arXiv subjects

Arnaud Sangnier

Publications and source records attributed to Arnaud Sangnier.

22 records · Page 2Linked to original sources

arXiv2013

On the Complexity of Verifying Regular Properties on Flat Counter Systems

Among the approximation methods for the verification of counter systems, one of them consists in model-checking their flat unfoldings. Unfortunately, the complexity characterization of model-checking problems for such operational models is not always well studied except for reachability queries or for Past LTL. In this paper, we characterize the complexity of model-checking problems on flat counter systems for the specification languages including first-order logic, linear mu-calculus, infinite automata, and related formalisms. Our results span different complexity classes (mainly from PTime to PSpace) and they apply to languages in which arithmetical constraints on counter values are systematically allowed. As far as the proof techniques are concerned, we provide a uniform approach that focuses on the main issues.

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arXiv2012

The Cost of Parameterized Reachability in Mobile Ad Hoc Networks

We investigate the impact of spontaneous movement in the complexity of verification problems for an automata-based protocol model of networks with selective broadcast communication. We first consider reachability of an error state and show that parameterized verification is decidable with polynomial complexity. We then move to richer queries and show how the complexity changes when considering properties with negation or cardinality constraints.

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arXiv2011

Parameterized Verification of Safety Properties in Ad Hoc Network Protocols

We summarize the main results proved in recent work on the parameterized verification of safety properties for ad hoc network protocols. We consider a model in which the communication topology of a network is represented as a graph. Nodes represent states of individual processes. Adjacent nodes represent single-hop neighbors. Processes are finite state automata that communicate via selective broadcast messages. Reception of a broadcast is restricted to single-hop neighbors. For this model we consider a decision problem that can be expressed as the verification of the existence of an initial topology in which the execution of the protocol can lead to a configuration with at least one node in a certain state. The decision problem is parametric both on the size and on the form of the communication topology of the initial configurations. We draw a complete picture of the decidability and complexity boundaries of this problem according to various assumptions on the possible topologies.

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arXiv2010

Model checking memoryful linear-time logics over one-counter automata

We study complexity of the model-checking problems for LTL with registers (also known as freeze LTL) and for first-order logic with data equality tests over one-counter automata. We consider several classes of one-counter automata (mainly deterministic vs. nondeterministic) and several logical fragments (restriction on the number of registers or variables and on the use of propositional variables for control locations). The logics have the ability to store a counter value and to test it later against the current counter value. We show that model checking over deterministic one-counter automata is PSPACE-complete with infinite and finite accepting runs. By constrast, we prove that model checking freeze LTL in which the until operator is restricted to the eventually operator over nondeterministic one-counter automata is undecidable even if only one register is used and with no propositional variable. As a corollary of our proof, this also holds for first-order logic with data equality tests restricted to two variables. This makes a difference with the facts that several verification problems for one-counter automata are known to be decidable with relatively low complexity, and that finitary satisfiability for the two logics are decidable. Our results pave the way for model-checking memoryful (linear-time) logics over other classes of operational models, such as reversal-bounded counter machines.

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