Theoretical Computer Science
Communication and concurrency
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Purely Logical Account of Sequentiality in Proof Search
ICLP '02 Proceedings of the 18th International Conference on Logic Programming
A Non-commutative Extension of Classical Linear Logic
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
A system of interaction and structure
ACM Transactions on Computational Logic (TOCL)
Reducing nondeterminism in the calculus of structures
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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System BV is an extension of multiplicative linear logic (MLL) with the rules mix, nullary mix, and a self-dual, non-commutative logical operator, called seq. While the rules mix and nullary mix extend the deductive system, the operator seq extends the language of MLL. Due to the operator seq, system BV extends the applications of MLL to those where sequential composition is crucial, e.g., concurrency theory. System FBV is an extension of MLL with the rules mix and nullary mix. In this paper, by relying on the fact that system BV is a conservative extension of system FBV, I show that system BV is NP-complete by encoding the 3-Partition problem in FBV. I provid a simple completeness proof of this encoding by resorting to a novel proof theoretical method for reducing the nondeterminism in proof search, which is also of independent interest.