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Extended regular expressions with counting and interleaving are widely used in practice. However the related theoretical studies for this kind of expressions currently cannot meet the need of practical work. This paper develops syntax…
We introduce the notion of multi-pattern, a combinatorial abstraction of polyphonic musical phrases. The interest of this approach lies in the fact that this offers a way to compose two multi-patterns in order to produce a longer one. This…
This is a book on weighted tree automata. We present the basic definitions and some of the important results in a coherent form with full proofs. The concept of weighted tree automata is part of Automata Theory and it touches the area of…
A generalization of the max-plus transformation, which is known as a method to derive cellular automata from integrable equations, is proposed for complex numbers. Operation rules for this transformation is also studied for general number…
We describe a mathematical structure that can give extensional denotational semantics to higher-order probabilistic programs. It is not limited to discrete probabilities, and it is compatible with integration in a way the models that have…
We propose a general algorithm of constructing an extended formulation for any given set of linear constraints with integer coefficients. Our algorithm consists of two phases: first construct a decision diagram $(V,E)$ that somehow…
We present logically based methods for constructing XP and FPT graph algorithms, parametrized by tree-width or clique-width. We will use fly-automata introduced in a previous article. They make possible to check properties that are not…
This text is an extended version of the chapter 'Automata and rational expressions' in the AutoMathA Handbook that will appear soon, published by the European Science Foundation and edited by JeanEricPin.
Existing approaches to the synthesis of reactive systems typically involve the construction of transition systems such as Mealy automata. However, in order to obtain a succinct representation of the desired system, structured programs can…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
Finite state transducers, multitape automata and weighted automata have a lot in common. By studying their universal foundations, one can discover some new insights into all of them. The main result presented here is the introduction of…
We introduce the notion of multi-patterns, a combinatorial abstraction of polyphonic musical phrases. The interest of this approach in encoding musical phrases lies in the fact that it becomes possible to compose multi-patterns in order to…
We give defining equations for function fields over finite fields with many rational places. They are obtained from composita of quadratic extensions of the rational function field.
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
A diagram is introduced for visualizing matrix product states which makes transparent a connection between matrix product factorizations of states and operators, and complex weighted finite state automata. It is then shown how one can…
Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of…
We propose an automated deduction method which allows us to produce proofs close to the human intuition and practice. This method is based on tableaux, which generate more natural proofs than similar methods relying on clausal forms, and…
We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally…
We define the notion of $k$-safe infinitary series over idempotent ordered totally generalized product $\omega $-valuation monoids that satisfy specific properties. For each element $k$ of the underlying structure (different from the…
We develop first steps in the study of factorizations of elements in ultraproducts of commutative cancellative monoids into irreducible elements. A complete characterization of the (multi-)sets of lengths in such objects is given. As…