A* shortest string decoding for non-idempotent semirings

Kyle Gorman, Cyril Allauzen


Abstract
Abstract: 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 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 a heuristic for A* search performed over a companion idempotent semiring, which is proven to return the shortest string. There may be exponentially more states in the DFA, but the proposed algorithm needs to visit only a small fraction of them if determinization is performed “on the fly”.
Anthology ID:
2024.eacl-long.43
Volume:
Proceedings of the 18th Conference of the European Chapter of the Association for Computational Linguistics (Volume 1: Long Papers)
Month:
March
Year:
2024
Address:
St. Julian’s, Malta
Editors:
Yvette Graham, Matthew Purver
Venue:
EACL
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
732–739
Language:
URL:
https://aclanthology.org/2024.eacl-long.43
DOI:
Bibkey:
Cite (ACL):
Kyle Gorman and Cyril Allauzen. 2024. A* shortest string decoding for non-idempotent semirings. In Proceedings of the 18th Conference of the European Chapter of the Association for Computational Linguistics (Volume 1: Long Papers), pages 732–739, St. Julian’s, Malta. Association for Computational Linguistics.
Cite (Informal):
A* shortest string decoding for non-idempotent semirings (Gorman & Allauzen, EACL 2024)
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