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Weights to lttoolbox[edit]


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[edit]

An arc weight in an FST gives the cost of taking that transition.

  • 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.
  • ApproxEqual :- This shows approximate equality (for inexact weights).