Clock Difference Diagrams

Larsen, Kim G.; Weise, Carsten; Wang, Yi; Pearson, Justin

doi:10.7146/brics.v5i46.19491

Cited by 23 publications

(32 citation statements)

References 3 publications

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“…The model checker is able to check invariants, reachability and some liveness properties by exploring the state space of a system in a symbolic way. To represent the state space, Uppaal can use Clock Difference Diagrams (CDDs) [LWYP98], or DBMs. Difference Decision Diagrams (DDDs) [MLAH01] are BDD-like data structures to handle boolean formulas over inequalities of the form x − y < c and x − y ≤ c, and can be used to represent and explore sets of states of a timed system.…”

Section: Related Workmentioning

confidence: 99%

“…Despite their efficiency, such techniques are basically explicit-state: a complete assignment to propositional variables is associated with a complete region, and the amount of required memory is the most limiting factor in the verification process. Recently proposed techniques, such as DDD [MLAH01], CDDs [LWYP98], and RED [Wan00], provide symbolic representations for the search space. Also in this case, however, the memory requirements can be substantial, because of the inheritance of the properties of Binary Decision Diagrams.…”

Section: Introductionmentioning

confidence: 99%

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Bounded Model Checking for Timed Systems

Audemard

Cimatti

Korniłowicz

et al. 2002

Formal Techniques for Networked and Distributed Sytems — FORTE 2002

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Abstract. 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.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bounded Model Checking for Timed Systems

Audemard

Cimatti

Korniłowicz

et al. 2002

Formal Techniques for Networked and Distributed Sytems — FORTE 2002

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“…Applications that employ the Octagon domain or related weaker domains [22,28,33] will therefore directly benefit from this work. The paper is structured as follows.…”

Section: Introductionmentioning

confidence: 99%

“…This paper adapts this work to the requirements of program optimization and program development by equipping this domain with the operations needed for abstract interpretation. Two variable inequality domains have already proven useful in areas as diverse as program verification [29,34], model checking of timed automata [22,28], parallelization [2], locating security vulnerabilities [36], detecting memory leaks [33] and verifying program termination in logic programming [24]. Thus the applicability of the domain extends beyond logic programming [4,17] to other analysis problems in verification and program development.…”

Section: Introductionmentioning

confidence: 99%

Two Variables per Linear Inequality as an Abstract Domain

Simon

King

Howe

2003

Logic Based Program Synthesis and Transformation

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Abstract. This paper explores the spatial domain of sets of inequalities where each inequality contains at most two variables -a domain that is richer than intervals and more tractable than general polyhedra. We present a complete suite of efficient domain operations for linear systems with two variables per inequality with unrestricted coefficients. We exploit a tactic in which a system of inequalities with at most two variables per inequality is decomposed into a series of projections -one for each two dimensional plane. The decomposition enables all domain operations required for abstract interpretation to be expressed in terms of the two dimensional case. The resulting operations are efficient and include a novel planar convex hull algorithm. Empirical evidence suggests that widening can be applied effectively, ensuring tractability.

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“…These techniques are well-suited when the sizes of the discrete state space and the numbers of different clock regions per location remain moderate. CDDs [12] make the attempt to represent unions of clock zones more compactly. CDDs are BDD-like data structures where nodes are labeled by clock differences x i − x j and the outgoing edges of nodes are labeled by (disjoint) intervals of rational numbers.…”

Section: Introductionmentioning

confidence: 99%

Fully Symbolic Model Checking for Timed Automata

Morbé

Pigorsch

Scholl

2011

Computer Aided Verification

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Abstract. In this paper we introduce a new formal model, called finite state machines with time (FSMT), to represent real-time systems. We present a model checking algorithm for FSMTs, which works on fully symbolic state sets containing both the clock values and the state variables. In order to verify timed automata (TAs) with our model checking algorithm, we present two different methods to convert TAs to FSMTs. In addition to pure interleaving semantics we can convert TAs to FSMTs having a parallelized interleaving behavior which allows parallelism of transitions causing no conflicts. This can dramatically reduce the number of steps during verification. Our experimental results show that our prototype implementation outperforms the state-of-the-art model checkers UPPAAL and RED.

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Clock Difference Diagrams

Abstract: We sketch a BDD-like structure for representing unions of simple convex polyhedra, describing the legal values of a set of clocks given bounds on the values of clocks and clock differences.

Cited by 23 publications

References 3 publications

Bounded Model Checking for Timed Systems

Bounded Model Checking for Timed Systems

Two Variables per Linear Inequality as an Abstract Domain

Fully Symbolic Model Checking for Timed Automata

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