OpenGrm SFst Available Operations

The following operations are provided for SFSTs. Care must be taken that the input FSTs meet the specified requirements (e.g. canonical, backoff-complete or normalized). The binary commands typically check their input requirements are satisfied or raise an error but the C++ versions may not check for efficiency (see the source code documentation for specific cases).

OperationSorted ascending Usage Description Complexity
Approx Approx(ifst, &backoff_fst, phi_label, delta) approximates a normalized stochastic FST wrt a provided backoff-complete FST same as ShortestDistance on the intersection of the input and output FSTs
Count Counter counter(phi_label, delta, &topfst)
counter.Count(infst)
counts from stochastic FST wrt to a provided backoff-complete FST same as ShortestDistance on the intersection of the input and output FSTs
CountNormalize CountNormalize(&fst) normalizes a count FST (e.g. as output by Count()) Time: O(sE) where s is max iterations per state, Space: O(V)
GlobalNormalize GlobalNormalize(&fst, phi_label, delta) globally normalizes, when possible1, a canonical weighted FST preserving total path weights (up to a global constant) same as ShortestDistance
Info sfstinfo [--phi_label=$l] in.fst prints out information about a stochastic FST Time, Space: O(V + E * max-phi-order)
Intersect Intersect(ifst1, ifst2, &ofst, phi_label, trim) intersects FSAs in the presence of failure transitions Time2: O(E1V2(max-label-multiplicity2 + max-phi-order2 log(max-out-degree2))
IsCanonical IsCanonical(fst, phi_label) checks the second property here holds for a weighted FST Time, Space: O(V + E)
IsNormalized IsNormalized(fst, phi_label, delta) checks the two properties here hold for a weighted FST Time, Space: O(V + E)
LocalNormalize LocalNormalize(&fst) locally normalizes, when possible, a canonical weighted FST preserving each state's out-going arc weights up to a state-specific constant Time, Space: O(V + E)
  sfstapprox[--phi_label=$l][--delta=$d] in.fst backoff.fst out.fst    
  sfstcount [--phi_label=$l] in.fst top.fst out.fst    
  sfstnormalize -method={kl_min,summed} [--phi_label=$l] in.fst out.fst    
  sfstnormalize [--method=global] [--phi_label=$l][--delta=$d] in.fst out.fst    
  sfstintersect [--trim] [--phi_label=$l] in1.fst in2.fst out.fst    
  sfstnormalize -method=local [--phi_label=$l] in.fst out.fst    
  sfstngramapprox [--order=$o][--phi_label=$l][--delta=$d] in.fst out.fst    
  sfstperplexity [--phi_label=$l] [--unknown_label=$u] q.fst [p.{fst,far}] (p.far is in FST archive format)  
  sfstnormalize --method=phi [--phi_label=$l][--delta=$d] in.fst out.fst    
  sfstrandgen [--phi_label=$l] [--max_length=$l] [--npath=$n] [--seed=$s] in.fst out.fst    
  sfstshorttestdistance [--phi_label=$l][--reversse][--delta=$d] in.fst    
  sfsttrim[- -phi_label=$l] in.fst out.fst    
NGramApprox NGramApprox(ifst, &ofst, order, phi_label, delta) approximates a normalized stochastic FST as an n-gram model (having phi_labels in OpenGrm NGram format) same as ShortestDistance on the intersection of the input and output FSTs
Perplexity Perplexity perp(qfst, phi_label, unknown_label)
[perp.SetTarget(pfst)]
perp.GetPerplexity()
computes self/cross perplexity for stochastic FSTs same as ShortestDistance on the intersection of the source and target FSTs
PhiNormalize PhiNormalize(&fst, phi_label) normalizes, when possible, a canonical weighted FST by only modifying the failure transitions Time, Space: O(V + E)
RandGen fst::RandGen(ifst, &ofst, fst::RandGenOptions<SFstArcSelector>(...)) randomly generates paths in a stochastic FST (correctly dealing with failure transitions) see RandGen
ShortestDistance ShortestDistance(fst, &distance, phi_label, reverse, delta) computes the shortest distance in the presence of failure transitions same as ShortestDistance
Topology sfstopology [--method=ngram] [--phi_label=$l] in.fst out.fst algorithms for constructing specific FST topologies Time, Space: O(V + E)
Trim Trim(&fst, phi_label) removes useless states and transitions in stochastic automata (irrespective of weights) Time, Space: O(V + E * max-phi-order)


1Possible when the sum of weight of all successful paths from the initial state is finite (and the input is trim).

2Assumes for each state (s1, s2) in the output, the out-degree of state s1 in FST1 is less than state s2 in FST2; otherwise the term for that state's contribution swaps s1 and s2.

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Topic revision: r8 - 2020-07-06 - MichaelRiley
 
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