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.
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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
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DOI: https://doi.org/10.1007/3-540-44904-3_17
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