On Simulation-Checking with Sequential Systems

Lecture Notes in Computer Science, 1998

In this paper we develop an approach to model-checking for timed automata via reachability testing. As our specification formalism, we consider a dense-time logic with clocks. This logic may be used to express safety and bounded liveness properties of real-time systems. We show how to automatically synthesize, for every logical formula ϕ, a socalled test automaton Tϕ in such a way that checking whether a system S satisfies the property ϕ can be reduced to a reachability question over the system obtained by making Tϕ interact with S. The testable logic we consider is both of practical and theoretical interest. On the practical side, we have used the logic, and the associated approach to model-checking via reachability testing it supports, in the specification and verification in Uppaal of a collision avoidance protocol. On the theoretical side, we show that the logic is powerful enough to permit the definition of characteristic properties, with respect to a timed version of the ready simulation preorder, for nodes of deterministic, τ -free timed automata. This allows one to compute behavioural relations via our model-checking technique, therefore effectively reducing the problem of checking the existence of a behavioural relation among states of a timed automaton to a reachability problem.

2005

In recent years, there has been much advancement in the area of verification of infinite-state systems. A system can have an infinite state-space due to unbounded data structures such as counters, clocks, stacks, queues, etc. It may also be infinitestate due to parameterization, i.e., the possibility of having an arbitrary number of components in the system. For parameterized systems, we are interested in checking correctness of all the instances in one verification step. In this thesis, we consider systems which contain both sources of infiniteness, namely: (a) real-valued clocks and (b) parameterization. More precisely, we consider two models : (a) the timed Petri net (TPN) model which is an extension of the classical Petri net model; and (b) the timed network (TN) model in which an arbitrary number of timed automata run in parallel. We consider verification of safety properties for timed Petri nets using forward analysis. Since forward analysis is necessarily incomplete, we provide a semi-algorithm augmented with an acceleration technique in order to make it terminate more often on practical examples. Then we consider a number of problems which are generalisations of the corresponding ones for timed automata and Petri nets. For instance, we consider zenoness where we check the existence of an infinite computation with a finite duration. We also consider two variants of the boundedness problem: syntactic boundedness in which both live and dead tokens are considered; semantic boundedness where only live tokens are considered. We show that the former problem is decidable, while the latter is not. Finally, we show undecidability of LTL model checking both for dense and discrete timed Petri nets. Next we consider timed networks. We show undecidability of safety properties in case each component is equipped with two or more clocks. This result contrasts previous decidability result for the case where each component has a single clock. Also, we show that the problem is decidable when clocks range over the discrete time domain. This decidability result holds when the processes have any finite number of clocks. Furthermore, we outline the border between decidability and undecidability of safety for TNs by considering several syntactic and semantic variants.

2005

Multi-agent systems (MAS) are a successful paradigm employed in the formalisation of many scenarios [30, 31], including communication protocols, security protocols, autonomous planning, etc. In many instances, MAS are modelled by means of multi-modal logics with modal operators to reason about temporal, epistemic, doxastic, and other properties of agents. As MAS being modelled grow larger, however, automatic techniques are crucially required for the formal verification of MAS specification.

2009

The model checking problem for CTL is known to be P-complete (Clarke, Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments of CTL obtained by restricting the use of temporal modalities or the use of negations-restrictions already studied for LTL by Sistla and Clarke (1985) and Markey (2004). For all these fragments, except for the trivial case without any temporal operator, we systematically prove model checking to be either inherently sequential (P-complete) or very efficiently parallelizable (LOGCFL-complete). For most fragments, however, model checking for CTL is already P-complete. Hence our results indicate that in most applications, approaching CTL model checking by parallelism will not result in the desired speed up. We also completely determine the complexity of the model checking problem for all fragments of the extensions ECTL, CTL + , and ECTL + .

Acta Informatica, 1998

We consider the model checking problem for Timed Probabilistic Computation Tree Logic (TPCTL) introduced by H. A. Hansson and D. Jonsson, and studied in a recent book by H. A. Hansson [Han94]. The semantics of TPCTL is defined in terms of probabilistic transition systems. It is shown in [Han94] that model checking for TPCTL has exponential time complexity, the latter being measured in terms of the size of formula, the size of transition system and the value of explicit time that appears in the formula. Besides that, [Han94] describes some polytime decidable classes, the proofs being rather voluminous. We show, by a short proof, that this model checking problem is polytime decidable in the general case. The proof is essentially based on results on the complexity of Markov decision processes.

Electronic Notes in Theoretical Computer Science, 2009

In a seminal paper from 1985, Sistla and Clarke showed that the model-checking problem for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If, in contrast, the set of propositional operators is restricted, the complexity may decrease. This paper systematically studies the model-checking problem for LTL formulae over restricted sets of propositional and temporal operators. For almost all combinations of temporal and propositional operators, we determine whether the model-checking problem is tractable (in P) or intractable (NP-hard). We then focus on the tractable cases, showing that they all are NL-complete or even logspace solvable. This leads to a surprising gap in complexity between tractable and intractable cases. It is worth noting that our analysis covers an infinite set of problems, since there are infinitely many sets of propositional operators.

Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science, 2002

In model checking, the state-explosion problem occurs when one checks a non-flat system, i.e., a system implicitly described as a synchronized product of elementary subsystems. In this paper, we investigate the complexity of a wide variety of modelchecking problems for non-flat systems under the light of parameterized complexity, taking the number of synchronized components as a parameter. We provide precise complexity measures (in the parameterized sense) for most of the problems we investigate, and evidence that the results are robust.

Theoretical Computer Science, 2006

We consider model checking of timed temporal formulae in durational transition graphs (DTGs), i.e., Kripke structures where transitions have integer durations. Two semantics for DTGs are presented and motivated. We consider timed versions of CTL where subscripts put quantitative constraints on the time it takes before a property is satisfied.

2003

The main contribution of the paper consists in showing that the BMC method is feasible for ACTL * (the universal fragment of CTL * which subsumes both ACTL and LTL. The extension to ACTL * is obtained by redefining the function returning the sufficient number of executions over which an ACTL * formula is checked, and then by combining two known translations to SAT for ACTL and LTL formulas. The proposed translation of ACTL * formulas is essentially different from the existing translations of both ACTL and LTL formulas. Moreover, ACTL * seems to be the largest set of temporal properties which can be verified by means of BMC. We have implemented our new BMC algorithm for discrete timed automata and we have presented a preliminary experimental results, which prove the efficiency of the method. The formal treatment is the basis for the implementation of the technique in the symbolic model checker $\surd$ erics.

State University of New York at Albany, Albany, NY, 1997

Given the increasing size and complexity of modern computing systems, the formal veri cation of hardware designs and distributed protocols has been gaining importance. Research in formal veri cation mainly involves the following activities : development of appropriate models for capturing essential aspects of systems; design of speci cation formalisms for describing desirable properties; development of algorithmic techniques to establish the conformance of systems to the desired properties; and analysis of the complexity of algorithmic problems arising in these contexts. The contributions of thesis are mainly in the last two of these areas, the main emphasis being on the development of uniform techniques.