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+// 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.
+//
+// Copyright 2005-2010 Google, Inc.
+// Author: allauzen@google.com (Cyril Allauzen)
+//
+// \file
+// Synchronize an FST with bounded delay.
+
+#ifndef FST_LIB_SYNCHRONIZE_H__
+#define FST_LIB_SYNCHRONIZE_H__
+
+#include <algorithm>
+#include <unordered_map>
+using std::tr1::unordered_map;
+using std::tr1::unordered_multimap;
+#include <unordered_set>
+using std::tr1::unordered_set;
+using std::tr1::unordered_multiset;
+#include <string>
+#include <utility>
+using std::pair; using std::make_pair;
+#include <vector>
+using std::vector;
+
+#include <fst/cache.h>
+#include <fst/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>::SetInputSymbols;
+  using FstImpl<A>::SetOutputSymbols;
+
+  using CacheBaseImpl< CacheState<A> >::PushArc;
+  using CacheBaseImpl< CacheState<A> >::HasArcs;
+  using CacheBaseImpl< CacheState<A> >::HasFinal;
+  using CacheBaseImpl< CacheState<A> >::HasStart;
+  using CacheBaseImpl< CacheState<A> >::SetArcs;
+  using CacheBaseImpl< CacheState<A> >::SetFinal;
+  using CacheBaseImpl< CacheState<A> >::SetStart;
+
+  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(const SynchronizeFstImpl &impl)
+      : CacheImpl<A>(impl),
+        fst_(impl.fst_->Copy(true)) {
+    SetType("synchronize");
+    SetProperties(impl.Properties(), kCopyProperties);
+    SetInputSymbols(impl.InputSymbols());
+    SetOutputSymbols(impl.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);
+  }
+
+  uint64 Properties() const { return Properties(kFstProperties); }
+
+  // Set error if found; return FST impl properties.
+  uint64 Properties(uint64 mask) const {
+    if ((mask & kError) && fst_->Properties(kError, false))
+      SetProperties(kError, kError);
+    return FstImpl<Arc>::Properties(mask);
+  }
+
+  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));
+          PushArc(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));
+          PushArc(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));
+      PushArc(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 unordered_map<Element, StateId, ElementKey, ElementEqual> ElementMap;
+  typedef 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_;
+
+  void operator=(const SynchronizeFstImpl<A> &);  // disallow
+};
+
+
+// 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).
+//
+// This class attaches interface to implementation and handles
+// reference counting, delegating most methods to ImplToFst.
+template <class A>
+class SynchronizeFst : public ImplToFst< SynchronizeFstImpl<A> > {
+ public:
+  friend class ArcIterator< SynchronizeFst<A> >;
+  friend class StateIterator< SynchronizeFst<A> >;
+
+  typedef A Arc;
+  typedef typename A::Weight Weight;
+  typedef typename A::StateId StateId;
+  typedef CacheState<A> State;
+  typedef SynchronizeFstImpl<A> Impl;
+
+  SynchronizeFst(const Fst<A> &fst)
+      : ImplToFst<Impl>(new Impl(fst, SynchronizeFstOptions())) {}
+
+  SynchronizeFst(const Fst<A> &fst,  const SynchronizeFstOptions &opts)
+      : ImplToFst<Impl>(new Impl(fst, opts)) {}
+
+  // See Fst<>::Copy() for doc.
+  SynchronizeFst(const SynchronizeFst<A> &fst, bool safe = false)
+      : ImplToFst<Impl>(fst, safe) {}
+
+  // Get a copy of this SynchronizeFst. See Fst<>::Copy() for further doc.
+  virtual SynchronizeFst<A> *Copy(bool safe = false) const {
+    return new SynchronizeFst<A>(*this, safe);
+  }
+
+  virtual inline void InitStateIterator(StateIteratorData<A> *data) const;
+
+  virtual void InitArcIterator(StateId s, ArcIteratorData<A> *data) const {
+    GetImpl()->InitArcIterator(s, data);
+  }
+
+ private:
+  // Makes visible to friends.
+  Impl *GetImpl() const { return ImplToFst<Impl>::GetImpl(); }
+
+  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, fst.GetImpl()) {}
+};
+
+
+// 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.GetImpl(), s) {
+    if (!fst.GetImpl()->HasArcs(s))
+      fst.GetImpl()->Expand(s);
+  }
+
+ private:
+  DISALLOW_COPY_AND_ASSIGN(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__