Paper Info
Title
Uniform Circuits, & Boolean Proof Nets
Abstract
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.
Year
DOI
Venue
2007
10.1007/978-3-540-72734-7_28
LFCS
Keywords
Field
DocType
boolean proof nets class,proof net,additive connective,boolean proof nets,ncand m,non-deterministic boolean circuit,boolean proof net,additive linear logic,non-deterministic variable,non-deterministic circuit class,boolean circuit,uniform circuits,boolean circuits,linear logic
Cook–Levin theorem,Karp–Lipton theorem,Discrete mathematics,Combinatorics,Boolean circuit,Parity function,Product term,Boolean algebra,Boolean expression,Two-element Boolean algebra,Mathematics
Conference
Volume
ISSN
Citations 
4514
0302-9743
2
PageRank 
References 
Authors
0.43
14
2
Name
Order
Citations
PageRank
Virgile Mogbil1696.77
Vincent Rahli2439.21