Expand description
Provides a trait that shall be implemented for all weights stored inside a wFST.
Structs
Traits
A semiring
(S, ⊕, ⊗, 0, 1) is said to be complete if for any index set I and any family
(ai)i ∈ I of elements of S, ⊕(ai)i∈I is an element of S whose definition
does not depend on the order of the terms in the ⊕-sum.
Note that in a complete semiring all weighted transducers are regulated since all
infinite sums are elements of S.
For more information : https://cs.nyu.edu/~mohri/pub/hwa.pdfFor some operations, the weight set associated to a wFST must have the structure of a semiring.
(S, +, *, 0, 1) is a semiring if (S, +, 0) is a commutative monoid with identity element 0,
(S, *, 1) is a monoid with identity element 1, * distributes over +,
0 is an annihilator for *.
Thus, a semiring is a ring that may lack negation.
For more information : https://cs.nyu.edu/~mohri/pub/hwa.pdfA complete semiring S is a starsemiring that is a semiring that can be augmented with an
internal unary closure operation ∗ defined by
a∗=⊕an (infinite sum) for any a ∈ S.
Furthermore, associativity, commutativity, and distributivity apply to these infinite sums.
For more information : https://cs.nyu.edu/~mohri/pub/hwa.pdfA semiring is said to be divisible if all non-0 elements admit an inverse,
that is if
S-{0} is a group.
(S, +, *, 0, 1) is said to be weakly divisible if
for any x and y in S such that x + y != 0,
there exists at least one z such that x = (x+y)*z.
For more information : https://cs.nyu.edu/~mohri/pub/hwa.pdf