Actual Arithmetic and Feasibility

Authors:
Jean-Yves Marion
Affiliations:
-
Venue:
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Year:
2001

Citing 13
Cited 0

Proofs and types

Proofs and types
Rewrite systems

Handbook of theoretical computer science (vol. B)
Recursive programming with proofs

Theoretical Computer Science - Special issue on discrete mathematics and applications to computer science
Bounded linear logic: a modular approach to polynomial-time computability

Theoretical Computer Science
Lambda-calculus, types and models

Lambda-calculus, types and models
A new recursion-theoretic characterization of the polytime functions

Computational Complexity
A foundational delineation of poly-time

Papers presented at the IEEE symposium on Logic in computer science
Light linear logic

Information and Computation
LOGSPACE and PTIME characterized by programming languages

Theoretical Computer Science - Special issue on mathematical foundations of programming semantics
A P-Time Completeness Proof for Light Logics

CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Intrinsic Theories and Computational Complexity

LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
Light Affine Logic

LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Reasoning about functional programs and complexity classes associated with type disciplines

SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents a methodology for reasoning about the computational complexity of functional programs. We introduce a first order arithmetic AT0 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.