Temporalized logics and automata for time granularity (original) (raw)
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Towards an automata-theoretic counterpart of combined temporal logics
2001
In this paper, we define a new class of combined automata, called temporalized automata, which can be viewed as the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Furthermore, we successfully apply temporalized automata to provide the full secondorder theory of k-refinable downward unbounded layered structures with a temporal logic counterpart. Finally, we show how temporalized automata can be used to deal with relevant classes of reactive systems, such as granular reactive systems and mobile reactive systems.
2003
Suitable extensions of monadic second-order theories of k successors have been proposed in the literature to specify in a concise way reactive systems whose behaviour can be naturally modeled with respect to a (possibly infinite) set of differently-grained temporal domains. This is the case, for instance, of the wide-ranging class of real-time reactive systems whose components have dynamic behaviours regulated by very different time constants, e.g., days, hours, and seconds. In this paper, we focus on the theory of k-refinable downward unbounded layered structures MSO[< tot , (↓ i ) k−1 i=0 ], that is, the theory of infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, whose satisfiability problem is nonelementarily decidable. We define a propositional temporal logic counterpart of MSO[< tot , (↓ i ) k−1 i=0 ] with set quantification restricted to infinite paths, called CTSL * k , which features an original mix of linear and branching temporal operators. We prove the expressive completeness of CTSL * k with respect to such a path fragment of MSO[<tot, (↓i) k−1 i=0 ] and show that its satisfiability problem is 2EXPTIME-complete.
Definability and decidability of binary predicates for time granularity
2003
In this paper we study the definability and decidability of binary predicates for time granularity with respect to monadic theories over finitely and infinitely layered structures. We focus our attention on the equi-level (resp. equicolumn) predicate constraining two time points to belong to the same layer (resp. column) and on the horizontal (resp. vertical) successor predicate relating a time point to its successor within a given layer (resp. column). We give a number of positive and negative results by reduction to/from a wide spectrum of decidable/undecidable problems.
Final report:‘Analysis and Mechanisation of Decidable First-Order Temporal Logics’
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.
Temporalising Tractable Description Logics
14th International Symposium on Temporal Representation and Reasoning (TIME'07), 2007
It is known that for temporal languages, such as firstorder LT L, reasoning about constant (time-independent) relations is almost always undecidable. This applies to temporal description logics as well: constant binary relations together with general concept subsumptions in combinations of LT L and the basic description logic ALC cause undecidability. In this paper, we explore temporal extensions of two recently introduced families of 'weak' description logics known as DL-Lite and EL. Our results are twofold: temporalisations of even rather expressive variants of DL-Lite turn out to be decidable, while the temporalisation of EL with general concept subsumptions and constant relations is undecidable.
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.
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.
2022
Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and synthesis of programs, as well as in knowledge representation and reasoning. In this paper, we focus on first-order temporal logic on finite traces. We first investigate preservation of equivalences and satisfiability of formulas between finite and infinite traces, by providing a set of semantic and syntactic conditions to guarantee when the distinction between reasoning in the two cases can be blurred. Moreover, we show that the satisfiability problem on finite traces for several decidable fragments of first-order temporal logic is ExpSpace-complete, as in the infinite trace case, while it decreases to NExpTime when finite traces bounded in the number of instants are considered. This leads also to new complexity results for temporal description logics...
A hierarchy of partial order temporal properties
Lecture Notes in Computer Science
We propose a classi cation of partial order temporal properties into a hierarchy, which is a generalization of the safety-progress hierarchy of Chang, Manna and Pnueli. The classes of the hierarchy are characterized through three views: language-theoretic, topological and temporal. Instead of the domain of strings, we take the domain of Mazurkiewicz traces as a basis for our considerations. For the language-theoretic view, we propose operations on trace languages which de ne the four main classes of properties: safety, guarantee, persistence and response. These four classes are shown to correspond precisely to the two lower levels of the Borel hierarchy of the Scott topology of the domain of traces relativized to the in nite traces. In addition, a syntactic characterization of the classes is provided in terms of a sublogic of the Generalized Interleaving Set Temporal Logic GISTL (an extension of ISTL).