Pierre‐Cyrille Héam

Luc Dartois, Pierre-Cyrille Héam, Ismaël Jecker et al.

We study bounded deviation of non-deterministic finite transducers under the Hamming distance: the bounded comparison problem asks, given two transducers and $k \in \mathbb{N}$, whether for every input the two transducers produce words at Hamming distance at most $k$. This problem is known to be decidable in polynomial time when $k$ is fixed, and in co-NP otherwise. We show that the problem is NL-complete when $k$ is fixed, co-NP-complete when $k$ is given in binary, and it is DP-complete to decide if the distance is exactly $k$. We also prove that if the two transducers have bounded comparison, then the maximal distance is at most quadratic in the size of both transducers, and that this bound is asymptotically tight. We prove the results on deviations problem, which asks similar questions on the distance of the pairs of input and output of a single transducer, and show that these two families of problems are logspace many-one equivalent.

Mathias Berry, Pierre-Cyrille Héam, Ismaël Jecker

Minimizing the size of finite automata is a fundamental problem in theoretical computer science. Beyond standard minimization, further reductions can be achieved by decomposing an automaton into smaller components whose languages combine via intersection or union to recover the original language. However, in general, no polynomial-time algorithm is known for computing such decompositions. In this paper, we focus on automata that recognize ideals, that is, languages at level 1/2 in the Straubing-Thérien hierarchy. Equivalently, these languages are expressible as a finite union of languages of the form $Σ^*a_1Σ^*\dotsΣ^*a_nΣ^*$ where $Σ$ is an alphabet and $a_i$ are letters of $Σ$. We show that the two problems of deciding whether such a language can be decomposed into an intersection or a union of smaller automata are decidable in NL. Moreover, we provide a polynomial-time algorithm that computes a decomposition into an intersection, if one exists, while ensuring that the resulting components also recognize ideal languages.

Julien Bernard, Pierre-Cyrille Héam, Olga Kouchnarenko

System modeling is a classical approach to ensure their reliability since it is suitable both for a formal verification and for software testing techniques. In the context of model-based testing an approach combining random testing and coverage based testing has been recently introduced [9]. However, this approach is not tractable on quite large models. In this paper we show how to use statistical approximations to make the approach work on larger models. Experimental results, on models of communicating protocols, are provided; they are very promising, both for the computation time and for the quality of the generated test suites.

Jacques M. Bahi, Christophe Guyeux, Pierre-Cyrille Heam

In this research work, security concepts are formalized in steganography, and the common paradigms based on information theory are replaced by another ones inspired from cryptography, more practicable are closer than what is usually done in other cryptographic domains. These preliminaries lead to a first proof of a cryptographically secure information hiding scheme.

Sylvain Contassot-Vivier, Jean-François Couchot, Christophe Guyeux et al.

Designing a pseudorandom number generator (PRNG) is a difficult and complex task. Many recent works have considered chaotic functions as the basis of built PRNGs: the quality of the output would indeed be an obvious consequence of some chaos properties. However, there is no direct reasoning that goes from chaotic functions to uniform distribution of the output. Moreover, embedding such kind of functions into a PRNG does not necessarily allow to get a chaotic output, which could be required for simulating some chaotic behaviors. In a previous work, some of the authors have proposed the idea of walking into a $\mathsf{N}$-cube where a balanced Hamiltonian cycle has been removed as the basis of a chaotic PRNG. In this article, all the difficult issues observed in the previous work have been tackled. The chaotic behavior of the whole PRNG is proven. The construction of the balanced Hamiltonian cycle is theoretically and practically solved. An upper bound of the expected length of the walk to obtain a uniform distribution is calculated. Finally practical experiments show that the generators successfully pass the classical statistical tests.

Alois Dreyfus, Pierre-Cyrille Heam, Olga Kouchnarenko

In the context of software testing, generating complex data inputs is frequently performed using a grammar-based specification. For combinatorial reasons, an exhaustive generation of the data -- of a given size -- is practically impossible, and most approaches are either based on random techniques or on coverage criteria. In this paper, we show how to combine these two techniques by biasing the random generation in order to optimise the probability of satisfying a coverage criterion.