8284967
Constraining Cycle Alternations in Model Checking for Interval Temporal Logic
Model checking is one of the most successful techniques in system verification. While a variety of methods and tools exist to check properties expressed in point-based temporal logics, like LTL and CTL, model checking for interval temporal logic has entered the research agenda only very recently. In previous work, we devised a non-elementary model checking procedure for Halpern and Shoham's modal logic of time intervals, interpreted over finite Kripke structures, and an EXPSPACE algorithm for two meaningful fragments of it. In this paper, we show that the latter algorithm can be suitably tailored in order to check a subset of the computations of a system, that satisfy a given bound on the number of cycle alternations, by making use of a polynomial (instead of exponential) working space. We also prove that such a revised algorithm turns out to be complete for Kripke structures whose strongly connected components are simple cycles.
5307889
A propositional modal logic of time intervals
In certain areas of artificial intelligence there is need to represent continuous change and to make statements that are interpreted with respect to time intervals rather than time points. To this end, a modal temporal loglc based on time intervals is developed, a logic that can be viewed as a generalization of point-based modal temporal logic. Related loglcs are discussed, an intuitive presentation of the new logic is given, and its formal syntax and semantics are defined. No assumption is made about the underlying nature of time, allowing it to be discrete (such as the natural numbers) or continuous (such as the rationals or the reals), linear or branching, complete (such as the reals), or not (such as the rational). It is shown, however, that there are formulas in the logic that allow us to distinguish all these situations. A translation of our logic into first-order logic is given, which allows the application of some results on first-order logic to our modal logic. Finally. the difficulty of validity problems for the logic is considered. This turns out to depend critically, and in surprising ways, on our assumptions about time. For example, if our underlying temporal structure is the ratlonals, then, the validity problem is r. e .-complete; if it is the reals, then validity n II ~-hard: and if it is the natural numbers, then validity is fI ] -complete.
60862315
Reasoning about Digital Circuits
Abstract : Predicate logic is a powerful and general descriptive formalism with a long history of development. However, since the logic's underlying semantics have no notion of time, statements such as I increases by 2 and The bit signal X rises from 0 to 1 can not be directly expressed. The author presents a formalism called interval temporal logic (ITL) that augments standard predicate logic with time-dependent operators. ITL is like discrete linear-time temporal logic but includes time intervals. The behavior of programs and hardware devices can often be decomposed into successively smaller intervals of activity. State transitions can be characterized by properties relating the initial and final values of variables over intervals. Furthermore, these time periods provide a convenient framework for introducing quantitative timing details. After giving some motivation for reasoning about hardware, he presents the propositional and first-order syntax and semantics of ITL. Demonstrated is ITL's utility for uniformly describing the structure and dynamics of a wide variety of timing-dependent digital circuits. Devices discussed include delay elements, adders, latches, flip-flops, counters, random-access memories, a clocked multiplication circuit and the Am2901 bit slice. ITL also provides a means for expressing properties of such specifications. Also examine are such concepts as device equivalence and internal states. Propositional ITL is shown to be undecidable although useful subsets are of relatively reasonable computational complexity. (Author)
7688013
Temporal prepositions and their logic
This extended abstract reports on the computational complexity of reasoning with English sentences featuring temporal prepositions. A fragment of English featuring these constructions, called TPE, is defined by means of a context-free grammar. The phrase-structures which this grammar assigns to the sentences it recognizes can be viewed as formulas of an interval temporal logic, called TPL, whose satisfaction-conditions faithfully represent the meanings of the corresponding English sentences. It is shown that the satisfiability problem for TPL is NEXPTIME-complete.
16729000
Maintaining knowledge about temporal intervals
An interval-based temporal logic is introduced, together with a computationally effective reasoning algorithm based on constraint propagation. This system is notable in offering a delicate balance between
4771204
Interval Temporal Logics: a Journey
We discuss a family of modal logics for reasoning about relational structures of intervals over (usually) linear orders, with modal operators associated with the various binary relations between such intervals, known as Allen’s interval relations. The formulae of these logics are evaluated at intervals rather than points and the main effect of that semantic feature is substantially higher expressiveness and computational complexity of the interval logics as compared to point-based ones. Without purporting to provide a comprehensive survey of the field, we take the reader to a journey through the main developments in it over the past 10 years and outline some landmark results on expressiveness and (un)decidability of the satisfiability problem for the family of interval logics.
645999
An Epistemic Halpern-Shoham Logic
We define a family of epistemic extensions of Halpern-Shoham logic for reasoning about temporal-epistemic properties of multi-agent systems. We exemplify their use and study the complexity of their model checking problem. We show a range of results ranging from PTIME to PSPACE-hard depending on the logic considered.
962467
Decidability of model checking multi-agent systems against a class of EHS specifications
We define and illustrate the expressiveness of the ABL fragment of the Epistemic Halpern-Shoham Logic as a specification language for multi-agent systems. We consider the model checking problem for systems against specifications given in the logic. We show its decidability by means of a novel technique that may be reused in other contexts for showing decidability of other logics based on intervals.
8346865
Checking interval properties of computations
Model checking is a powerful method widely explored in formal verification. Given a model of a system, e.g., a Kripke structure, and a formula specifying its expected behaviour, one can verify whether the system meets the behaviour by checking the formula against the model. Classically, system behaviour is expressed by a formula of a temporal logic, such as LTL and the like. These logics are “point-wise” interpreted, as they describe how the system evolves state-by-state. However, there are relevant properties, such as those constraining the temporal relations between pairs of temporally extended events or involving temporal aggregations, which are inherently “interval-based”, and thus asking for an interval temporal logic. In this paper, we give a formalization of the model checking problem in an interval logic setting. First, we provide an interpretation of formulas of Halpern and Shoham’s interval temporal logic HS over finite Kripke structures, which allows one to check interval properties of computations. Then, we prove that the model checking problem for HS against finite Kripke structures is decidable by a suitable small model theorem, and we provide a lower bound to its computational complexity.
17883836
A Model Checking Procedure for Interval Temporal Logics based on Track Representatives
Model checking is commonly recognized as one of the most effective tool in system verification. While it has been systematically investigated in the context of classical, point-based temporal logics, it is still largely unexplored in the interval logic setting. Recently, a non-elementary model checking algorithm for Halpern and Shoham's modal logic of time intervals HS, interpreted over finite Kripke structures, has been proposed, together with a proof of the EXPSPACE-hardness of the problem. In this paper, we devise an EXPSPACE model checking procedure for two meaningful HS fragments. It exploits a suitable contraction technique, that allows one to replace long enough tracks of a Kripke structure by equivalent shorter ones.
47361379
Checking Interval Properties of Computations
Model checking is a powerful method widely explored in formal verification. Given a model of a system, e.g. A Kripke structure, and a formula specifying its expected behavior, one can verify whether the system meets the behavior by checking the formula against the model. Classically, system behavior is given as a formula of a temporal logic, such as LTL and the like. These logics are "point-wise" interpreted, as they describe how the system evolves state-by-state. However, there are relevant properties, such as those involving temporal aggregations, which are inherently "interval-based", and thus asking for an interval temporal logic. In this paper, we give a formalization of the model checking problem in an interval logic setting. First, we provide an interpretation of formulas of Halpern and Shoham's interval temporal logic HS over Kripke structures, which allows one to check interval properties of computations. Then, we prove that the model checking problem for HS against Kripke structures is decidable by a suitable small model theorem, and we outline a PSpace decision procedure for the meaningful fragments AAbarBBbar and AAbarEEbar.
195862303
Symbolic model checking using SAT procedures instead of BDDs
In this paper, we study the application of propositional decision procedures in hardware verification. In particular, we apply bounded model checking to equivalence and invariant checking. We present several optimizations that reduce the size of generated propositional formulas. In many instances, our SAT-based approach can significantly outperform BDD-based approaches. We observe that SAT-based techniques are particularly efficient in detecting errors in both combinational and sequential designs.