Abstract
This paper relates two distinct traditions: the one of complexity classes characterisations through light logics and models of nondeterminism. Light logics provide an implicit characterisation of P-Time algorithms through the Curry-Howard isomorphism: every derivation reduces to its normal form in polynomial time and every polynomial Turing machine can be simulated by a derivation. In this paper, we extend Intuitionistic Light Affine Logic, a logic with full weakening, with a simple rule for nondeterminism and get a completeness result for NP-Time algorithms which is, as far as we know, the first Curry-Howard characterisation of NP complexity. We conclude by a reformulation of the P ≠ NP conjecture.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Asperti A., Light Affine Logic. LICS98, 1998.
Asperti A., Roversi L., Intuitionistic Light Affine Logic. ACM Transactions on Computational Logic, 2002.
Baillot P., Stratified coherent spaces: a denotational semantics for Light Linear Logic. ICC00, 2000.
Bellantoni S., Cook S., A new recursion-theoretic characterisation of the polytime functions. Computational Complexity, 1992.
Ehrhard T., Regnier L., The Differential Lambda-Calculus. 2001.
Girard J.-Y., Proof-nets: the parallel syntax for proof-theory. Logic and Algebra. eds Ursini and Agliano, Marcel Dekker, New York 1996.
Girard J.-Y., Light Linear Logic. Information and Computation, 1998.
Girard J.-Y., Locus Solum. Mathematical Structures in Computer Science 11(3), 2001.
Hofmann M., Linear types and non-size increasing polynomial time computation. To appear in TCS, 1999.
Kanovich M. I., Okada M., Scedrov A., Phase semantics for light linear logic. Technical report, 1997.
Lafont Y., Soft Linear Logic and Polynomial Time. To appear in TCS.
Laurent O., Polarized games. Seventeenth annual IEEE symposium on Logic In Computer Science, IEEE Computer Society, 2002.
Leivant D., Marion J.Y., Lambda calculus characterisations of poly-time. TLCA 1993.
Murawski A. S., Ong C.-H. L., Can safe recursion be interpreted in light logic?. Second International Workshop on Implicit Computational Complexity, 2000.
Papadimitriou C., Computational complexity. Addison Wesley, 1994.
Roversi L., A P-Time Completeness Proof for Light Logics. CSL99, 1999.
Roversi L., Flexible Affine Light Logic. Submitted, 2001.
Terui K., Light Affine Calculus and Polytime Strong Normalisation. LICS01, 2001.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Maurel, F. (2003). Nondeterministic Light Logics and NP-Time. In: Hofmann, M. (eds) Typed Lambda Calculi and Applications. TLCA 2003. Lecture Notes in Computer Science, vol 2701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44904-3_17
Download citation
DOI: https://doi.org/10.1007/3-540-44904-3_17
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40332-6
Online ISBN: 978-3-540-44904-1
eBook Packages: Springer Book Archive