arXiv subjects

Arnaud Sangnier

Publications and source records attributed to Arnaud Sangnier.

At least 19 recordsLinked to original sources

arXiv2026

Safety Verification of Wait-Only Non-Blocking Broadcast Protocols

Broadcast protocols are programs designed to be executed by networks of processes. Each process runs the same protocol, and communication between them occurs in synchronously in two ways: broadcast, where one process sends a message to all others, and rendez-vous, where one process sends a message to at most one other process. In both cases, communication is non-blocking, meaning the message is sent even if no process is able to receive it. We consider two coverability problems: the state coverability problem asks whether there exists a number of processes that allows reaching a given state of the protocol, and the configuration coverability problem asks whether there exists a number of processes that allows covering a given configuration. These two problems are known to be decidable and Ackermann-hard. We show that when the protocol is Wait-Only (i.e., it has no state from which a process can both send and receive messages), these problems become P-complete and PSPACE-complete, respectively.

cs.LO↗

arXiv2025

Wait-Only Broadcast Protocols are Easier to Verify

We study networks of processes that all execute the same finite-state protocol and communicate via broadcasts. We are interested in two problems with a parameterized number of processes: the synchronization problem which asks whether there is an execution which puts all processes on a given state; and the repeated coverability problem which asks if there is an infinite execution where a given transition is taken infinitely often. Since both problems are undecidable in the general case, we investigate those problems when the protocol is Wait-Only, i.e., it has no state from which a process can both broadcast and receive messages. We establish that the synchronization problem becomes Ackermann-complete, and the repeated coverability problem is in EXPSPACE, and PSPACE-hard.

cs.LO↗

arXiv2025

Verifying Parameterized Networks Specified by Vertex-Replacement Graph Grammars

We consider the parametric reachability problem (PRP) for families of networks described by vertex-replacement (VR) graph grammars, where network nodes run replicas of finite-state processes that communicate via binary handshaking. We show that the PRP problem for VR grammars can be effectively reduced to the PRP problem for hyperedge-replacement (HR) grammars at the cost of introducing extra edges for routing messages. This transformation is motivated by the existence of several parametric verification techniques for families of networks specified by HR grammars, or similar inductive formalisms. Our reduction enables applying the verification techniques for HR systems to systems with dense architectures, such as user-specified cliques and multi-partite graphs.

cs.FL↗

arXiv2025

Decidability Problems for Micro-Stipula

Micro-Stipula is a stateful calculus in which clauses can be activated either through interactions with the external environment or by the evaluation of time expressions. Despite the apparent simplicity of its syntax and operational model, the combination of state evolution, time reasoning, and nondeterminism gives rise to significant analytical challenges. In particular, we show that determining whether a clause is never executed is undecidable. We formally prove that this undecidability result holds even for syntactically restricted fragments: namely, the time-ahead fragment, where all time expressions are strictly positive, and the instantaneous fragment, where all time expressions evaluate to zero. On the other hand, we identify a decidable subfragment: within the instantaneous fragment, reachability becomes decidable when the initial states of functions and events are disjoint.

cs.LO↗

arXiv2025

Counting Abstraction for the Verification of Structured Parameterized Networks

We consider the verification of parameterized networks of replicated processes whose architecture is described by hyperedge-replacement graph grammars. Due to the undecidability of verification problems such as reachability or coverability of a given configuration, in which we count the number of replicas in each local state, we develop two orthogonal verification techniques. We present a counting abstraction able to produce, from a graph grammar describing a parameterized system, a finite set of Petri nets that over-approximate the behaviors of the original system. The counting abstraction is implemented in a prototype tool, evalutated on a non-trivial set of test cases. Moreover, we identify a decidable fragment, for which the coverability problem is in 2EXPTIME and PSPACE-hard.

cs.FL↗

arXiv2024

Phase-Bounded Broadcast Networks over Topologies of Communication

We study networks of processes that all execute the same finite state protocol and that communicate through broadcasts. The processes are organized in a graph (a topology) and only the neighbors of a process in this graph can receive its broadcasts. The coverability problem asks, given a protocol and a state of the protocol, whether there is a topology for the processes such that one of them (at least) reaches the given state. This problem is undecidable. We study here an under-approximation of the problem where processes alternate a bounded number of times $k$ between phases of broadcasting and phases of receiving messages. We show that, if the problem remains undecidable when $k$ is greater than 6, it becomes decidable for $k=2$, and EXPSPACE-complete for $k=1$. Furthermore, we show that if we restrict ourselves to line topologies, the problem is in $P$ for $k=1$ and $k=2$.

cs.LO↗

arXiv2024

On the Satisfiability of Local First-Order Logics with Data

We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain. Data values can be compared wrt.\ equality. As the satisfiability problem for this logic is undecidable in general, we introduce a family of local fragments. They restrict quantification to the neighbourhood of a given reference point that is bounded by some radius. Our first main result establishes decidability of the satisfiability problem for the local radius-1 fragment in presence of one "diagonal relation". On the other hand, extending the radius leads to undecidability. In a second part, we provide the precise decidability and complexity landscape of the satisfiability problem for the existential fragments of local logic, which are parameterized by the number of data values carried by each element and the radius of the considered neighbourhoods. Altogether, we draw a landscape of formalisms that are suitable for the specification of systems with data and open up new avenues for future research.

cs.LO↗

arXiv2023

Safety Analysis of Parameterised Networks with Non-Blocking Rendez-Vous

We consider networks of processes that all execute the same finite-state protocol and communicate via a rendez-vous mechanism. When a process requests a rendez-vous, another process can respond to it and they both change their control states accordingly. We focus here on a specific semantics, called non-blocking, where the process requesting a rendez-vous can change its state even if no process can respond to it. In this context, we study the parameterised coverability problem of a configuration, which consists in determining whether there is an initialnumber of processes and an execution allowing to reach a configuration bigger than a given one. We show that this problem is EXPSPACE-complete and can be solved in polynomial time if the protocol is partitioned into two sets of states, the states from which a process can request a rendez-vous and the ones from which it can answer one. We also prove that the problem of the existence of an execution bringing all the processes in a final state is undecidable in our context. These two problems can be solved in polynomial time with the classical rendez-vous semantics.

cs.LO↗

arXiv2022

On the Existential Fragments of Local First-Order Logics with Data

We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain which can be compared wrt. equality. As the satisfiability problem for this logic is undecidable in general, in a previous work, we have introduced a family of local fragments that restrict quantification to neighbourhoods of a given reference point. We provide here the precise complexity characterisation of the satisfiability problem for the existential fragments of this local logic depending on the number of data values carried by each element and the radius of the considered neighbourhoods.

cs.LO↗

arXiv2020

Deciding the existence of cut-off in parameterized rendez-vous networks

We study networks of processes which all execute the same finite-state protocol and communicate thanks to a rendez-vous mechanism. Given a protocol, we are interested in checking whether there exists a number, called a cut-off, such that in any networks with a bigger number of participants, there is an execution where all the entities end in some final states. We provide decidability and complexity results of this problem under various assumptions, such as absence/presence of a leader or symmetric/asymmetric rendez-vous.

cs.LO↗

arXiv2019

The Complexity of Flat Freeze LTL

We consider the model-checking problem for freeze LTL on one-counter automata (OCA). Freeze LTL extends LTL with the freeze quantifier, which allows one to store different counter values of a run in registers so that they can be compared with one another. As the model-checking problem is undecidable in general, we focus on the flat fragment of freeze LTL, in which the usage of the freeze quantifier is restricted. In a previous work, Lechner et al. showed that model checking for flat freeze LTL on OCA with binary encoding of counter updates is decidable and in 2NEXPTIME. In this paper, we prove that the problem is, in fact, NEXPTIME-complete no matter whether counter updates are encoded in unary or binary. Like Lechner et al., we rely on a reduction to the reachability problem in OCA with parameterized tests (OCA(P)). The new aspect is that we simulate OCA(P) by alternating two-way automata over words. This implies an exponential upper bound on the parameter values that we exploit towards an NP algorithm for reachability in OCA(P) with unary updates. We obtain our main result as a corollary. As another application, relying on a reduction by Bundala and Ouaknine, one obtains an alternative proof of the known fact that reachability in closed parametric timed automata with one parametric clock is in NEXPTIME.

cs.FL↗

arXiv2017

Model-checking Counting Temporal Logics on Flat Structures

We study several extensions of linear-time and computation-tree temporal logics with quantifiers that allow for counting how often certain properties hold. For most of these extensions, the model-checking problem is undecidable, but we show that decidability can be recovered by considering flat Kripke structures where each state belongs to at most one simple loop. Most decision procedures are based on results on (flat) counter systems where counters are used to implement the evaluation of counting operators.

cs.LO↗

arXiv2017

Parameterized Verification of Algorithms for Oblivious Robots on a Ring

We study verification problems for autonomous swarms of mobile robots that self-organize and cooperate to solve global objectives. In particular, we focus in this paper on the model proposed by Suzuki and Yamashita of anonymous robots evolving in a discrete space with a finite number of locations (here, a ring). A large number of algorithms have been proposed working for rings whose size is not a priori fixed and can be hence considered as a parameter. Handmade correctness proofs of these algorithms have been shown to be error-prone, and recent attention had been given to the application of formal methods to automatically prove those. Our work is the first to study the verification problem of such algorithms in the parameter-ized case. We show that safety and reachability problems are undecidable for robots evolving asynchronously. On the positive side, we show that safety properties are decidable in the synchronous case, as well as in the asynchronous case for a particular class of algorithms. Several properties on the protocol can be decided as well. Decision procedures rely on an encoding in Presburger arithmetics formulae that can be verified by an SMT-solver. Feasibility of our approach is demonstrated by the encoding of several case studies.

cs.DC↗

arXiv2016

How hard is it to verify flat affine counter systems with the finite monoid property ?

We study several decision problems for counter systems with guards defined by convex polyhedra and updates defined by affine transformations. In general, the reachability problem is undecidable for such systems. Decidability can be achieved by imposing two restrictions: (i) the control structure of the counter system is flat, meaning that nested loops are forbidden, and (ii) the set of matrix powers is finite, for any affine update matrix in the system. We provide tight complexity bounds for several decision problems of such systems, by proving that reachability and model checking for Past Linear Temporal Logic are complete for the second level of the polynomial hierarchy $Σ^P_2$, while model checking for First Order Logic is PSPACE-complete.

cs.CC↗

arXiv2016

Reachability in Networks of Register Protocols under Stochastic Schedulers

We study the almost-sure reachability problem in a distributed system obtained as the asynchronous composition of N copies (called processes) of the same automaton (called protocol), that can communicate via a shared register with finite domain. The automaton has two types of transitions: write-transitions update the value of the register, while read-transitions move to a new state depending on the content of the register. Non-determinism is resolved by a stochastic scheduler. Given a protocol, we focus on almost-sure reachability of a target state by one of the processes. The answer to this problem naturally depends on the number N of processes. However, we prove that our setting has a cut-off property: the answer to the almost-sure reachability problem is constant when N is large enough; we then develop an EXPSPACE algorithm deciding whether this constant answer is positive or negative.

cs.LO↗

arXiv2016

Qualitative Analysis of VASS-Induced MDPs

We consider infinite-state Markov decision processes (MDPs) that are induced by extensions of vector addition systems with states (VASS). Verification conditions for these MDPs are described by reachability and Buchi objectives w.r.t. given sets of control-states. We study the decidability of some qualitative versions of these objectives, i.e., the decidability of whether such objectives can be achieved surely, almost-surely, or limit-surely. While most such problems are undecidable in general, some are decidable for large subclasses in which either only the controller or only the random environment can change the counter values (while the other side can only change control-states).

cs.LO↗

arXiv2015

ATLsc with partial observation

Alternating-time temporal logic with strategy contexts (ATLsc) is a powerful formalism for expressing properties of multi-agent systems: it extends CTL with strategy quantifiers, offering a convenient way of expressing both collaboration and antagonism between several agents. Incomplete observation of the state space is a desirable feature in such a framework, but it quickly leads to undecidable verification problems. In this paper, we prove that uniform incomplete observation (where all players have the same observation) preserves decidability of the model-checking problem, even for very expressive logics such as ATLsc.

cs.LO↗

arXiv2013

Solving Parity Games on Integer Vectors

We consider parity games on infinite graphs where configurations are represented by control-states and integer vectors. This framework subsumes two classic game problems: parity games on vector addition systems with states (vass) and multidimensional energy parity games. We show that the multidimensional energy parity game problem is inter-reducible with a subclass of single-sided parity games on vass where just one player can modify the integer counters and the opponent can only change control-states. Our main result is that the minimal elements of the upward-closed winning set of these single-sided parity games on vass are computable. This implies that the Pareto frontier of the minimal initial credit needed to win multidimensional energy parity games is also computable, solving an open question from the literature. Moreover, our main result implies the decidability of weak simulation preorder/equivalence between finite-state systems and vass, and the decidability of model checking vass with a large fragment of the modal mu-calculus.

cs.LO↗