Deterministic Temporal Logics and Interval Constraints (original) (raw)

Timed Context-Free Temporal Logics

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.

Temporal Logics with Language Parameters

Lecture Notes in Computer Science, 2021

Computation Tree Logic (CTL) and its extensions CTL * and CTL + are widely used in automated verification as a basis for common model checking tools. But while they can express many properties of interest like reachability, even simple regular properties like "Every other index is labelled a" cannot be expressed in these logics. While many extensions were developed to include regular or even non-regular (e.g. visibly pushdown) languages, the first generic framework, Extended CTL, for CTL with arbitrary language classes was given by Axelsson et. al. and applied to regular, visibly pushdown and (deterministic) context-free languages. We extend this framework to CTL * and CTL + and analyse it with regard to decidability, complexity, expressivity and satisfiability.

SALT—Structured Assertion Language for Temporal Logic

Lecture Notes in Computer Science, 2006

This paper presents Salt. Salt is a general purpose specification and assertion language developed for creating concise temporal specifications to be used in industrial verification environments. It incorporates ideas of existing approaches, such as specification patterns, but also provides nested scopes, exceptions, support for regular expressions and real-time. The latter is needed in particular for verification tasks to do with reactive systems imposing strict execution times and deadlines. However, unlike other formalisms used for temporal specification of properties, Salt does not target a specific domain. The paper details on the design rationale, syntax and semantics of Salt in terms of a translation to temporal (real-time) logic, as well as on the realisation in form of a compiler. Our results will show that the higher level of abstraction introduced with Salt does not deprave the efficiency of the subsequent verification tools-rather, on the contrary.

Implementing Temporal Logics: Tools for Execution and Proof (Tutorial Paper)

In this article I will present an overview of a selection of tools for execution and proof based on temporal logic, and outline both the general techniques used and problems encountered in implementing them. This selection is quite subjective, mainly concerning work that has involved researchers I have collaborated with at Liverpool (and, previously, Manchester). The tools considered will mainly be theorem-provers and (logic-based) agent programming languages

Implementing Temporal Logics: Tools for Execution and Proof

2006

In this article I will present an overview of a selection of tools for execution and proof based on temporal logic, and outline both the general techniques used and problems en-countered in implementing them. This selection is quite subjective, mainly concerning work that has involved researchers I have collaborated with at Liverpool (and, previ-ously, Manchester). The tools considered will mainly be theorem-provers and (logic-based) agent programming languages. Specifically:

Extended temporal logic revisited

2001

A key issue in the design of a model-checking tool is the choice of the formal language with which properties are specified. It is now recognized that a good language should extend linear temporal logic with the ability to specify all ω-regular properties. Also, designers, who are familiar with finite-state machines, prefer extensions based on automata than these based on fixed points or propositional quantification. Early extensions of linear temporal logic with automata use nondeterministic Büchi automata.

Temporal Description Logics: A Survey

2008 15th International Symposium on Temporal Representation and Reasoning, 2008

We survey temporal description logics that are based on standard temporal logics such as LTL and CTL. In particular, we concentrate on the computational complexity of the satisfiability problem and algorithms for deciding it.

On the Verification of Temporal Properties

Protocol Specification, Testing and Verification, Xiii: Proceedings of the IFIP TC6/WG6. 1. Thirteenth International Symposium on Protocol Specification, Testing and Verification, Liége, Belgium, 25-28 May, 1993, 1993

We present a new algorithm that can be used for solving the model−checking problem for linear−time temporal logic. This algorithm can be viewed as the combination of two existing algorithms plus a new state representation technique introduced in this paper. The new algorithm is simpler than the traditional algorithm of Tarjan to check for maximal strongly connected components in a directed graph which is the classical algorithm used for model−checking. It has the same time complexity as Tarjan's algorithm, but requires less memory. Our algorithm is also compatible with other important complexity management techniques, such as bit−state hashing and state space caching.