2021/05/20 by Shankara Narayanan Krishna, Khushraj Madnani, Krishna, Shankara Narayanan +6 · 1 citation
Computer Science · #FOS: Computer and information sciences #Formal Methods in Verification #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #cs.LO
paper · pdf · doi:10.48550/arxiv.2105.09534
Accepted for Publication in International Symposium on Formal Methods, FM 2021
openalex publication_date 2021/05/20 · arxiv created 2021/09/05 · arxiv updated 2021/09/07 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are prominent real-time extensions of Linear Temporal Logic (LTL). In general, the satisfiability checking problem for these extensions is undecidable when both the future U and the past S modalities are used. In a classical result, the satisfiability checking for MITL[U,S], a non punctual fragment of MTL[U,S], is shown to be decidable with EXPSPACE complete complexity. Given that this notion of non punctuality does not recover decidability in the case of TPTL[U,S], we propose a generalization of non punctuality called non adjacency for TPTL[U,S], and focus on its 1-variable fragment, 1-TPTL[U,S]. While non adjacent 1-TPTL[U,S] appears to be be a very small fragment, it is strictly more expressive than MITL. As our main result, we show that the satisfiability checking problem for non adjacent 1-TPTL[U,S] is decidable with EXPSPACE complete complexity.