A Decidable Temporal Logic of Repeating Values

2002

We show undecidability of (action based) linear-time temporal logic (LTL) for timed Petri nets. This is to be contrasted with decidability of both the problem of checking safety properties for timed Petri nets, and the problem of checking LTL formulae for (untimed) Petri nets. The undecidability result is shown through a reduction from a similar problem for lossy counter machines [May00].

Electronic Proceedings in Theoretical Computer Science, 2018

The paper is focused on temporal logics for the description of the behaviour of real-time pushdown reactive systems. The paper is motivated to bridge tractable logics specialized for expressing separately dense-time real-time properties and context-free properties by ensuring decidability and tractability in the combined setting. To this end we introduce two real-time linear temporal logics for specifying quantitative timing context-free requirements in a pointwise semantics setting: Event-Clock Nested Temporal Logic (EC NTL) and Nested Metric Temporal Logic (NMTL). The logic EC NTL is an extension of both the logic CaRet (a context-free extension of standard LTL) and Event-Clock Temporal Logic (a tractable real-time logical framework related to the class of Event-Clock automata). We prove that satisfiability of EC NTL and visibly model-checking of Visibly Pushdown Timed Automata (VPTA) against EC NTL are decidable and EXPTIME-complete. The other proposed logic NMTL is a context-free extension of standard Metric Temporal Logic (MTL). It is well known that satisfiability of future MTL is undecidable when interpreted over infinite timed words but decidable over finite timed words. On the other hand, we show that by augmenting future MTL with future context-free temporal operators, the satisfiability problem turns out to be undecidable also for finite timed words. On the positive side, we devise a meaningful and decidable fragment of the logic NMTL which is expressively equivalent to EC NTL and for which satisfiability and visibly model-checking of VPTA are EXPTIME-complete. * The work by Adriano Peron and Aniello Murano has been partially supported by the GNCS project Formal methods for verification and synthesis of discrete and hybrid systems and by Dept. project MODAL MOdel-Driven Analysis of Critical Industrial Systems.

Lecture Notes in Computer Science, 2004

Q -a set of all the concrete states of A P V -a set of propositional variables

Electronic Proceedings in Theoretical Computer Science, 2017

First-order temporal logic (FOTL) has long been regarded by many as a perfect formalism for program specification and verification, temporal databases, synthesis of programs, model checking, temporal knowledge representation and reasoning, etc. The fatal problem was that mechanisation seemed out of the question, because only 'negative' results (undecidability, non-recursive enumerability) were known. The starting point of this project was the discovery in [HWZ00] of decidable and yet rather expressive 'monodic' fragments of FOTL, which opened new and exciting opportunities for using FOTL in various areas of computer science and artificial intelligence.

Formal Aspects of Computing, 2022

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 (Until, U) and the past (Since, S) modalities are used (denoted by MTL[U,S] and TPTL[U,S]). In a classical result, the satisfiability checking for Metric Interval Temporal Logic

Formal Methods, 2021

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

1994

This is a survey of some decidability results for Petri nets, covering the last three decades. The presentation is structured around decidability of specific properties, various behavioural equivalences and finally the model checking problem for temporal logics.

IEEE Transactions on Software Engineering, 1994

The problem of formally analyzing properties of real-time systems is addressed. A method is proposed that allows specifying system properties in the TRIO language (an extension of temporal logic suitable to deal explicitly with the "time" variable and to measure it) and modeling the system as a timed Petri net. It is argued that such an approach is more general than analyzing program properties. The proof method is based on an axiomatization of timed Petri nets in terms of TRIO so that their properties can be derived as suitable theorems in much the same spirit as classical Hoare's method allows proving properties of programs coded in a Pascal-like language. The method is then exemplified through two classical "benchmarks" of the literature on concurrent and real-time systems, namely an elevator system and the dining philosophers problem. A thorough review of the related literature and a comparison thereof with the new method is also provided. Possible alternative methods, theoretical extensions, and practical applications are briefly discussed.

ACM Transactions on Programming Languages and Systems, 1989

An approach to proving temporal properties of concurrent programs that does not use temporal logic as an inference system is presented. The approach is based on using Buchi automata to specify properties. To show that a program satisfies a given property, proof obligations are derived from the Buchi automata specifying that property. These obligations are discharged by devising suitable invariant assertions and variant functions for the program. The approach is shown to be sound and relatively complete. A mutual exclusion protocol illustrates its application.