Symbolic model checking of timed guarded commands using difference decision diagrams

Møller, Jesper B.; Hulgaard, Henrik; Andersen, Henrik Reif

doi:10.1016/s1567-8326(02)00023-1

Cited by 13 publications

(24 citation statements)

References 47 publications

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“…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. The associated tool can verify a real time system modeled as a timed guarded command program in a fully symbolic way, by performing reachability analysis and model checking of TCTL formulas using standard fixed-point iteration algorithms.…”

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

View full text Add to dashboard Cite

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“…Several verification tools for TA have been devised and implemented so far [15,19,23,24,28,33,34,35,36,37,40]. UPPAAL [6,28] is one of the popular tool with DBM technology.…”

Section: Related Workmentioning

confidence: 99%

“…DDD is a reachability analyzer based on BDD-like data-structures for TA [23,24]. SGM [37] is a compositional safety (reachability) analyzer for TA, also based on DBM technology.…”

Section: Related Workmentioning

confidence: 99%

“…∀ properties are called safety properties while ∀♦'s are usually called inevitability properties [16,27]. In the domain of dense-time system verification, people have focused on the efficient analysis of safety properties [15,19,23,24,28,33,34,35,36,37,40]. Inevitability properties in Timed CTL (TCTL) [1,17] are comparatively more complex to analyze due to the following reason.…”

Section: Introductionmentioning

confidence: 99%

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TCTL Inevitability Analysis of Dense-Time Systems

Wang

Hwang

2003

Implementation and Application of Automata

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Inevitability properties in branching temporal logics are of the syntax ∀♦φ, where φ is an arbitrary (timed) CTL formula. In the sense that "good things will happen", they are parallel to the "liveness" properties in linear temporal logics. Such inevitability properties in dense-time logics can be analyzed with greatest fixpoint calculation. We present algorithms to model-check inevitability properties both with and without requirement of non-Zeno computations. We discuss a technique for early decision on greatest fixpoints in the temporal logics. Our algorithms come with a d-parameter for the measurement of time-progress. We have experimented with various issues, which may affect the performance of TCTL inevitability analysis. Specifically, we report the performance of our implementation w.r.t. various d-parameter values and with or without the non-Zeno computation requirement in the evaluation of greatest fixpoints. We have also experimented with safe abstration techniques for model-checking TCTL inevitability properties. Analysis on the experiment data helps clarify how various techniques can be used to improve verification of inevitability properties.

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An MTBDD-Based Implementation of Forward Reachability for Probabilistic Timed Automata

Wang

Kwiatkowska

2005

Automated Technology for Verification and Analysis

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Abstract. Multi-Terminal Binary Decision Diagrams (MTBDDs) have been successfully applied in symbolic model checking of probabilistic systems. In this paper we propose an encoding method for Probabilistic Timed Automata (PTA) based on MTBDDs. The timing information is encoded via placeholders stored in the MTBDDs that are independent of how the timing information is represented. Using the Colorado University Decision Diagrams (CUDD) package, an experimental model checker is implemented, which supports probabilistic reachability model checking via the forward algorithm. We use Difference Bound Matrices (DBMs) and Difference Decision Diagrams (DDDs) for representing timing information and present experimental results on three case studies. Our key contribution is a general placeholder encoding method for Probabilistic Timed Automata and an experimental MTBDD-based model checker which has been partly integrated with PRISM. This is the first symbolic implementation of the forward probabilistic reachability algorithm.

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Symbolic model checking of timed guarded commands using difference decision diagrams

Cited by 13 publications

References 47 publications

Bounded Model Checking for Timed Systems

Bounded Model Checking for Timed Systems

TCTL Inevitability Analysis of Dense-Time Systems

An MTBDD-Based Implementation of Forward Reachability for Probabilistic Timed Automata

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