The research topics of the ESCAPE team cover a wide range of theoretical discrete complex systems and computational models (tilings, cellular automata, infinite words, etc.). We study the connections between these objects and the many notions of complexity associated (algorithmic, descriptive, combinatorial, etc.). We are particularly interested in using results and techniques that were developped for the study of one such object to obtain new insight into the properties of another..

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Entropy Shannon entropy Approximation Factor complexity Shannon inequalities Pavages Real time Universalité Arithmetical hierarchy Minimal SFT S-adicity 2D Finite-state dimension Bilinear systems Generalizations of Sturmian words Partage de secret Information theory Algorithmic information theory Bilinear maps Ideal gas law Corpuscular concepts Network coding Random bits Sofic shifts Expanders Halting problem Biclique cover Aperiodicity Copy lemma Secret sharing Information Theory Canonical single-corpuscle thermodynamics Kolmorogov complexity Algorithms Analytical models Symmetries Information inequalities Infinite words Automates cellulaires Algorithmic learning theory Property preserving morphisms Algorithmic statistics Subword complexity Expander mixing lemma Kolmogorov Complexity Repetitions Sturmian words Linear complexity Error-correcting codes Théorie de l'information Normal sequences Non-Shannon-type information inequalities OBDD Algorithmic complexity Guessing games Automata Secret key agreement Generic algorithms Combinatorics on Words Langages formels Complexité de Kolmogorov Combinatorics on words Quasiperiodic S-adic conjecture Linear programming Algorithmique du texte Entropie de Shannon Morphisms Symbolic dynamics Tilings Logic Palindromes Two dimension words Nanolaser Formal languages Mutual information Proof complexity Cellular automata Kolmogorov complexity Information-theoretic cryptography Tseitin formulas Semiconductor lasers Entropy region Cellular automaton Morphism Palindromic length Multiple unicast Almost entropic points Algorithm Factorization Algorithmic randomness Computability Communication complexity Aperiodic tilings Quasiperiodicity Kolmogorov structure function Ammann tilings Atmospheric modeling Classical gas theory Uniform recurrence