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'''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. |
'''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. |
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For weight in lttoolbox which currently supports |
For weight in lttoolbox which currently supports NDFA system, we need '''Semi-ring''' for calculating weight. |
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A '''Semiring''' is defined by two binary operations '''⊕''' and '''⊗''' and two designated elements '''0''' and '''1''' with following properties:- |
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:- |
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* '''⊕''' shows associative, commutative and has 0 as its own identity. |
* '''⊕''' shows associative, commutative and has 0 as its own identity. |
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* '''⊗''' shows associative and has 1 as its own identity. |
* '''⊗''' shows associative and has 1 as its own identity. |
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A '''left semiring''' distributes on the left and also a '''right semiring''' is similarly defined. |
A '''left semiring''' distributes on the left and also a '''right semiring''' is similarly defined. |
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'''⊕''' is used to combine the weight of two identically labeled alternative paths. |
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'''⊗''' is used to combine weights along a path or when matching paths in composition or intersection. |
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An '''arc weight''' in an FST gives the cost of taking that transition. |
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* A <code>Weight</code> class must have binary functions <code>Plus</code> and <code>Times</code> these must form a left or right semiring. |
* A <code>Weight</code> class must have binary functions <code>Plus</code> and <code>Times</code> these must form a left or right semiring. |
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Also in class <code>Weight</code>, there are some additions which must be defined like the following:- |
Also in class <code>Weight</code>, there are some additions which must be defined like the following:- |
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* <code>>></code> :- This reads textual representation of a weight. |
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* <code><<</code> :- This prints textual representation of a weight. |
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* <code>LeftSemiring</code> :- This indicates how weights form a left semi-ring. |
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* <code>RightSemiring</code> :- This indicates how weights form a right semi-ring. |
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* <code>Read(istream &)</code> :- This reads binary representation of a weight. |
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* <code>Write(ostream &)</code> :- This writes binary representation of a weight. |
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* <code>ApproxEqual</code> :- This shows approximate equality (for inexact weights). |
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Latest revision as of 17:38, 6 January 2018
Weights to lttoolbox[edit]
Theory[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
Weightclass must have binary functionsPlusandTimesthese 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).
