Theoretical Computer Science
Journal of the ACM (JACM)
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Circuit definitions of nondeterministic complexity classes
SIAM Journal on Computing
Nondeterministic circuits, space complexity and quasigroups
Theoretical Computer Science
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
Additives of linear logic and normalization: part I: A (restricted) Church--Rosser property
Theoretical Computer Science - Linear logic
Proof Nets for Unit-free Multiplicative-Additive Linear Logic (Extended abstract)
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Proof Nets and Boolean Circuits
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Proof nets for unit-free multiplicative-additive linear logic
ACM Transactions on Computational Logic (TOCL)
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Non-deterministic Boolean proof nets
FOPARA'09 Proceedings of the First international conference on Foundational and practical aspects of resource analysis
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The relationship between Boolean proof nets of multiplicative linear logic ( APN) and Boolean circuits has been studied [Ter04] in a non-uniform setting. We refine this results by taking care of uniformity: the relationship can be expressed in term of the (Turing) polynomial hierarchy. We give a proofs-as-programs correspondence between proof nets and deterministic as well as non-deterministic Boolean circuits with a uniform depth-preserving simulation of each other. The Boolean proof nets class m&BN(poly) is built on multiplicative and additive linear logic with a polynomial amount of additive connectives as the non-deterministic circuit class NNC(poly) is with non-deterministic variables. We obtain uniform-APN= NCand m& BN(poly) = NNC(poly)=NP.