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Cegielski P.,CNRS Complex and Logical Algorithm Laboratory | Guessarian I.,CNRS Laboratory of Algorithmic Informatics: Fundamentals and Applications
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2010

We compare the control structures of Abstract State Machines (in short ASM) defined by Yuri Gurevich and AsmL, a language implementing it. AsmL is not an algorithmically complete language, as opposed to ASM, but it is closer to usual programming languages allowing until and while iterations and sequential composition. We here give a formal definition of AsmL, its semantics, and we construct, for each AsmL program Π, a normal form (which is an ASM program) Π n computing the same function as Π. The number of comparisons and updates during the execution of the normal form is at most three times the number of comparisons and updates in the original program. © 2010 Springer-Verlag Berlin Heidelberg. Source


Choffrut C.,CNRS Laboratory of Algorithmic Informatics: Fundamentals and Applications | Malcher A.,Justus Liebig University | Mereghetti C.,University of Milan | Palano B.,University of Milan
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2010

The characterization of the class of FO[∈+∈]-definable languages by some generating or recognizing device is still an open problem. We prove that, restricted to bounded languages, this class coincides with the class of semilinear languages. We also study some closure properties of FO[∈+∈]-definable languages which, as a by-product, allow us to give an alternative proof that the Dyck languages cannot be defined in FO[∈+∈]. © 2010 Springer-Verlag Berlin Heidelberg. Source


Choffrut C.,CNRS Laboratory of Algorithmic Informatics: Fundamentals and Applications | Malcher A.,Justus Liebig University | Mereghetti C.,University of Milan | Palano B.,University of Milan
Acta Informatica | Year: 2012

The characterization of the class of FO[+]-definable languages by some generating or recognizing device is still an open problem. We prove that, restricted to word bounded languages, this class coincides with the class of semilinear languages. We also study the closure properties of the classes of languages definable in FO[+1], FO[<], FO[+] and FOC[+] under the main classical operations. © 2012 Springer-Verlag. Source


Frougny C.,CNRS Laboratory of Algorithmic Informatics: Fundamentals and Applications | Klouda K.,Czech Technical University
Acta Polytechnica | Year: 2013

Two infinite words that are connected with some significant univoque numbers are studied. It is shown that their factor and palindromic complexities almost coincide with the factor and palindromic complexities of the famous Thue-Morse word. © Czech Technical University in Prague, 2013. Source


Cegielski P.,CNRS Complex and Logical Algorithm Laboratory | Grigorieff S.,CNRS Laboratory of Algorithmic Informatics: Fundamentals and Applications | Guessarian I.,CNRS Laboratory of Algorithmic Informatics: Fundamentals and Applications
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2015

Various problems on integers lead to the class of functions defined on a ring of numbers (or a subset of such a ring) and verifying a−b divides f(a)−f(b) for all a, b.We say that such functions are “congruence preserving”. In previous works, we characterized these classes of functions for the cases ℕ → ℤ, ℤ → ℤ and ℤ/nℤ → ℤ/mℤ in terms of sums series of rational polynomials (taking only integral values) and the function giving the least common multiple of 1, 2,..., k. In this paper we relate the finite and infinite cases via a notion of “lifting”: if π: X → Y is a surjective morphism and f is a function Y → Y a lifting of f is a function F: X → X such that π ◦ F = f ◦ π. We prove that the finite case ℤ/nℤ → ℤ/nℤ can be so lifted to the infinite cases ℕ → ℕ and ℤ → ℤ. We also use such liftings to extend the characterization to the rings of p-adic and profinite integers, using Mahler representation of continuous functions on these rings. © Springer International Publishing Switzerland 2015. Source

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