From Non-punctuality to Non-adjacency: A Quest for Decidability of Timed Temporal Logics with Quantifiers

Metric Temporal Logic (MTL) and Timed Propositional (TPTL) are prominent real-time extensions of Linear (LTL). In general, the satisfiability checking problem for these is undecidable when both future (Until, U) past (Since, S) modalities used (denoted by MTL[U,S] TPTL[U,S]). a classical result, Interval (MITL[U,S]), non-punctual fragment MTL[U,S], shown to be decidable with EXPSPACE complete complexity. A straightforward adoption non-punctuality does not recover decidability in case TPTL[U,S]. Hence, we propose more refined notion called non-adjacency TPTL[U,S] focus on its 1-variable fragment, 1-TPTL[U,S]. We show that non-adjacent 1-TPTL[U,S] strictly expressive than MITL. As one our main results, Our proof relies novel technique anchored interval word abstraction reduction version newly proposed logic PnEMTL. further an extension MSO [<] (Monadic Second Order Orders) Guarded Quantifiers (GQMSO) it characterizes expressiveness That apart, introduce context GQMSO (NA-GQMSO), which syntactic generalization Q2MLO due Hirshfeld Rabinovich NA-GQMSO.