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We investigate sets of Mutually Orthogonal Latin Squares (MOLS) generated by Cellular Automata (CA) over finite fields. After introducing how a CA defined by a bipermutive local rule of diameter d over an alphabet of q elements generates a Latin square of order q d−1 , we study the conditions under which two CA generate a pair of orthogonal Latin squares. In particular, we prove that the Latin squares induced by two Linear Bipermutive CA (LBCA) over the finite field F q are orthogonal if and only if the polynomials associated to their local rules are relatively prime. Next, we enumerate all such pairs of orthogonal Latin squares by counting the pairs of coprime monic polynomials with nonzero constant term and degree n over F q . Finally, we present a construction of MOLS generated by LBCA with irreducible polynomials and prove the maximality of the resulting sets, as well as a lower bound which is asymptotically close to their actual number.

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International audienceWe investigate the computational complexity of deciding the occurrence of many different dynamical behaviours in reaction systems, with an emphasis on biologically relevant problems (i.e., existence of fixed points and fixed point attractors). We show that the decision problems of recognising these dynamical behaviours span a number of complexity classes ranging from FO-uniform AC^0 to Π_2^P-completeness with several intermediate problems being either NP or coNP-complete

International audienceReaction systems are a recent formal model inspired by the chemical reactions that happen inside cells and possess many different dynamical behaviours. In this work we continue a recent investigation of the complexity of detecting some interesting dynamical behaviours in reaction system. We prove that detecting global behaviours such as the presence of global attractors is PSPACE - complete. Deciding the presence of cycles in the dynamics and many other related problems are also PSPACE - complete. Deciding bijectivity is, on the other hand, a coNP - complete problem

International audienceWe introduce a new model for simulating natural phenomena. We address several issues: topology, basic set properties like injectivity and surjectivity, reversibility, and decidability questions about a special kind of conservation law called grain conservation and ultimate periodicity

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