Rust re-implementation of OpenFST - library for constructing, combining, optimizing, and searching weighted finite-state transducers (FSTs). A Python binding is also available.
According to the definition in the docs for WeaklyDivisibleSemiring, BooleanWeight (S = bool, + = |, * = &, 0 = false, 1 = true) should be weakly divisible: there are three combinations (x, y) such that x + y != 0:
x = true, y = true: in this case, we can set z = true so that true = (true | true) & true.
x = true, y = false: we can set z = true so that true = (true | false) & true.
x = false, y = true: we can set z = false so that false = (false | true) & false.
In fact, BooleanWeight is divisible because the inverse of true is true.
This PR adds an implementation of WeaklyDivisibleSemiring for BooleanWeight.
According to the definition in the docs for
WeaklyDivisibleSemiring,BooleanWeight(S = bool,+ = |,* = &,0 = false,1 = true) should be weakly divisible: there are three combinations(x, y)such thatx + y != 0:x = true,y = true: in this case, we can setz = trueso thattrue = (true | true) & true.x = true,y = false: we can setz = trueso thattrue = (true | false) & true.x = false,y = true: we can setz = falseso thatfalse = (false | true) & false.In fact,
BooleanWeightis divisible because the inverse oftrueistrue.This PR adds an implementation of
WeaklyDivisibleSemiringforBooleanWeight.