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Nonelementary Complexities for Branching VASS, MELL, and Extensions

Nonelementary Complexities for Branching VASS, MELL, and Extensions Nonelementary Complexities for Branching VASS, MELL, and Extensions ´ RANKO LAZIC, DIMAP, Department of Computer Science, University of Warwick, SYLVAIN SCHMITZ, ENS Cachan & INRIA We study the complexity of reachability problems on branching extensions of vector addition systems, which allows us to derive new non-elementary complexity bounds for fragments and variants of propositional linear logic. We show that provability in the multiplicative exponential fragment is TOWER-hard already in the affine case--and hence non-elementary. We match this lower bound for the full propositional affine linear logic, proving its TOWER-completeness. We also show that provability in propositional contractive linear logic is ACKERMANN-complete. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems--Complexity of proof procedures; F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic General Terms: Theory Additional Key Words and Phrases: Fast-growing complexity, linear logic, vector addition systems ACM Reference Format: Ranko Lazi´ and Sylvain Schmitz. 2015. Nonelementary complexities for branching VASS, MELL, and c extensions. ACM Trans. Comput. Logic 16, 3, Article 20 (May 2015), 30 pages. DOI: http://dx.doi.org/10.1145/2733375 1. INTRODUCTION The use of various classes of counter machines to provide computational counterparts to propositional substructural logics has been highly fruitful, allowing us http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Nonelementary Complexities for Branching VASS, MELL, and Extensions

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2015 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2733375
Publisher site
See Article on Publisher Site

Abstract

Nonelementary Complexities for Branching VASS, MELL, and Extensions ´ RANKO LAZIC, DIMAP, Department of Computer Science, University of Warwick, SYLVAIN SCHMITZ, ENS Cachan & INRIA We study the complexity of reachability problems on branching extensions of vector addition systems, which allows us to derive new non-elementary complexity bounds for fragments and variants of propositional linear logic. We show that provability in the multiplicative exponential fragment is TOWER-hard already in the affine case--and hence non-elementary. We match this lower bound for the full propositional affine linear logic, proving its TOWER-completeness. We also show that provability in propositional contractive linear logic is ACKERMANN-complete. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems--Complexity of proof procedures; F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic General Terms: Theory Additional Key Words and Phrases: Fast-growing complexity, linear logic, vector addition systems ACM Reference Format: Ranko Lazi´ and Sylvain Schmitz. 2015. Nonelementary complexities for branching VASS, MELL, and c extensions. ACM Trans. Comput. Logic 16, 3, Article 20 (May 2015), 30 pages. DOI: http://dx.doi.org/10.1145/2733375 1. INTRODUCTION The use of various classes of counter machines to provide computational counterparts to propositional substructural logics has been highly fruitful, allowing us

Journal

ACM Transactions on Computational Logic (TOCL)Association for Computing Machinery

Published: Jun 2, 2015

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