RAIRO - Theoretical Informatics and Applications, 2008
Abstract We give a complete characterization of the class of functions that are the intensional b... more Abstract We give a complete characterization of the class of functions that are the intensional behaviours of primitive recursive (PR) algorithms. This class is the set of primitive recursive functions that have a null basic case of recursion. This result is obtained using the property of ultimate unarity and a geometrical approach of sequential functions on N the set of positive integers.
Abstract. We investigate the structure of worst-case quasi reduced ordered decision diagrams (o... more Abstract. We investigate the structure of worst-case quasi reduced ordered decision diagrams (or boolean graphs) and boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity ...
Abstract We consider computable functionals mapping the Baire space into the set of integers. By ... more Abstract We consider computable functionals mapping the Baire space into the set of integers. By continuity, the value of the functional on a given function depends only on a``critical" finite part of this function. Care: there is in general no way to compute this critical finite part without querying the function on an arbitrarily larger finite part! Nevertheless, things are different in case there is a uniform bound on the size of the domain of this critical finite part.
Abstract We discuss two questions about algorithmic completeness (in the operational sense). Firs... more Abstract We discuss two questions about algorithmic completeness (in the operational sense). First, how to get a mathematical characterization of the classes of algorithms associated to the diverse computation models? Second, how to define a robust and satisfactory notion of primitive recursive algorithm? We propose solutions based on Gurevich's Abstract State Machines.
Concurrency and Parallelism, Programming, …, Jan 1, 1996
Abstract, The set of primitive recursive functions (pr) accepts many definitions. We study three ... more Abstract, The set of primitive recursive functions (pr) accepts many definitions. We study three languages (presented as rewriting rules) that compute pr functions and show that they do not have the same inten-sional behaviour (a new function associate to algorithm) from an in- ...
Nous étudions dans cette thèse la manière dont un algorithme écrit sur sa sortie en fonction de c... more Nous étudions dans cette thèse la manière dont un algorithme écrit sur sa sortie en fonction de ce qu'il a déjà lu sur ses entrées(ce qu'on appelle comportement intentionnel). Ce travail complète des travaux initiés par L. Colson et T. Coquand qui ont étudié certains systèmes fonctionnels. Nous étudions le comportement intentionnel des algorithmes définissables dans différents langages: le langage de la récursion primitive(PR), le langage de la récursion avec substitution de paramètres(PRV) et le langage de la récursion sur les listes ...
RAIRO - Theoretical Informatics and Applications, 2008
Abstract We give a complete characterization of the class of functions that are the intensional b... more Abstract We give a complete characterization of the class of functions that are the intensional behaviours of primitive recursive (PR) algorithms. This class is the set of primitive recursive functions that have a null basic case of recursion. This result is obtained using the property of ultimate unarity and a geometrical approach of sequential functions on N the set of positive integers.
Abstract. We investigate the structure of worst-case quasi reduced ordered decision diagrams (o... more Abstract. We investigate the structure of worst-case quasi reduced ordered decision diagrams (or boolean graphs) and boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity ...
Abstract We consider computable functionals mapping the Baire space into the set of integers. By ... more Abstract We consider computable functionals mapping the Baire space into the set of integers. By continuity, the value of the functional on a given function depends only on a``critical" finite part of this function. Care: there is in general no way to compute this critical finite part without querying the function on an arbitrarily larger finite part! Nevertheless, things are different in case there is a uniform bound on the size of the domain of this critical finite part.
Abstract We discuss two questions about algorithmic completeness (in the operational sense). Firs... more Abstract We discuss two questions about algorithmic completeness (in the operational sense). First, how to get a mathematical characterization of the classes of algorithms associated to the diverse computation models? Second, how to define a robust and satisfactory notion of primitive recursive algorithm? We propose solutions based on Gurevich's Abstract State Machines.
Concurrency and Parallelism, Programming, …, Jan 1, 1996
Abstract, The set of primitive recursive functions (pr) accepts many definitions. We study three ... more Abstract, The set of primitive recursive functions (pr) accepts many definitions. We study three languages (presented as rewriting rules) that compute pr functions and show that they do not have the same inten-sional behaviour (a new function associate to algorithm) from an in- ...
Nous étudions dans cette thèse la manière dont un algorithme écrit sur sa sortie en fonction de c... more Nous étudions dans cette thèse la manière dont un algorithme écrit sur sa sortie en fonction de ce qu'il a déjà lu sur ses entrées(ce qu'on appelle comportement intentionnel). Ce travail complète des travaux initiés par L. Colson et T. Coquand qui ont étudié certains systèmes fonctionnels. Nous étudions le comportement intentionnel des algorithmes définissables dans différents langages: le langage de la récursion primitive(PR), le langage de la récursion avec substitution de paramètres(PRV) et le langage de la récursion sur les listes ...
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