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 NDFA system, we need Semi-ring for calculating weight.

A Semiring is defined by two binary operations ⊕ and ⊗ and two designated elements 0 and 1 and it consists of a system like K, ⊕, ⊗, 0, 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.

⊕ is used to combine the weight of two identically labeled alternative paths.

⊗ is used to combine weights along a path or when matching paths in composition or intersection.

Calculation of 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:-

• >> :- This reads textual representation of a weight.
• << :- This prints textual representation of a weight.
• LeftSemiring :- This indicates how weights form a left semi-ring.
• RightSemiring :- This indicates how weights form a right semi-ring.
• Read(istream &) :- This reads binary representation of a weight.
• Write(ostream &) :- This writes binary representation of a weight.
• NoWeight :- This is a static member function that returns an element which is not a set member and used to signal an error.
• ApproxEqual :- This shows approximate equality (for inexact weights).
• ReverseWeight :- This a type of the corresponding reverse weight and the same type as Weight for a both left and right semiring. For the left string semiring, it is the right string semiring.