InforLorV4, PascalFrancis, Corpus, bibRecord, 000932

Actual arithmetic and feasibility

Identifieur interne : 000932 ( PascalFrancis/Corpus ); précédent : 000931; suivant : 000933

Actual arithmetic and feasibility

Auteurs : Jean-Yves Marion

Source :

Lecture notes in computer science [ 0302-9743 ] ; 2001.

RBID : Pascal:01-0486082

Descripteurs français

Pascal (Inist)
- Logique ordre 1, Programmation fonctionnelle, Arithmétique ordinateur, Complexité calcul, Complexité programme, Faisabilité, Temps polynomial, Arithmétique Péano.

English descriptors

KwdEn :
- Computational complexity, Computer arithmetic, Feasibility, First order logic, Functional programming, Peano arithmetics, Polynomial time, Program complexity.

Abstract

This paper presents a methodology for reasoning about the computational complexity of functional programs. We introduce a first order arithmetic AT° which is a syntactic restriction of Peano arithmetic. We establish that the set of functions which are provably total in AT⁰, is exactly the set of polynomial time functions.The cut-elimination process is polynomial time computable. Compared to others feasible arithmetics, AT⁰ is conceptually simpler. The main feature of AT⁰ concerns the treatment of the quantification. The range of quantifiers is restricted to the set of actual terms which is the set of constructor terms with variables. The inductive formulas are restricted to conjunctions of atomic formulas.

Notice en format standard (ISO 2709)

Pour connaître la documentation sur le format Inist Standard.

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A05				`@2 2142`
A08	`01`	`1`	`ENG`	`@1 Actual arithmetic and feasibility`
A09	`01`	`1`	`ENG`	`@1 CSL 2001 : computer science logic : Paris, 10-13 September 2001`
A11	`01`	`1`		`@1 MARION (Jean-Yves)`
A12	`01`	`1`		`@1 FRIBOURG (Laurent) @9 ed.`
A14	`01`			`@1 Loria, B.P. 239 @2 54506 Vandœuvre-lès-Nancy @3 FRA @Z 1 aut.`
A20				`@1 115-129`
A21				`@1 2001`
A23	`01`			`@0 ENG`
A26	`01`			`@0 3-540-42554-3`
A43	`01`			`@1 INIST @2 16343 @5 354000097008900090`
A44				`@0 0000 @1 © 2001 INIST-CNRS. All rights reserved.`
A45				`@0 28 ref.`
A47	`01`	`1`		`@0 01-0486082`
A60				`@1 P @2 C`
A61				`@0 A`
A64	`01`	`1`		`@0 Lecture notes in computer science`
A66	`01`			`@0 DEU`
A66	`02`			`@0 USA`
C01	`01`		`ENG`	@0 This paper presents a methodology for reasoning about the computational complexity of functional programs. We introduce a first order arithmetic AT° which is a syntactic restriction of Peano arithmetic. We establish that the set of functions which are provably total in AT⁰, is exactly the set of polynomial time functions.The cut-elimination process is polynomial time computable. Compared to others feasible arithmetics, AT⁰ is conceptually simpler. The main feature of AT⁰ concerns the treatment of the quantification. The range of quantifiers is restricted to the set of actual terms which is the set of constructor terms with variables. The inductive formulas are restricted to conjunctions of atomic formulas.
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C03	`02`	`X`	`FRE`	`@0 Programmation fonctionnelle @5 15`
C03	`02`	`X`	`ENG`	`@0 Functional programming @5 15`
C03	`02`	`X`	`SPA`	`@0 Programación funcional @5 15`
C03	`03`	`X`	`FRE`	`@0 Arithmétique ordinateur @5 16`
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C03	`03`	`X`	`SPA`	`@0 Aritmética ordenador @5 16`
C03	`04`	`X`	`FRE`	`@0 Complexité calcul @5 19`
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C03	`04`	`X`	`SPA`	`@0 Complejidad computación @5 19`
C03	`05`	`X`	`FRE`	`@0 Complexité programme @5 20`
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C03	`06`	`X`	`FRE`	`@0 Faisabilité @5 21`
C03	`06`	`X`	`ENG`	`@0 Feasibility @5 21`
C03	`06`	`X`	`SPA`	`@0 Practicabilidad @5 21`
C03	`07`	`X`	`FRE`	`@0 Temps polynomial @5 22`
C03	`07`	`X`	`ENG`	`@0 Polynomial time @5 22`
C03	`07`	`X`	`SPA`	`@0 Tiempo polinomial @5 22`
C03	`08`	`X`	`FRE`	`@0 Arithmétique Péano @4 CD @5 96`
C03	`08`	`X`	`ENG`	`@0 Peano arithmetics @4 CD @5 96`
C03	`08`	`X`	`SPA`	`@0 Aritmético Péano @4 CD @5 96`
N21				`@1 344`

A30	`01`	`1`	`ENG`	`@1 Computer science logic. International workshop @2 15 @3 Paris FRA @4 2001-09-10`
A30	`02`	`1`	`ENG`	`@1 EACSL. Annual conference @2 10 @3 Paris FRA @4 2001-09-10`

Format Inist (serveur)

NO :	PASCAL 01-0486082 INIST
ET :	Actual arithmetic and feasibility
AU :	MARION (Jean-Yves); FRIBOURG (Laurent)
AF :	Loria, B.P. 239/54506 Vandœuvre-lès-Nancy/France (1 aut.)
DT :	Publication en série; Congrès; Niveau analytique
SO :	Lecture notes in computer science; ISSN 0302-9743; Allemagne; Da. 2001; Vol. 2142; Pp. 115-129; Bibl. 28 ref.
LA :	Anglais
EA :	This paper presents a methodology for reasoning about the computational complexity of functional programs. We introduce a first order arithmetic AT° which is a syntactic restriction of Peano arithmetic. We establish that the set of functions which are provably total in AT⁰, is exactly the set of polynomial time functions.The cut-elimination process is polynomial time computable. Compared to others feasible arithmetics, AT⁰ is conceptually simpler. The main feature of AT⁰ concerns the treatment of the quantification. The range of quantifiers is restricted to the set of actual terms which is the set of constructor terms with variables. The inductive formulas are restricted to conjunctions of atomic formulas.
CC :	001D02A05; 001D02A04
FD :	Logique ordre 1; Programmation fonctionnelle; Arithmétique ordinateur; Complexité calcul; Complexité programme; Faisabilité; Temps polynomial; Arithmétique Péano
ED :	First order logic; Functional programming; Computer arithmetic; Computational complexity; Program complexity; Feasibility; Polynomial time; Peano arithmetics
SD :	Lógica orden 1; Programación funcional; Aritmética ordenador; Complejidad computación; Complejidad programa; Practicabilidad; Tiempo polinomial; Aritmético Péano
LO :	INIST-16343.354000097008900090
ID :	01-0486082

Links to Exploration step

Pascal:01-0486082

Le document en format XML

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Actual arithmetic and feasibility

Actual arithmetic and feasibility

Source :

Descripteurs français

English descriptors

Abstract

Notice en format standard (ISO 2709)

Format Inist (serveur)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri