// fstext/determinize-lattice.h

// Copyright 2009-2011  Microsoft Corporation

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#ifndef KALDI_FSTEXT_DETERMINIZE_LATTICE_H_
#define KALDI_FSTEXT_DETERMINIZE_LATTICE_H_
#include <fst/fst-decl.h>
#include <fst/fstlib.h>
#include <algorithm>
#include <map>
#include <set>
#include <vector>
#include "fstext/lattice-weight.h"

namespace fst {

/// \addtogroup fst_extensions
///  @{

// For example of usage, see test-determinize-lattice.cc

/*
   DeterminizeLattice implements a special form of determinization
   with epsilon removal, optimized for a phase of lattice generation.
   Its input is an FST with weight-type BaseWeightType (usually a pair of
   floats, with a lexicographical type of order, such as
   LatticeWeightTpl<float>). Typically this would be a state-level lattice, with
   input symbols equal to words, and output-symbols equal to p.d.f's (so like
   the inverse of HCLG).  Imagine representing this as an acceptor of type
   CompactLatticeWeightTpl<float>, in which the input/output symbols are words,
   and the weights contain the original weights together with strings (with zero
   or one symbol in them) containing the original output labels (the p.d.f.'s).
   We determinize this using acceptor determinization with epsilon removal.
   Remember (from lattice-weight.h) that CompactLatticeWeightTpl has a special
   kind of semiring where we always take the string corresponding to the best
   cost (of type BaseWeightType), and discard the other.  This corresponds to
   taking the best output-label sequence (of p.d.f.'s) for each input-label
   sequence (of words).  We couldn't use the Gallic weight for this, or it would
   die as soon as it detected that the input FST was non-functional.  In our
   case, any acyclic FST (and many cyclic ones) can be determinized. We assume
   that there is a function Compare(const BaseWeightType &a, const
   BaseWeightType &b) that returns (-1, 0, 1) according to whether (a < b, a ==
   b, a > b) in the total order on the BaseWeightType... this information should
   be the same as NaturalLess would give, but it's more efficient to do it this
   way. You can define this for things like TropicalWeight if you need to
   instantiate this class for that weight type.

   We implement this determinization in a special way to make it efficient for
   the types of FSTs that we will apply it to.  One issue is that if we
   explicitly represent the strings (in CompactLatticeWeightTpl) as vectors of
   type vector<IntType>, the algorithm takes time quadratic in the length of
   words (in states), because propagating each arc involves copying a whole
   vector (of integers representing p.d.f.'s).  Instead we use a hash structure
   where each string is a pointer (Entry*), and uses a hash from (Entry*,
   IntType), to the successor string (and a way to get the latest IntType and
   the ancestor Entry*).  [this is the class LatticeStringRepository].

   Another issue is that rather than representing a determinized-state as a
   collection of (state, weight), we represent it in a couple of reduced forms.
   Suppose a determinized-state is a collection of (state, weight) pairs; call
   this the "canonical representation".  Note: these collections are always
   normalized to remove any common weight and string part.  Define end-states as
   the subset of states that have an arc out of them with a label on, or are
   final.  If we represent a determinized-state a the set of just its
   (end-state, weight) pairs, this will be a valid and more compact
   representation, and will lead to a smaller set of determinized states (like
   early minimization).  Call this collection of (end-state, weight) pairs the
   "minimal representation".  As a mechanism to reduce compute, we can also
   consider another representation. In the determinization algorithm, we start
   off with a set of (begin-state, weight) pairs (where the "begin-states" are
   initial or have a label on the transition into them), and the "canonical
   representation" consists of the epsilon-closure of this set (i.e. follow
   epsilons).  Call this set of (begin-state, weight) pairs, appropriately
   normalized, the "initial representation".  If two initial representations are
   the same, the "canonical representation" and hence the "minimal
   representation" will be the same.  We can use this to reduce compute.  Note
   that if two initial representations are different, this does not preclude the
   other representations from being the same.

*/

struct DeterminizeLatticeOptions {
  float delta;  // A small offset used to measure equality of weights.
  int max_mem;  // If >0, determinization will fail and return false
  // when the algorithm's (approximate) memory consumption crosses this
  // threshold.
  int max_loop;  // If >0, can be used to detect non-determinizable input
  // (a case that wouldn't be caught by max_mem).
  DeterminizeLatticeOptions() : delta(kDelta), max_mem(-1), max_loop(-1) {}
};

/**
    This function implements the normal version of DeterminizeLattice, in which
    the output strings are represented using sequences of arcs, where all but
    the first one has an epsilon on the input side.  The debug_ptr argument is
    an optional pointer to a bool that, if it becomes true while the algorithm
    is executing, the algorithm will print a traceback and terminate (used in
    fstdeterminizestar.cc debug non-terminating determinization).  More
    efficient if ifst is arc-sorted on input label.  If the number of arcs gets
    more than max_states, it will throw std::runtime_error (otherwise this code
    does not use exceptions).  This is mainly useful for debug.  */
template <class Weight, class IntType>
bool DeterminizeLattice(
    const Fst<ArcTpl<Weight> > &ifst, MutableFst<ArcTpl<Weight> > *ofst,
    DeterminizeLatticeOptions opts = DeterminizeLatticeOptions(),
    bool *debug_ptr = NULL);

/*  This is a version of DeterminizeLattice with a slightly more "natural"
   output format, where the output sequences are encoded using the
   CompactLatticeArcTpl template (i.e. the sequences of output symbols are
   represented directly as strings) More efficient if ifst is arc-sorted on
   input label. If the #arcs gets more than max_arcs, it will throw
   std::runtime_error (otherwise this code does not use exceptions).  This is
   mainly useful for debug.
*/
template <class Weight, class IntType>
bool DeterminizeLattice(
    const Fst<ArcTpl<Weight> > &ifst,
    MutableFst<ArcTpl<CompactLatticeWeightTpl<Weight, IntType> > > *ofst,
    DeterminizeLatticeOptions opts = DeterminizeLatticeOptions(),
    bool *debug_ptr = NULL);

/// @} end "addtogroup fst_extensions"

}  // end namespace fst

#include "fstext/determinize-lattice-inl.h"

#endif  // KALDI_FSTEXT_DETERMINIZE_LATTICE_H_