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Timed Automata for the Development of Real-Time Systems
, 2011
"... Timed automata are a popular formalism to model real-time systems. They were introduced two decades ago to support formal verification. Since then they have also been used for other purposes and a large has been introduced to be able to deal with the many different kinds of requirements of real-time ..."
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Timed automata are a popular formalism to model real-time systems. They were introduced two decades ago to support formal verification. Since then they have also been used for other purposes and a large has been introduced to be able to deal with the many different kinds of requirements of real-time system. This paper presents a fairly comprehensive survey, comprised of eighty variants of timed automata. The paper classifies all these eighty variants of timed automata in an effort to determine current developments. It uses analysis techniques, formal properties, and decision problems to draw distinctions between different versions. Moreover, the paper discusses the challenges behind using a timed automata specification to derive an implementation of a working real-time system and presents some solutions. Finally, the paper lists and classifies forty tools supporting timed automata. The paper does not only discuss many variants and their supporting concepts (e.g., closure properties, decision problems), techniques (e.g., for analysis), and tools, but it also attempts to help the reader navigate the vast literature in the field, to highlight differences and similarities between variants, and to reveal research trends and promising avenues for future exploration.
Bounded model checking real-time multi-agent systems with clock differences: theory and implementation
- Department of Computer Science, University College London, Gower Street, London
, 2006
"... Abstract. We present a methodology for verifying epistemic and real-time temporal properties of multi-agent systems. We introduce an interpreted systems semantics based on diagonal timed automata and use a real-time temporal epistemic language to describe properties of multi-agent systems. We develo ..."
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Abstract. We present a methodology for verifying epistemic and real-time temporal properties of multi-agent systems. We introduce an interpreted systems semantics based on diagonal timed automata and use a real-time temporal epistemic language to describe properties of multi-agent systems. We develop a bounded model checking algorithm for this setting and present experimental results for a real-time version of the alternating bit-transmission problem obtained by means of a preliminary implementation of the technique. 1
Extended Timed Automata and Time Petri Nets
, 2006
"... Timed Automata (TA) and Time Petri Nets (TPN) are two well-established formal models for real-time systems. Recently, a linear transformation of TA to TPNs preserving reachability properties and timed languages has been proposed, which does however not extend to larger classes of TA which would allo ..."
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Timed Automata (TA) and Time Petri Nets (TPN) are two well-established formal models for real-time systems. Recently, a linear transformation of TA to TPNs preserving reachability properties and timed languages has been proposed, which does however not extend to larger classes of TA which would allow diagonal constraints or more general resets of clocks. Though these features do not add expressiveness, they yield exponentially more concise models. In this work, we propose two translations: one from extended TA to TPNs whose size is either linear or quadratic in the size of the original TA, depending on the features which are allowed; another one from a parallel composition of TA to TPNs, which is also linear. As a consequence, we get that TPNs are exponentially more concise than TA.
Lazy abstractions for timed automata
, 2013
"... Abstract. We consider the reachability problem for timed automata. A standard solution to this problem involves computing a search tree whose nodes are abstractions of zones. For efficiency reasons, they are parametrized by the maximal lower and upper bounds (LU-bounds) occurring in the guards of th ..."
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Abstract. We consider the reachability problem for timed automata. A standard solution to this problem involves computing a search tree whose nodes are abstractions of zones. For efficiency reasons, they are parametrized by the maximal lower and upper bounds (LU-bounds) occurring in the guards of the automaton. We propose an algorithm that is updating LU-bounds during exploration of the search tree. In order to keep them as small as possible, the bounds are refined only when they enable a transition that is impossible in the unabstracted system. So our algorithm can be seen as a kind of lazy CEGAR algorithm for timed automata. We show that on several standard benchmarks, the algorithm is capable of keeping very small LU-bounds, and in consequence reduce the search space substantially. 1
Diagonal constraints handled efficiently in UPPAAL
"... Abstract. Timed automata (TA) are widely used to model real-time systems, and UPPAAL is one of the most popular model-checker for this framework which has been successfully applied over numerous industrial case studies. Diagonal constraints are a natural extension of TA, that does not increase expre ..."
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Abstract. Timed automata (TA) are widely used to model real-time systems, and UPPAAL is one of the most popular model-checker for this framework which has been successfully applied over numerous industrial case studies. Diagonal constraints are a natural extension of TA, that does not increase expressive power, but gives conciseness. Unfortunately the classical forward algorithm for reachability analysis cannot be used to deal directly with diagonal constraints. Thus the current method implemented consists in removing them on-the-fly, which implies a complexity blow-up. In [8], a counter-example guided refinement algorithm has been proposed. In this paper, we present its implementation, and give some benchmarks on a variant of Fischer’s protocol.
Automatic Generation of Inductive Invariants by SUP(LA)
, 2012
"... The hierarchic combination of linear arithmetic and first-order logic with free function symbols, FOL(LA), results in a strictly more expressive logic than its two parts. The SUP(LA) calculus can be turned into a decision procedure for interesting fragments of FOL(LA).For example, reachability probl ..."
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The hierarchic combination of linear arithmetic and first-order logic with free function symbols, FOL(LA), results in a strictly more expressive logic than its two parts. The SUP(LA) calculus can be turned into a decision procedure for interesting fragments of FOL(LA).For example, reachability problems for timed automata can be decided by SUP(LA) using an appropriate translation into FOL(LA). In this paper, we extend the SUP(LA) calculus with an additional inference rule, automatically generating inductive invariants from partial SUP(LA) derivations. The rule enables decidability of more expressive fragments, including reachability for timed automata with unbounded integer variables. We have implemented the rule in the SPASS(LA) theorem prover with promising results, showing that it can considerably speed up proof search and enable termination of saturation for practically relevant
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"... Bounded model checking real-time multi-agent systems with clock differences: theory and implementation ..."
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Bounded model checking real-time multi-agent systems with clock differences: theory and implementation
Pierre-Alain Reynier Diagonal Constraints handled efficiently in
, 2007
"... Abstract. Timed automata (TA) are widely used to model real-time systems, and UPPAAL is one of the most popular model-checker for this framework which has been successfully applied over numerous industrial case studies. Diagonal constraints are a natural extension of TA, that does not increase expre ..."
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Abstract. Timed automata (TA) are widely used to model real-time systems, and UPPAAL is one of the most popular model-checker for this framework which has been successfully applied over numerous industrial case studies. Diagonal constraints are a natural extension of TA, that does not increase expressive power, but gives conciseness. Unfortunately the classical forward algorithm for reachability analysis cannot be used to deal directly with diagonal constraints. Thus the current method implemented consists in removing them on-the-fly, which implies a complexity blow-up. In [8], a counter-example guided refinement algorithm has been proposed. In this paper, we present its implementation, and give some benchmarks on a variant of Fischer’s protocol.
Decomposition of Decidable First-Order Logics over Integers and Reals
"... We tackle the issue of representing infinite sets of real-valued vectors. This paper introduces an operator for combining integer and real sets. Using this operator, we decompose three well-known logics extending Presburger with reals. Our decomposition splits a logic into two parts: one integer, an ..."
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We tackle the issue of representing infinite sets of real-valued vectors. This paper introduces an operator for combining integer and real sets. Using this operator, we decompose three well-known logics extending Presburger with reals. Our decomposition splits a logic into two parts: one integer, and one decimal (i.e. on the interval [0, 1[). We also give a basis for an implementation of our representation.
Exact Incremental Analysis of Timed Automata with an SMT-Solver
"... Abstract. Timed automata as acceptors of languages of finite timed words form a very useful framework for the verification of safety prop-erties of real-time systems. Many of the classical automata-theoretic de-cision problems are undecidable for timed automata, for instance the inclusion or the uni ..."
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Abstract. Timed automata as acceptors of languages of finite timed words form a very useful framework for the verification of safety prop-erties of real-time systems. Many of the classical automata-theoretic de-cision problems are undecidable for timed automata, for instance the inclusion or the universality problem. In this paper we consider restric-tions of these problems: universality for deterministic timed automata and inclusion of a nondeterministic one by a deterministic one. We then advocate the use of SMT solvers for the exact incremental analysis of timed automata via these problems. We stratify these problems by con-sidering domains of timed words of bounded length only and show that each bounded instance is in (co-)NP. We present some experimental data obtained from a prototypical implementation measuring the practical feasibility of the approach to timed automata via SMT solvers. 1
