User:Himanshu40

Weights to lttoolbox

Theory

Weighted transducers are automata in which each transition in addition to its usual input label is augmented with an output label from a possible new alphabet, and carries some weight element of a semiring.

For weight in lttoolbox which currently supports DFA system, we need Semi-ring for calculating weight.

A Semiring is defined by two binary operations ⊕ and ⊗ and two designated elements 0 and 1 with following properties:-

• ⊕ shows associative, commutative and has 0 as its own identity.
• ⊗ shows associative and has 1 as its own identity.

A left semiring distributes on the left and also a right semiring is similarly defined.

Store weights in lttoolbox

• A Weight class must have binary functions Plus and Times these must form a left or right semiring.

Also in class Weight, there are some additions which must be defined like the following:-