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2006, Theory and Practice of Logic Programming
The language Timed Concurrent Constraint (tccp) is the extension over time of the Concurrent Constraint Programming (cc) paradigm that allows us to specify concurrent systems where timing is critical, for example reactive systems. Systems which may have an infinite number of states can be specified in tccp. Model checking is a technique which is able to verify finite-state systems with a huge number of states in an automatic way. In the last years several studies have investigated how to extend model checking techniques to systems with an infinite number of states. In this paper we propose an approach which exploits the computation model of tccp. Constraint based computations allow us to define a methodology for applying a model checking algorithm to (a class of) infinite-state systems. We extend the classical algorithm of model checking for LTL to a specific logic defined for the verification of tccp and to the tccp Structure which we define in this work for modeling the program be...
Electronic Notes in …, 2005
The Timed Concurrent Constraint programming language (tccp) introduces time aspects into the Concurrent Constraint paradigm. This makes tccp especially appropriate to analyze by model checking timing properties of concurrent systems. However, even if very compact state representations are obtained thanks to the use of constraints in tccp, large state spaces can be still generated which may prevent model checking tools from verifying tccp programs completely. In this paper, we introduce an abstract methodology which is based on over-and under-approximating tccp models and mitigates the state explosion problem which is common to traditional model checking algorithms. We ascertain the conditions for the correctness of the abstract technique and show that, due to the timing aspects of the language, this semantics does not correctly simulate the suspension behavior, which is a key feature of tccp. Then, we present a refined abstract semantics which correctly models suspension.
Theoretical Computer …, 2005
The Timed Concurrent Constraint programming language (tccp) introduces time aspects into the Concurrent Constraint paradigm. This makes tccp especially appropriate for analyzing timing properties of concurrent systems by model checking. However, even if very compact state representations are obtained thanks to the use of constraints in tccp, large state spaces can still be generated, which may prevent model-checking tools from verifying tccp programs completely. Model checking tccp programs is a difficult task due to the subtleties of the underlying operational semantics, which combines constraints, concurrency, non-determinism and time. Currently, there is no practical model-checking tool that is applicable to tccp. In this work, we introduce an abstract methodology which is based on over-and under-approximating tccp models and which mitigates the state explosion problem that is common to traditional model-checking algorithms. We ascertain the conditions for the correctness of the abstract technique and show that this preliminary abstract semantics does not correctly simulate the suspension behavior, which is a key feature of tccp. Then, we present a refined abstract semantics which correctly models suspension. Finally, we complete our methodology by approximating the temporal properties that must be verified.
ACM Transactions on Computational Logic, 2004
A temporal logic is presented for reasoning about the correctness of timed concurrent constraint programs. The logic is based on modalities which allow one to specify what a process produces as a reaction to what its environment inputs. These modalities provide an assumption/commitment style of specification which allows a sound and complete compositional axiomatization of the reactive behavior of timed concurrent constraint programs.
2003
Rapid growth of distributed systems stimulates many attempts to describe precisely the behavior of concurrent systems. The target of the research is to model complex systems, to automatically generate an executable code from abstract models, and to check the correctness of concurrent systems. In this thesis, a new concept of concurrent system verification is presented. The idea is based on building a new version of CTL temporal logic (QsCTL) over reachability graphs of systems defined by concurrent automata CSM. The proposed method is addressed to verify control-dominated systems. Many questions on concurrent system behavior may be asked easier in QsCTL than in traditional CTL. An original algorithm CBS (Checking By Spheres) for automatic evaluation of temporal formulas in this logic is presented. Another algorithm of state space reduction is designed. The presented ideas are implemented in TempoRG program, the element of the COSMA environment developed in ICS, WUT. The purpose of COSMA is to integrate formal verification methodology with concurrent systems design environment. The formulated theoretical concepts are illustrated with several examples concerning verification processes including quite complex industrial system.
2002
Enormous progress has been achieved in the last decade in the verification of timed systems, making it possible to analyze significant real-world protocols. An open challenge is the identification of fully symbolic verification techniques, able to deal effectively with the finite state component as well as with the timing aspects. In this paper we propose a new, symbolic verification technique that extends the Bounded Model Checking (BMC) approach for the verification of timed systems. The approach is based on the following ingredients. First, a BMC problem for timed systems is reduced to the satisfiability of a math-formula, i.e., a boolean combination of propositional variables and linear mathematical relations over real variables (used to represent clocks). Then, an appropriate solver, called MATHSAT, is used to check the satisfiability of the math-formula. The solver is based on the integration of SAT techniques with some specialized decision procedures for linear mathematical constraints, and requires polynomial memory. Our methods allow for handling expressive properties in a fully-symbolic way. A preliminary experimental evaluation confirms the potential of the approach.
1999
This paper describes how to analyze a timed system symbolically. That is, given a symbolic representation of a set of (timed) states (as an expression), we describe how to determine an expression that represents the set of states that can be reached either by firing a discrete transition or by advancing time. These operations are used to determine the set of reachable states symbolically. We also show how to symbolically determine the set of states that can reach a given set of states (i.e., a backwards step), thus making it possible to verify TCTL-formulae symbolically. The analysis is fully symbolic in the sense that both the discrete and the continuous part of the state space are represented symbolically. Furthermore, both the synchronous and asynchronous concurrent composition of timed systems can be performed symbolically. The symbolic representations are given as formulae expressed in a simple first-order logic over difference constraints containing only the Boolean operators and existential quantification. Together with a recently developed data structure for efficient manipulations of the logic, the symbolic representation provides the potential of drastically increasing the size of timed systems that can be verified in practice.
Information and Computation, 2000
We study a timed concurrent constraint language, called tccp, which is obtained by a natural timed interpretation of the usual ccp constructs: action-prefixing is interpreted as the next-time operator and the parallel execution of agents follows the scheduling policy of maximal parallelism. Additionally, tccp includes a simple primitive which allows one to specify timing constraints. We define the operational semantics of tccp by means of a transition system and we define a denotational model which is fully abstract with respect to the usual notion of observables (that is, the results of terminating computations). Moreover, we study the semantics and expressive power of the notion of maximal parallelism underlying the computational model of tccp: We define a fully abstract semantics for a sublanguage of tccp, called ccpm, which essentially is concurrent constraint programming, provided that we interpret the parallel operator in terms of maximal parallelism rather than of interleaving. We show that tccp is strictly more expressive than ccpm which, in its turn, is strictly more expressive than ccp.
Proceedings of the 31st annual conference on Design automation conference - DAC '94, 1994
An important practical approach to automatic verification of finite state concurrent systems is temporal logic model checking. However, a major barrier towards wider application of such methods is the state explosion problem that often occurs during the composition of complex communicating systems. In addition to being large, many systems have very deep state spaces as well.
Innovations in Systems and Software Engineering, 2010
The real-time process calculus Timed CSP is capable of expressing properties such as deadlock-freedom and real-time constraints. It is therefore well-suited to model and verify embedded software. However, proofs about Timed CSP specifications are not ensured to be correct since comprehensive machine-assistance for Timed CSP is not yet available. In this paper, we present our formalization of Timed CSP in the Isabelle/HOL theorem prover, which we have formulated as an operational coalgebraic semantics together with bisimulation equivalences and coalgebraic invariants. This allows for semi-automated and mechanically checked proofs about Timed CSP specifications. Mechanically checked proofs enhance confidence in verification because corner cases cannot be overlooked. We additionally apply our formalization to an abstract specification with real-time constraints. This is the basis for our current work, in which we verify a simple real-time operating system deployed on a satellite. As this operating system has to cope with arbitrarily many threads, we use verification techniques from the area of parameterized systems for which we outline their formalization.
Proceedings Eighth International Symposium on Temporal Representation and Reasoning. TIME 2001, 2000
We present a new real-time temporal logic for the specification and verification of discrete quantitative temporal properties. This logic is an extension of the well-known logic CTL. Its semantics is defined on discrete time transition systems which are in turn interpreted in an abstract manner instead of the usual stuttering interpretation. Hence, our approach directly supports abstractions of real-time systems by ignoring irrelevant qualitative properties, but without loosing any quantitative information. We analyse the complexity of the presented model checking algorithm and furthermore present a fragment of the logic that can be efficiently checked.
In this work we extend the Emerson and Kahlon's cutoff theorems for process skeletons with conjunctive guards to Parameterized Networks of Timed Automata, i.e. systems obtained by an apriori unknown number of Timed Automata instantiated from a finite set U1, . . . , Un of Timed Automata templates. In this way we aim at giving a tool to universally verify software systems where an unknown number of software components (i.e. processes) interact with continuous time temporal constraints. It is often the case, indeed, that distributed algorithms show an heterogeneous nature, combining dynamic aspects with real-time aspects. In the paper we will also show how to model check a protocol that uses special variables storing identifiers of the participating processes (i.e. PIDs) in Timed Automata with conjunctive guards. This is non-trivial, since solutions to the parameterized verification problem often relies on the processes to be symmetric, i.e. indistinguishable. On the other side, many popular distributed algorithms make use of PIDs and thus cannot directly apply those solutions.
ArXiv, 2014
In this work we extend the Emerson and Kahlon's cutoff theorems for process skeletons with conjunctive guards to Parameterized Networks of Timed Automata, i.e. systems obtained by an \emph{apriori} unknown number of Timed Automata instantiated from a finite set $U_1, \dots, U_n$ of Timed Automata templates. In this way we aim at giving a tool to universally verify software systems where an unknown number of software components (i.e. processes) interact with continuous time temporal constraints. It is often the case, indeed, that distributed algorithms show an heterogeneous nature, combining dynamic aspects with real-time aspects. In the paper we will also show how to model check a protocol that uses special variables storing identifiers of the participating processes (i.e. PIDs) in Timed Automata with conjunctive guards. This is non-trivial, since solutions to the parameterized verification problem often relies on the processes to be symmetric, i.e. indistinguishable. On the other side, many popular distributed algorithms make use of PIDs and thus cannot directly apply those solutions.
2002
Enormous progress has been achieved in the last decade in the verification of timed systems, making it possible to analyze significant real-world protocols. An open challenge is the identification of fully symbolic verification techniques, able to deal effectively with the finite state component as well as with the timing aspects. In this paper we propose a new, symbolic verification technique that extends the Bounded Model Checking (BMC) approach for the verification of timed systems. The approach is based on the following ingredients. First, a BMC problem for timed systems is reduced to the satisfiability of a math-formula, i.e., a boolean combination of propositional variables and linear mathematical relations over real variables (used to represent clocks). Then, an appropriate solver, called MATHSAT, is used to check the satisfiability of the math-formula. The solver is based on the integration of SAT techniques with some specialized decision procedures for linear mathematical constraints, and requires polynomial memory. Our methods allow for handling expressive properties in a fully-symbolic way. A preliminary experimental evaluation confirms the potential of the approach.
1994
Abstract. In this paper, an algebra of timed processes with real-valued clocks is presented, which may serve as a description language for networks of timed automata. We show that requirements such as a process will never reach an undesired state" can be verified by solving a simple class of constraints on the clock-variables. A symbolic on-the-fly reachability algorithm for the language has been developed and implemented as a software tool based on constraint-solving techniques.
Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science, 1994
We develop a model for timed, reactive computation by extending the asynchronous, untimed concurrent constraint programming model in a simple and uniform way. In the spirit of process algebras, we develop some combinators expressible in this model, and reconcile their operational, logical and denotational character. We show how programs may be compiled into finite-state machines with loop-free computations at each state, thus guaranteeing bounded response time.
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.
2002
The tcc paradigm is a formalism for timed concurrent constraint programming. Several tcc languages differing in their way of expressing infinite behavior have been proposed in the literature. In this paper we study the expressive power of some of these languages. In particular, we show that: (1) recursive procedures with parameters can be encoded into parameterless recursive procedures with dynamic scoping, and viceversa. (2) replication can be encoded into parameterless recursive procedures with static scoping, and viceversa. (3) the languages from (1) are strictly more expressive than the languages from (2). Furthermore, we show that behavioral equivalence is undecidable for the languages from (1), but decidable for the languages from (2). The undecidability result holds even if the process variables take values from a fixed finite domain.
… on Foundations of …, 2010
Abstract. We consider the problem of model checking message-passing systems with real-time requirements. As behavioural specifications, we use message sequence charts (MSCs) annotated with timing constraints. Our system model is a network of communicating finite state ...
Lecture Notes in Computer Science, 2005
We present a new model-checking technique for CSP-OZ-DC, a combination of CSP, Object-Z and Duration Calculus, that allows reasoning about systems exhibiting communication, data and real-time aspects. As intermediate layer we will use a new kind of timed automata that preserve events and data variables of the specification. These automata have a simple operational semantics that is amenable to verification by a constraint-based abstraction-refinement model checker. By means of a case study, a simple elevator parameterised by the number of floors, we show that this approach admits model-checking parameterised and infinite state real-time systems.
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.
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