Undecidable Verification Problems for Programs with Unreliable Channels

Abdulla, Parosh Aziz; Jönsson, Bengt

doi:10.1006/inco.1996.0083

Cited by 66 publications

(50 citation statements)

References 28 publications

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“…As shown in our earlier work, it is decidable whether a protocol satisfies a safety property [5], but undecidable whether a protocol satisfies a liveness property [4]. Using our technique, we can prove liveness properties for some of these protocols.…”

Section: Alternating Bit Protocolmentioning

confidence: 79%

“…The second example is the well-known alternating bit protocol. This is an example of a lossy channel system, for which liveness properties are undecidable [4]. Our example shows that backwards reachability analysis (which is guaranteed to terminate [5]) can prove liveness properties for some of these systems, although in general they are undecidable.…”

Section: Introductionmentioning

confidence: 90%

“…For general infinite-state systems, the difference between safety and liveness properties is even larger. For some classes of systems, such as lossy channel systems, checking safety properties is decidable [5], whereas checking liveness properties is undecidable [4].…”

Section: Introductionmentioning

confidence: 99%

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Proving Liveness by Backwards Reachability

Abdulla

Jönsson

Rezine

et al. 2006

CONCUR 2006 – Concurrency Theory

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Abstract. We present a new method for proving liveness and termination properties for fair concurrent programs, which does not rely on finding a ranking function or on computing the transitive closure of the transition relation. The set of states from which termination or some liveness property is guaranteed is computed by a backwards reachability analysis. A central technique for handling concurrency is a check for certain commutativity properties. The method is not complete. However, it can be seen as a complement to other methods for proving termination, in that it transforms a termination problem into a simpler one with a larger set of terminated states. We show the usefulness of our method by applying it to existing programs from the literature. We have also implemented it in the framework of Regular Model Checking, and used it to automatically verify non-starvation for parameterized algorithms.

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Section: Alternating Bit Protocolmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 90%

See 1 more Smart Citation

Proving Liveness by Backwards Reachability

Abdulla

Jönsson

Rezine

et al. 2006

CONCUR 2006 – Concurrency Theory

Self Cite

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“…Early undecidability proofs for lossy systems (e.g. [6,39,1]) are sometimes hard to understand and then to adapt to related problems.…”

Section: Proving Undecidabilitymentioning

confidence: 99%

“…In general, the results come from [11,42,39] when they are specific to lossy counter machines. Some results have been first shown for lossy channel systems [15,7,6] or even well-structured systems [25,26,5,28,29].…”

Section: Introductionmentioning

confidence: 97%

Lossy Counter Machines Decidability Cheat Sheet

Schnoebelen

2010

Lecture Notes in Computer Science

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Abstract. Lossy counter machines (LCM's) are a variant of Minsky counter machines based on weak (or unreliable) counters in the sense that they can decrease nondeterministically and without notification. This model, introduced by R. Mayr [TCS 297:337-354 (2003)], is not yet very well known, even though it has already proven useful for establishing hardness results. In this paper we survey the basic theory of LCM's and their verification problems, with a focus on the decidability/undecidability divide.

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Algorithmic Analysis of Programs with Well Quasi-ordered Domains

Abdulla

Čerāns

Jönsson

et al. 2000

Information and Computation

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156

183

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Over the past few years increasing research effort has been directed towards the automatic verification of infinite-state systems. This paper is concerned with identifying general mathematical structures which can serve as sufficient conditions for achieving decidability. We present decidability results for a class of systems (called well-structured systems) which consist of a finite control part operating on an infinite data domain. The results assume that the data domain is equipped with a preorder which is a well quasi-ordering, such that the transition relation is`m onotonic'' (a simulation) with respect to the preorder. We show that the following properties are decidable for well-structured systems: v Reachability: whether a certain set of control states is reachable. Other safety properties can be reduced to the reachability problem.

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Undecidable Verification Problems for Programs with Unreliable Channels

Cited by 66 publications

References 28 publications

Proving Liveness by Backwards Reachability

Proving Liveness by Backwards Reachability

Lossy Counter Machines Decidability Cheat Sheet

Algorithmic Analysis of Programs with Well Quasi-ordered Domains

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