Regular Model Checking Revisited

Lin, Anthony W.; Rümmer, Philipp

doi:10.1007/978-3-030-91384-7_6

Cited by 6 publications

(3 citation statements)

References 40 publications

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“…On the other hand, our abstraction function induces infinite abstract systems, for which we employ infinite-state model checking techniques (i.e. regular model checking Lin and Rümmer 2022]).…”

Section: Related Workmentioning

confidence: 99%

“…The second ingredient answers why we use string rewriting systems as abstractions: this subclass of array systems has been more amenable to solutions than the general case of arrays. In fact, several powerful verification methods over string rewriting systems (for both safety and liveness, among others) have been developed in the last decade or so, which include methods in the framework regular model checking [Abdulla 2012; Bouajjani et al 2004Bouajjani et al , 2000Lin and Rümmer 2022]. This framework relies on the decidable first-order theory over words with prefix-of-relation, regular constraints, and the equal-length predicate (a.k.a.…”

Section: Introductionmentioning

confidence: 99%

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Regular Abstractions for Array Systems

Hong,

Lin

2024

Proc. ACM Program. Lang.

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Verifying safety and liveness over array systems is a highly challenging problem. Array systems naturally capture parameterized systems such as distributed protocols with an unbounded number of processes. Such distributed protocols often exploit process IDs during their computation, resulting in array systems whose element values range over an infinite domain. In this paper, we develop a novel framework for proving safety and liveness over array systems. The crux of the framework is to overapproximate an array system as a string rewriting system (i.e. over a finite alphabet) by means of a new predicate abstraction that exploits the so-called indexed predicates. This allows us to tap into powerful verification methods for string rewriting systems that have been heavily developed in the last two decades or so (e.g. regular model checking). We demonstrate how our method yields simple, automatically verifiable proofs of safety and liveness properties for challenging examples, including Dijkstra's self-stabilizing protocol and the Chang-Roberts leader election protocol.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Regular Abstractions for Array Systems

Hong,

Lin

2024

Proc. ACM Program. Lang.

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“…Liveness in Regular Model Checking. Regular model checking (RMC) is a generic verification framework that exploits regular languages and relations (e.g., over finite/words or trees) as symbolic representations of infinite systems [1,2,20]. Various flavors of automata and transducers for representing the transition relations are employed, e.g., word/tree automatic relations (or subsets thereof),automatic relations (or subsets thereof), and rational relations.…”

Section: Introductionmentioning

confidence: 99%

Ramsey Quantifiers over Automatic Structures: Complexity and Applications to Verification

Bergsträßer¹,

Ganardi²,

Lin³

et al. 2022

Preprint

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Automatic structures are infinite structures that are finitely represented by synchronized finite-state automata. This paper concerns specifically automatic structures over finite words and trees (ranked/unranked). We investigate the "directed version" of Ramsey quantifiers, which express the existence of an infinite directed clique. This subsumes the standard "undirected version" of Ramsey quantifiers. Interesting connections between Ramsey quantifiers and two problems in verification are firstly observed: (1) reachability with Büchi and generalized Büchi conditions in regular model checking can be seen as Ramsey quantification over transitive automatic graphs (i.e., whose edge relations are transitive), (2) checking monadic decomposability (a.k.a. recognizability) of automatic relations can be viewed as Ramsey quantification over co-transitive automatic graphs (i.e., the complements of whose edge relations are transitive). We provide a comprehensive complexity landscape of Ramsey quantifiers in these three cases (general, transitive, cotransitive), all between NL and EXP. In turn, this yields a wealth of new results with precise complexity, e.g., verification of subtree/flat prefix rewriting, as well as monadic decomposability over tree-automatic relations. We also obtain substantially simpler proofs, e.g., for NL complexity for monadic decomposability over word-automatic relations (given by DFAs).

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Model Checking, Synthesis, and Learning

Olderog

Steffen

2021

Model Checking, Synthesis, and Learning

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Regular Model Checking Revisited

Cited by 6 publications

References 40 publications

Regular Abstractions for Array Systems

Regular Abstractions for Array Systems

Ramsey Quantifiers over Automatic Structures: Complexity and Applications to Verification

Model Checking, Synthesis, and Learning

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