Denis Thérien

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We show a property of strings is expressible in the two-variable fragment of first-order logic if and only if it is expressible by both a 2 and a 2 sentence. We thereby establish: UTL = FO2 = 2 \ 2 = UL ; where UTL stands for the string properties expressible in the temporal logic with ‘eventually in the future’ and ‘eventually in the past’ as the only(More)
We use tools from the algebraic theory of automata to investigate the class of languages recognized by two models of Quantum Finite Automata (QFA): Brodsky and Pippenger's end-decisive model (which we call BPQFA) and a new QFA model (which we call LQFA) whose definition is motivated by implementations of quantum computers using nucleo-magnetic resonance(More)
A language L over an alphabet A is said to have a neutral letter if there is a letter e ∈ A such that inserting or deleting e’s from any word in A∗ does not change its membership or non-membership in L. The presence of a neutral letter affects the definability of a language in firstorder logic. It was conjectured that it renders all numerical predicates(More)
A new model, non-uniform deterministic finite automata (NUDFA’s) over general tinite monoids, has recently been developed as a strong link between the theory of finite automata and low-level parallel complexity. Achievements of this model include the proof that width 5 branching programs recognize exactly the languages in non-uniform NC’, NUDFA(More)
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Büchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical formalism required to define them. The algebraic point of view on automata is an essential complement of this(More)