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Proof nets and Boolean circuits

2004
*
Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
*

We study the relationship between

doi:10.1109/lics.2004.1319612
dblp:conf/lics/Terui04
fatcat:xo6xld5qbrbxhl45yfc4e4566i
*proof**nets*for mutiplicative linear logic (with unbounded fan-in logical connectives)*and**Boolean**circuits*. ... We give simulations of each other in the style of the*proofs*-as-programs correspondence;*proof**nets*correspond to*Boolean**circuits**and*cutelimination corresponds to evaluation. ... Acknowledgments We would like to thank Noriko Arai, Harry Mairson*and*the anonymous referees for helpful suggestions. ...##
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Sublogarithmic uniform Boolean proof nets

2012
*
Electronic Proceedings in Theoretical Computer Science
*

Using a

doi:10.4204/eptcs.75.2
fatcat:mxdz7yxowbdmdndsso35kfseyq
*proofs*-as-programs correspondence, Terui was able to compare two models of parallel computation:*Boolean**circuits**and**proof**nets*for multiplicative linear logic. ... This paper presents a novel translation in AC0*and*focuses on a simpler restricted notion of uniform*Boolean**proof**nets*. ...*Boolean**proof**nets*In order to compare the complexities of*proof**nets**and*of*Boolean**circuits*, we need to define how*proof**nets*represent*Boolean*values (definition 12)*and**Boolean*functions (definition ...##
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Non-deterministic Boolean Proof Nets
[chapter]

2010
*
Lecture Notes in Computer Science
*

With the restriction of

doi:10.1007/978-3-642-15331-0_9
fatcat:3n44bgqvcnge3harcbmqz36jhi
*proof**nets*to*Boolean*types, we prove that the cut-elimination procedure corresponds to Non-deterministic*Boolean**circuit*evaluation*and*reciprocally. ... We introduce Non-deterministic*Boolean**proof**nets*to study the correspondence with*Boolean**circuits*, a parallel model of computation. ... I would like to thank the reviewers for their remarks*and*the improvements which they suggested. ...##
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Page 808 of Neural Computation Vol. 8, Issue 4
[page]

1996
*
Neural Computation
*

A

*circuit*corresponds (using the notation of this paper) to a [-*net*, where [ is a class of*Boolean*functions*and*where functions in [ are assigned to the vertices of the*net*-architecture. ... The*proof*of 1.1 uses techniques of*circuit*theory. ...##
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Image Computation and Predicate Refinement for RTL Verilog using Word Level Proofs

2007
*
2007 Design, Automation & Test in Europe Conference & Exhibition
*

Existing algorithms use a

doi:10.1109/date.2007.364481
fatcat:exzz46eexbgdfjy2dohjrycmku
*net*-list-level*circuit*model for computing predicate images. 1) This paper describes a*proof*-based algorithm that computes an over-approximation of the predicate image at the ... wordlevel,*and*thus, scales to larger*circuits*. 2) The previous work relies on the computation of the weakest preconditions in order to refine the set of predicates. ... [9] introduce a SAT-based technique for predicate abstraction of*circuits*given in Verilog. The*circuit*is synthesized*and*transformed into*net*-list level. ...##
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Page 3489 of Mathematical Reviews Vol. , Issue 94f
[page]

1994
*
Mathematical Reviews
*

The

*proof*uses*circuit*techniques along the lines of those of T. Gundermann, N. A. Nasser*and*G. ... The*proofs*are well-presented*and*elementary. Rodney G. Downey (NZ-VCTR; Wellington) 94f:68083 68Q15 03G05 06E30 68Q25 Beynon, W. ...##
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Page 404 of Neural Computation Vol. 8, Issue 2
[page]

1996
*
Neural Computation
*

[This is also the input convention followed in standard

*Boolean**circuit*complexity theory (Wegener 1987).] ... Since a recurrent*net*of s units converging in time f may be “un- wound” into a feedforward*circuit*of size s-t, the class of*Boolean*func- tions computed by polynomial size, polynomial time asymmetric ...##
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Universal Boolean Systems

2008
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Electronical Notes in Theoretical Computer Science
*

*Boolean*interaction systems

*and*hard interaction systems define

*nets*of interacting cells. ... With

*boolean*

*nets*, it is not possible to create or destroy cells or links between existing cells. ... Introduction Interaction

*nets*[6] are a programming paradigm inspired by Girard's

*proof*

*nets*for linear logic [3] . ...

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Error diagnosis for transistor-level verification

1994
*
Proceedings of the 31st annual conference on Design automation conference - DAC '94
*

The method eciently propagates mismatched p atterns from erroneous outputs backward into the network

doi:10.1145/196244.196358
dblp:conf/dac/KuehlmannCSL94
fatcat:3xvpkbgg5nd6ncpuxlyg3hdsb4
*and*calculates*circuit*regions which most likely contain the error(s). ... Therefore, it is more general*and*especially suitable for transistor-level*circuits*, which have a broader variety of possible design errors than gate-level implementations. ... Additional thanks are extended to IBM designers Christopher Durham*and*David Appenzeller for contributing*circuit*examples. ...##
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Page 1450 of Mathematical Reviews Vol. 52, Issue 4
[page]

1976
*
Mathematical Reviews
*

Chen, Chuan 10244 Realizability of communication

*nets*: an application of the Zadeh criterion. IEEE Trans.*Circuits**and*Systems CAS-21 (1974), 150-151. ... The authors consider the decomposition of*Boolean*functions, presenting a method that uses*Boolean*matrix algebra*and*has been realized with a computer program. ...##
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Page 8764 of Mathematical Reviews Vol. , Issue 99m
[page]

1999
*
Mathematical Reviews
*

We then look at the

*Boolean**circuit*satisfiability problem*and*give non-interactive zero-knowledge*proofs**and*argu- ments with preprocessing. ... We prove that*Boolean**circuits*, algebraic*circuits*, programs over nondeterministic finite automata,*and*programs over constant integer matrices yield equivalent definitions of the latter three classes. ...##
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Positive Versions of Polynomial Time

1998
*
Information and Computation
*

Perhaps the best known is in the context of

doi:10.1006/inco.1998.2742
fatcat:vdydd4332vellid2eozlndtluu
*boolean**circuits*where Razborov [25] proved that there exist monotone*boolean*functions which are computable by polynomial-size sequences of*boolean**circuits*... Grigni*and*Sipser [17] considered positive versions of a variety of computational models such as*boolean**circuits*, branching programs,*and*nondeterministic Turing machines*and*, in a natural way, made them ...*Proof*. The construction of a random-access ATM to evaluate a*boolean**circuit*is standard (see, for example, Theorem 4.4 of [3] ). ...##
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Mapping finite state machines to zk-SNARKS Using Category Theory
[article]

2019
*
arXiv
*
pre-print

We provide a categorical procedure to turn graphs corresponding to state spaces of finite state machines into

arXiv:1909.02893v2
fatcat:4yxprnoicngb7ezf6vlkeushbi
*boolean**circuits*, leveraging on the fact that*boolean**circuits*can be easily turned into zk-SNARKS ... Our*circuits*verify that a given sequence of edges*and*nodes is indeed a path in the graph they represent. We then generalize to*circuits*verifying paths in arbitrary graphs. ... Instead, we deem a wiser course of action turning*boolean**circuits*in B G Graph into*boolean**circuits*,*and*feed them to an already implemented*and*audited solution. ...##
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Analog versus Discrete Neural Networks

1996
*
Neural Computation
*

Thus, for a large class of activation functions, analog neural networks can be more powerful than discrete neural networks, even when computing

doi:10.1162/neco.1996.8.4.805
pmid:8624961
fatcat:kiornkelvvcf3hrsujncdicw6q
*Boolean*functions. ... We show that neural networks with three-times continuously di erentiable activation functions are capable of computing a certain family of n-bit*Boolean*functions with two gates, whereas networks composed ... A*circuit*corresponds (using the notation of this paper) to a ;-*net*, where ; is a class of*Boolean*functions*and*where functions in ; are assigned to the vertices of the*net*-architecture. f*AND*, OR, NOTg-*circuits*...##
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A Structural Approach for Transistor Circuit Synthesis

2006
*
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
*

Experimental results on a benchmark suite targeting standard cell implementations demonstrate the feasibility

doi:10.1093/ietfec/e89-a.12.3529
fatcat:du3sz7andva5na5rj5fg2wiq3e
*and*effectiveness of the proposed approach. ... To make the problem tractable, the solution space is restricted to the*circuit*structures which can be obtained by performing algebraic transformations on an arbitrary primeand-irredundant two-level*circuit*... Lemma 4. 1 . 1 For an arbitrary prime-*and*-irredundant twolevel*Boolean*network η, every AND2/INV decomposition of the*Boolean*network η is contained in Ψ(µ Λ P ).*Proof*. ...
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