Model Checking Parameterised Multi-token Systems via the Composition Method

Aminof, Benjamin; Rubin, Sasha

doi:10.1007/978-3-319-40229-1_34

Cited by 7 publications

(6 citation statements)

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“…, T r ) where E ⊆ V × V , and the T i ⊆ V partition V . 6 The type of v ∈ V denoted t ype(v) is the unique j ≤ r such that v ∈ T j . We might write V G , E G and t ype G to stress G.…”

Section: Process Template Topology Pairwise Rendezvous Systemmentioning

confidence: 99%

“…We encode a characterization of the CTL * d \X-indistinguishability equivalence relation from [6] in MSO and utilize the composition property of CTL * d \X proved there. We prove the existence of decidable cutoffs for the PMCP problem in this setting and show a lower bound on the cutoffs of iteratively-constructible parameterized topologies for indexed LTL\X.…”

Section: Token Passing Systemsmentioning

confidence: 99%

“…We now define for a given TPS P G two abstractions used in the above-mentioned characterization [6]. The first abstraction simulates P G , keeping track only of the local states of processes indexed byḡ.…”

Section: Two Abstractions Of a Token-passing Systemmentioning

confidence: 99%

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Parameterized model checking of rendezvous systems

et al. 2017

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Parameterized model checking is the problem of deciding if a given formula holds irrespective of the number of participating processes. A standard approach for solving the parameterized model checking problem is to reduce it to model checking finitely many finite-state systems. This work considers the theoretical power and limitations of this technique. We focus on concurrent systems in which processes communicate via pairwise rendezvous, as well as the special cases of disjunctive guards and token passing; specifications are expressed in indexed temporal logic without the next operator; and the underlying network topologies are generated by suitable formulas and graph operations. First, we settle the exact computational complexity of the parameterized model checking problem for some of our concurrent systems, and establish new decidability results for others. Second, we consider the cases where model checking the parameterized system can be reduced to model checking some fixed number of processes, the number is known as a cutoff. We provide many cases for when such cutoffs can be computed, establish lower bounds on the size of such cutoffs, and identify cases where no cutoff exists. Third, we consider cases for which the parameterized system is equivalent to a single finite-state system (more precisely a Büchi word automaton), and establish tight bounds on the sizes of such automata.

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Section: Process Template Topology Pairwise Rendezvous Systemmentioning

confidence: 99%

Section: Token Passing Systemsmentioning

confidence: 99%

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Parameterized model checking of rendezvous systems

et al. 2017

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“…that each guard g ∈ G is a singleton. 4 4 This is not a restriction as any local transition (qU , g, q ′ U ) with a guard g ∈ G and |g| > 1 can be split into |g| transitions (qU , g1, q ′ U ), . .…”

Section: Introductionmentioning

confidence: 99%

Automatic Repair and Deadlock Detection for Parameterized Systems

Jacobs¹,

Sakr²,

Völp³

2021

Preprint

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We present an algorithm for the repair of parameterized systems. The repair problem is, for a given process implementation, to find a refinement such that a given property is satisfied by the resulting parameterized system, and deadlocks are avoided. Our algorithm employs a constraint-based search for candidate repairs, and uses a parameterized model checker to determine their correctness and update the constraint system in case errors are reachable. We apply this algorithm on systems that can be represented as well-structured transition systems (WSTS), including disjunctive systems, pairwise rendezvous systems, and broadcast protocols. Moreover, we show that parameterized deadlock detection can be decided in NEXPTIME for disjunctive systems, vastly improving on the best known lower bound, and that it is in general undecidable for broadcast protocols.Contributions. Our main contribution is a counterexample-guided parameterized repair approach, based on model checking of well-structured transition systems (WSTS) [1,30]. We investigate which information a parameterized model checker needs to provide to guide the search for candidate repairs, and how this information can be encoded into propositional constraints. Moreover, we investigate how to systematically avoid deadlocks in the repaired system. Our repair algorithm supports many classes of systems, including guarded protocols with disjunctive guards [20], rendezvous systems [33] and broadcast protocols [24].Since existing model checking algorithms for WSTS do not support deadlock detection, our approach has a subprocedure to solve this problem, which relies on new theoretical results: for disjunctive systems, we provide a novel deadlock detection algorithm that vastly improves on the complexity of the best known solution, while for broadcast protocols we prove that deadlock detection is in general undecidable, so approximate methods have to be used. We evaluate an implementation of our algorithm on benchmarks from different application domains, including a distributed lock service and a robot-flocking protocol.This paper is organized as follows. In Sect. 2 we present our basic system model for disjunctive systems. In Sect. 3 we define the parameterized repair problem, propose a solution, and highlight three research challenges. In Sect. 4 we develop algorithms for parameterized model checking and deadlock detection that provide information on error paths for our repair approach. In Sect. 5 we introduce our parameterized repair algorithm, and in Sect. 6 we extend it to more general properties and systems. We provide our experimental evaluation in Sect. 7, followed by a discussion of related work in Sect. 8, and our conclusion and discussion of future work in Sect. 9. System ModelIn the following, let Q be a finite set of states.Processes. A process template is a transition system U = (Q U , init U , G U , δ U ), where Q U ⊆ Q is a finite set of states including the initial state init U , G U ⊆ P(Q) is a set of guards, and δ U :We denote by t U a transition of U ,...

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“…Techniques for solving the general case include identifying decidable/tractable subcases (as we do) and designing algorithms that are not guaranteed to terminate, e.g., with acceleration and approximation techniques [AST18,ZP04]. The border between decidability and undecidability for various models is surveyed in [BJK + 15], including token-passing systems [AR16,AJKR14], rendezvous and broadcast [GS92, EFM99, AKR + 18], guarded protocols [JS18], ad hoc networks [DSZ10].…”

Section: Introductionmentioning

confidence: 99%

Parameterized Model Checking of Rendezvous Systems

Aminof

Kotek

Rubin

et al. 2014

CONCUR 2014 – Concurrency Theory

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We study the complexity of the model-checking problem for parameterized discrete-timed systems with arbitrarily many anonymous and identical contributors, with and without a distinguished "controller" process. Processes communicate via synchronous rendezvous. Our work extends the seminal work on untimed systems [German, Sistla: Reasoning about Systems with Many Processes. J. ACM 39(3), 1992] by the addition of discrete-time clocks, thus allowing one to model more realistic protocols.For the case without a controller, we show that the systems can be efficiently simulated -and vice versa -by systems of untimed processes that communicate via rendezvous and symmetric broadcast, which we call "RB-systems". Symmetric broadcast is a novel communication primitive that, like ordinary asymmetric broadcast allows all processes to synchronize; however, it has no distinction between sender/receiver processes.We show that the complexity of the parameterized model-checking problem for safety specifications is pspace-complete, and for liveness specifications it is decidable and in exptime. The latter result is proved using automata theory, rational linear programming, and geometric reasoning for solving certain reachability questions in a new variant of vector addition systems called "vector rendezvous systems". We believe these proof techniques are of independent interest and will be useful in solving related problems.For the case with a controller, we show that the parameterized model-checking problems for RB-systems and systems with asymmetric broadcast as a primitive are inter-reducible. This allows us to prove that for discrete timed-networks with a controller the parameterized model-checking problem is undecidable for liveness specifications.Our work exploits the intimate and fruitful connection between parameterized discretetimed systems and systems of processes communicating via broadcast. This allows us to provide a rare and surprising decidability result for liveness properties of parameterized timed-systems, as well as extend work from untimed systems to timed systems.

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Model Checking Parameterised Multi-token Systems via the Composition Method

Cited by 7 publications

References 28 publications

Parameterized model checking of rendezvous systems

Parameterized model checking of rendezvous systems

Automatic Repair and Deadlock Detection for Parameterized Systems

Parameterized Model Checking of Rendezvous Systems

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