronizeFst() { if (!impl_->DecrRefCount()) delete impl_; }

  virtual StateId Start() const { return impl_->Start(); }

  virtual Weight Final(StateId s) const { return impl_->Final(s); }

  virtual size_t NumArcs(StateId s) const { return impl_->NumArcs(s); }

  virtual size_t NumInputEpsilons(StateId s) const {
    return impl_->NumInputEpsilons(s);
  }

  virtual size_t NumOutputEpsilons(StateId s) const {
    return impl_->NumOutputEpsilons(s);
  }

  virtual uint64 Properties(uint64 mask, bool test) const {
    if (test) {
      uint64 known, test = TestProperties(*this, mask, &known);
      impl_->SetProperties(test, known);
      return test & mask;
    } else {
      return impl_->Properties(mask);
    }
  }

  virtual const string& Type() const { return impl_->Type(); }

  virtual SynchronizeFst<A> *Copy() const {
    return new SynchronizeFst<A>(*this);
  }

  virtual const SymbolTable* InputSymbols() const {
    return impl_->InputSymbols();
  }

  virtual const SymbolTable* OutputSymbols() const {
    return impl_->OutputSymbols();
  }

  virtual inline void InitStateIterator(StateIteratorData<A> *data) const;

  virtual void InitArcIterator(StateId s, ArcIteratorData<A> *data) const {
    impl_->InitArcIterator(s, data);
  }

 private:
  SynchronizeFstImpl<A> *Impl() { return impl_; }

  SynchronizeFstImpl<A> *impl_;

  void operator=(const SynchronizeFst<A> &fst);  // Disallow
};


// Specialization for SynchronizeFst.
template<class A>
class StateIterator< SynchronizeFst<A> >
    : public CacheStateIterator< SynchronizeFst<A> > {
 public:
  explicit StateIterator(const SynchronizeFst<A> &fst)
      : CacheStateIterator< SynchronizeFst<A> >(fst) {}
};


// Specialization for SynchronizeFst.
template <class A>
class ArcIterator< SynchronizeFst<A> >
    : public CacheArcIterator< SynchronizeFst<A> > {
 public:
  typedef typename A::StateId StateId;

  ArcIterator(const SynchronizeFst<A> &fst, StateId s)
      : CacheArcIterator< SynchronizeFst<A> >(fst, s) {
    if (!fst.impl_->HasArcs(s))
      fst.impl_->Expand(s);
  }

 private:
  DISALLOW_EVIL_CONSTRUCTORS(ArcIterator);
};


template <class A> inline
void SynchronizeFst<A>::InitStateIterator(StateIteratorData<A> *data) const
{
  data->base = new StateIterator< SynchronizeFst<A> >(*this);
}


// Synchronizes a transducer. This version writes the synchronized
// result to a MutableFst.  The result will be an equivalent FST that
// has the property that during the traversal of a path, the delay is
// either zero or strictly increasing, where the delay is the
// difference between the number of non-epsilon output labels and
// input labels along the path.
//
// For the algorithm to terminate, the input transducer must have
// bounded delay, i.e., the delay of every cycle must be zero.
//
// Complexity:
// - A has bounded delay: exponential
// - A does not have bounded delay: does not terminate
//
// References:
// - Mehryar Mohri. Edit-Distance of Weighted Automata: General
//   Definitions and Algorithms, International Journal of Computer
//   Science, 14(6): 957-982 (2003).
template<class Arc>
void Synchronize(const Fst<Arc> &ifst, MutableFst<Arc> *ofst) {
  SynchronizeFstOptions opts;
  opts.gc_limit = 0;  // Cache only the last state for fastest copy.
  *ofst = SynchronizeFst<Arc>(ifst, opts);
}

}  // namespace fst

#endif // FST_LIB_SYNCHRONIZE_H__