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On the Computational Complexity of Cut-Elimination in Linear Logic

  • Harry G. Mairson
  • Kazushige Terui
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2841)

Abstract

Given two proofs in a logical system with a confluent cut-elimination procedure, the cut-elimination problem (CEP) is to decide whether these proofs reduce to the same normal form. This decision problem has been shown to be ptime-complete for Multiplicative Linear Logic (Mairson 2003). The latter result depends upon a restricted simulation of weakening and contraction for boolean values in MLL; in this paper, we analyze how and when this technique can be generalized to other MLL formulas, and then consider CEPfor other subsystems of Linear Logic. We also show that while additives play the role of nondeterminism in cut-elimination, they are not needed to express deterministic ptime computation. As a consequence, affine features are irrelevant to expressing ptime computation. In particular, Multiplicative Light Linear Logic (MLLL) and Multiplicative Soft Linear Logic (MSLL) capture ptime even without additives nor unrestricted weakening. We establish hierarchical results on the cut-elimination problem for MLL (ptime-complete), MALL (coNP-complete), MLLL (EXPTIME-complete), and for MLLL (2EXPTIME-complete).

Keywords

Normal Form Turing Machine Linear Logic Reduction Rule Boolean Circuit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Harry G. Mairson
    • 1
  • Kazushige Terui
    • 2
  1. 1.Computer Science DepartmentBrandeis UniversityWalthamUSA
  2. 2.National Institute of InformaticsTokyoJapan

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