Computer Science > Formal Languages and Automata Theory
[Submitted on 27 Jul 2021 (v1), last revised 26 Feb 2022 (this version, v2)]
Title:Logics Meet 2-Way 1-Clock Alternating Timed Automata
View PDFAbstract:In this paper, we study the extension of 1-clock Alternating Timed Automata (1-ATA) with the ability to read in both forward and backward direction, the 2-Way 1-clock Alternating Timed Automata (2-Way 1-ATA). We show that subclass of 2-Way 1-ATA with reset free loops (2-Way 1-ATA-rfl) is expressively equivalent to MSO[<] extended with Guarded Metric Quantifiers (GQMSO). Emptiness Checking problem for 2-Way 1-ATA-rfl (and hence GQMSO) is undecidable, in general. We propose a "non-punctuality" like restriction, called non-adjacency, for 2-Way 1-ATA-rfl, and also for GQMSO, for which the emptiness (respectively, satisfiability) checking becomes decidable. Non-Adjacent 2-Way 1-ATA is the first such class of Timed Automata with alternations and 2-wayness for which the emptiness checking is decidable (and that too with elementary complexity). We also show that 2-Way 1-ATA-rfl, even with the non-adjacent restrictions, can express properties is not recognizable using 1-ATA.
Submission history
From: Khushraj Madnani [view email][v1] Tue, 27 Jul 2021 17:55:36 UTC (391 KB)
[v2] Sat, 26 Feb 2022 08:25:24 UTC (2,627 KB)
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