A* shortest string decoding for non-idempotent semirings. (arXiv:2204.07236v1 [cs.FL])

The single shortest path algorithm is undefined for weighted finite-state
automata over non-idempotent semirings because such semirings do not guarantee
the existence of a shortest path. However, in non-idempotent semirings
admitting an order satisfying a monotonicity condition (such as the plus-times
or log semirings), the notion of shortest string is well-defined. We describe
an algorithm which finds the shortest string for a weighted non-deterministic
automaton over such semirings using the backwards shortest distance of an
equivalent deterministic automaton (DFA) as …

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