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).

Operation | 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.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 possible^{1}, 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 | Time^{2}: O(E_{1}V_{2}(max-label-multiplicity_{2} + max-phi-order_{2} log(max-out-degree_{2})) |

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) |

^{2}Assumes 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.

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

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