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Computer Science > Logic in Computer Science

arXiv:1609.04094 (cs)
[Submitted on 14 Sep 2016]

Title:Weighted Linear Dynamic Logic

Authors:Manfred Droste (Leipzig, Germany), George Rahonis (Thessaloniki, Greece)
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Abstract:We introduce a weighted linear dynamic logic (weighted LDL for short) and show the expressive equivalence of its formulas to weighted rational expressions. This adds a new characterization for recognizable series to the fundamental Schützenberger theorem. Surprisingly, the equivalence does not require any restriction to our weighted LDL. Our results hold over arbitrary (resp. totally complete) semirings for finite (resp. infinite) words. As a consequence, the equivalence problem for weighted LDL formulas over fields is decidable in doubly exponential time. In contrast to classical logics, we show that our weighted LDL is expressively incomparable to weighted LTL for finite words. We determine a fragment of the weighted LTL such that series over finite and infinite words definable by LTL formulas in this fragment are definable also by weighted LDL formulas.
Comments: In Proceedings GandALF 2016, arXiv:1609.03648
Subjects: Logic in Computer Science (cs.LO)
Cite as: arXiv:1609.04094 [cs.LO]
  (or arXiv:1609.04094v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.1609.04094
Journal reference: EPTCS 226, 2016, pp. 149-163
Related DOI: https://doi.org/10.4204/EPTCS.226.11

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Wed, 14 Sep 2016 00:59:07 UTC (22 KB)
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