arXiv subjects

Paulin Fournier

Publications and source records attributed to Paulin Fournier.

7 recordsLinked to original sources

arXiv2025

Decisiveness for countable MDPs and insights for NPLCSs and POMDPs

Markov chains and Markov decision processes (MDPs) are well-established probabilistic models. While finite Markov models are well-understood, analysing their infinite counterparts remains a significant challenge. Decisiveness has proven to be an elegant property for countable Markov chains: it is general enough to be satisfied by several natural classes of countable Markov chains, and it is a sufficient condition for simple qualitative and approximate quantitative model-checking algorithms to exist. In contrast, existing works on the formal analysis of countable MDPs usually rely on ad hoc techniques tailored to specific classes. We provide here a general framework to analyse countable MDPs by extending the notion of decisiveness. Compared to Markov chains, MDPs exhibit extra non-determinism that can be resolved in an adversarial or cooperative way, leading to multiple natural notions of decisiveness. We show that these notions enable the approximation of reachability and safety probabilities in countable MDPs using simple model-checking procedures. We then instantiate our generic approach to two concrete classes of models inducing countable MDPs: non-deterministic probabilistic lossy channel systems and partially observable MDPs. This leads to an algorithm to approximately compute safety probabilities in each of these classes.

cs.LO↗

arXiv2020

The CLEARSY Safety Platform: 5 Years of Research, Development and Deployment

The CLEARSY Safety Platform (CSSP) was designed to ease the development of safety critical systems and to reduce the overall costs (development, deployment, and certification) under the pressure of the worldwide market. A smart combination of hardware features (double processor) and formal method (B method and code generators) was used to produce a SIL4-ready platform where safety principles are built-in and cannot be altered by the developer. Summarizing a 5-year return of experience in the effective application in the railways, this article explains how this approach is a game-changer and tries to anticipate the future of this platform for safety critical systems. In particular, the education of future engineers and the seamless integration in existing engineering processes with the support of Domain Specific Languages are key topics for a successful deployment in other domains. DSL like Robosim to program mobile robots and relay circuits to design railway signalling systems are connected to the platform.

cs.SE↗

arXiv2019

Equivalence kernels of sequential functions and sequential observation synthesis

We show that one can decide if a rational equivalence relation can be given as the equivalence kernel of a sequential letter-to-letter transduction. This problem comes from the setting of games with imperfect information. In [1, p. 6] the authors propose to model imperfect information by a rational equivalence relation and leave open the problem of deciding if one can synthesize a sequential letter-to-letter transducer (Mealy machine) which maps equivalent histories to the same sequence of observations. We also show that knowing if an equivalence relation can be given as the equivalence kernel of a sequential transducer is undecidable, even if the relation is given as a letter-to-letter transducer.

cs.FL↗

arXiv2019

Consistency in Parametric Interval Probabilistic Timed Automata

We propose a new abstract formalism for probabilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Automata and Interval Markov Chains. In this context, we consider the consistency problem that amounts to deciding whether a given specification admits at least one implementation. In the context of Interval Probabilistic Timed Automata (with no timing parameters), we show that this problem is decidable and propose a constructive algorithm for its resolution. We show that the existence of timing parameter valuations ensuring consistency is undecidable in the general context, but still exhibit a syntactic condition on parameters to ensure decidability. We also propose procedures that resolve both the consistency and the consistent reachability problems when the parametric probabilistic zone graph is finite.

cs.FL↗

arXiv2019

Parametric Timed Broadcast Protocols

In this paper we consider state reachability in networks composed of many identical processes running a parametric timed broadcast protocol (PTBP). PTBP are a new model extending both broadcast protocols and parametric timed automata. This work is, up to our knowledge, the first to consider the combination of both a parametric network size and timing parameters in clock guard constraints. Since the communication topology is of utmost importance in broadcast protocols, we investigate reachability problems in both clique semantics where every message reaches every processes, and in reconfigurable semantics where the set of receivers is chosen non-deterministically. In addition, we investigate the decidability status depending on whether the timing parameters in guards appear only as upper bounds in guards, as lower bounds or when the set of parameters is partitioned in lower-bound and upper-bound parameters.

cs.LO↗

arXiv2018

Alternating Nonzero Automata

We introduce a new class of automata on infinite trees called \emph{alternating nonzero automata}, which extends the class of non-deterministic nonzero automata. We reduce the emptiness problem for alternating nonzero automata to the same problem for non-deterministic ones, which implies decidability. We obtain as a corollary algorithms for the satisfiability of a probabilistic temporal logic extending both CTL* and the qualitative fragment of pCTL*.

cs.LO↗

arXiv2017

On Reversible Transducers

Deterministic two-way transducers define the robust class of regular functions which is, among other good properties, closed under composition. However, the best known algorithms for composing two-way transducers cause a double exponential blow-up in the size of the inputs. In this paper, we introduce a class of transducers for which the composition has polynomial complexity. It is the class of reversible transducers, for which the computation steps can be reversed deterministically. While in the one-way setting this class is not very expressive, we prove that any two-way transducer can be made reversible through a single exponential blow-up. As a consequence, we prove that the composition of two-way transducers can be done with a single exponential blow-up in the number of states. A uniformization of a relation is a function with the same domain and which is included in the original relation. Our main result actually states that we can uniformize any non-deterministic two-way transducer by a reversible transducer with a single exponential blow-up, improving the known result by de Souza which has a quadruple exponential complexity. As a side result, our construction also gives a quadratic transformation from copyless streaming string transducers to two-way transducers, improving the exponential previous bound.

cs.FL↗