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The Complexity of the Comparator Circuit Value Problem
[article]

2013
*
arXiv
*
pre-print

In 1990 Subramanian defined

arXiv:1208.2721v3
fatcat:xq5dhydghrb4xaikamyputsmxa
*the**complexity*class CC as*the*set*of**problems*log-space reducible to*the**comparator**circuit**value**problem*(CCV). ... We give several alternative definitions*of*CC, including (among others)*the*class*of**problems*computed by uniform polynomial-size families*of**comparator**circuits*supplied with copies*of**the*input and its ... Acknowledgment We would like to thank Yuli Ye for his contribution in*the*early parts*of*this research. ...##
###
The complexity of the comparator circuit value problem

2014
*
ACM Transactions on Computation Theory
*

In 1990 Subramanian defined

doi:10.1145/2635822
fatcat:koqu6ezg5zgtfogjiqtki56vgu
*the**complexity*class CC as*the*set*of**problems*log-space reducible to*the**comparator**circuit**value**problem*(Ccv). ... We give several alternative definitions*of*CC, including (among others)*the*class*of**problems*computed by uniform polynomial-size families*of**comparator**circuits*supplied with copies*of**the*input and its ...*The**complexity**of**the**comparator**circuit**value**problem*-AC 0 -CCV is*the*class*of*relations AC 0 -many-one reducible to CCV. ...##
###
The complexity of circuit value and network stability

1992
*
Journal of computer and system sciences (Print)
*

We develop a method for nontrivially restricting fanout in a

doi:10.1016/0022-0000(92)90024-d
fatcat:m6t6ddbkabgc3mqzyz42cs7zp4
*circuit*. We study*the**complexity**of**the**circuit**value**problem*and a new*problem*, network stability, when fanout is limited. ... One*of*these classes, %'V, contains several natural complete*problems*, including*circuit**value*for*comparator**circuits*, lex-first maximal matching, and*problems*related to stable marriage and stable roommates ...*THE*CLASS Gf%?*The**Comparator**Circuit**Value**Problem**The**comparator**circuit**value**problem*, (C)-CV, is*the**circuit**value**problem*over*the*monotone scatter-free basis {C}. ...##
###
A Formal Theory for the Complexity Class Associated with the Stable Marriage Problem

2011
*
Annual Conference for Computer Science Logic
*

Motivation Classify theorems according to

doi:10.4230/lipics.csl.2011.381
dblp:conf/csl/LeCY11
fatcat:nqcy6nxozfd5ljmc74ezle7lii
*the*computational*complexity**of*concepts needed to prove them. ...*The*theory VCC * for CC **Comparator**Circuit**Value*(Ccv)*Problem*(decision) Given a*comparator**circuit*with specified Boolean inputs Determine*the*output*value**of*a designated wire. 1 w0 • • 1 w1 • 1 ...*complexity*class CC Interesting natural complete*problems*: stable marriage, lex-first maximal matching,*comparator**circuit**value**problem*. . . ...##
###
Comparator Circuits over Finite Bounded Posets
[article]

2017
*
arXiv
*
pre-print

*The*class CC is

*the*

*complexity*class

*of*

*problems*many-one logspace reducible to

*the*

*Comparator*

*Circuit*

*Value*

*Problem*and we know that NL is contained in CC which is inturn contained in P. ... We study generalizations

*of*

*the*

*comparator*

*circuit*model that work over fixed finite bounded posets. ...

*The*reviewer also had outlined an argument

*the*details

*of*which we have incoroporated in this version as

*the*proof

*of*Theorem 9. ...

##
###
Improved Complexity of Quantum Oracles for Ternary Grover Algorithm for Graph Coloring

2011
*
2011 41st IEEE International Symposium on Multiple-Valued Logic
*

Can be reused Binary Inequality

doi:10.1109/ismvl.2011.42
dblp:conf/ismvl/WangP11
fatcat:hnhxc2hugjgvlknkihzkeyyo3y
*Comparator**circuit*•*Compare*two strings*of*digits and operates on an ancilla bit. • If*the*two strings are exactly*the*same, output is flipped from 1 to 0. • If*the*two ... • Mathematicians who create quantum algorithms (Grover, Shor, Phase Estimation, Many Body Dynamics, etc) do not pay attention to how*the**circuit*is designed and to its*complexity*• They write: "let be ... binary oracles. •*The*multi-*valued*extensions*of*binary oracles can be created for*comparators*, arithmetic*circuits*and Toffoli gates. • Thus, any*problem*, even those requiring strictly binary outputs ...##
###
Complexity of the Exact Solution to the Test Sequencing Problem

2015
*
Conference on Uncertainty in Artificial Intelligence
*

We prove that this decision

dblp:conf/uai/LiuS15
fatcat:23bzgh7itzf2xnrfe4iqg2fyyu
*circuit*formulation achieves*the*lower bound*complexity*for any method for*the*general test sequencing*problem*that examines*the*entire policy space. ... In this paper, we analyze*the*time*complexity**of*classic symmetric and asymmetric formulations, using influence diagrams and decision trees, to*the*general test sequencing*problem*, making no assumptions ... Acknowledgements We thank*the*anonymous referees for their suggestions and Yuval Shahar for inspiring*the*research. ...##
###
Minimization of the Complexity of the digital Circuit using Genetic Algorithm

IJARCCE - Computer and Communication Engineering

2015
*
IJARCCE
*

IJARCCE - Computer and Communication Engineering

*The*

*comparative*analysis is done on

*the*speed

*of*

*the*digital

*circuit*using

*the*genetic algorithm and sequential search algorithm & was found that GA is more efficient & faster in propagation delay. ...

*The*Optimization

*of*

*the*digital

*circuit*is done on

*the*basis

*of*Genetic Algorithm (GA) for achieving maximum output

*of*

*the*digital

*circuit*in terms

*of*speed. ... I wish to express my thanks to all

*the*people who helped turn

*the*World-Wide Web into

*the*useful and popular distributed hypertext. ...

##
###
Complexity Classes and Theories for the Comparator Circuit Value Problem
[article]

2011
*
arXiv
*
pre-print

Subramanian defined

arXiv:1106.4142v2
fatcat:dpewd4po2nfnnoe6obigbloc2a
*the**complexity*class CC as*the*set*of**problems*log-space reducible to*the**comparator**circuit**value**problem*. ... He proved that several other*problems*are complete for CC, including*the*stable marriage*problem*, and finding*the*lexicographical first maximal matching in a bipartite graph. ... That is, each class can be defined as*the*AC 0 many-one closure*of*a complete*problem*, and*the*result turns out to be also closed under AC 0 oracle reducibilities. ...##
###
Logic restructuring for delay balancing in wave-pipelined circuits: an integer programming approach

2005
*
Seventh International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC'05)
*

We also

doi:10.1109/synasc.2005.42
dblp:conf/synasc/SethupathyPP05
fatcat:fyvqamp6ybadjbdfllfubnlhhm
*compare**the*proposed technique with application -to*the*same*problem*-*of*a linear programming solver. ... After a weighted graph representation*of**the**circuit*is formed a node collapsing procedure is used to preprocess (reduce*the*size*of*)*the*system and obtain*the*final formulation*of**the*IP*problem*, which ...*Circuit**Complexity*: As*the*number*of*nodes in*the**circuit*increase,*the*non-linear*problem*solvers in LP techniques become more*complex*in nature. This increases*the*optimization time [11] . ...##
###
Bureaucratic protocols for secure two-party sorting, selection, and permuting

2010
*
Proceedings of the 5th ACM Symposium on Information, Computer and Communications Security - ASIACCS '10
*

In a nutshell,

doi:10.1145/1755688.1755716
dblp:conf/ccs/WangLGDZ10
fatcat:o7cvqtufpnhntouqama672n2s4
*the*main idea behind bureaucratic computing is to design data-oblivious algorithms that push all knowledge and influence*of*input*values*down to small black-box*circuits*, which are simulated ...*The*practical benefit*of*this approach is that it maintains*the*zero-knowledge features*of*secure two-party computations while avoiding*the*significant computational overheads that come from trying to ...*The*second algorithm does not have*the**problem*, however, since it has no conditions that depend on any*values**of*S, so*the**complexity**of**the*resulting*circuit*is O(n). ...##
###
Variational Quantum Circuit-Based Reinforcement Learning for POMDP and Experimental Implementation

2021
*
Mathematical Problems in Engineering
*

*The*learned parameters are then tested on IBMQ systems to demonstrate

*the*applicability

*of*our approach for real-machine-based predictions. ... Variational quantum

*circuit*is proposed for applications in supervised learning and reinforcement learning to harness potential quantum advantage. ... Acknowledgments e authors gratefully acknowledge

*the*funding from New Energy and Industrial Technology Development Organization (NEDO) under grant number NEDO P20015. e authors acknowledge use

*of*

*the*IBM ...

##
###
High-Level vs. RTL Combinational Equivalence: An Introduction

2006
*
Computer Design (ICCD '99), IEEE International Conference on
*

Other papers in this invited session discuss techniques for dealing with

doi:10.1109/iccd.2006.4380828
dblp:conf/iccd/Hu06
fatcat:33jdicviszcardg2wknzaffnkm
*the*sequential aspects*of*this*problem*. ... With increasing use*of*higher-than-RTL specifications as*the*starting point*of*designs, a pressing need has emerged for equivalence verification between a high-level (e.g., non-synthesizable software) ... Thanks to*the*organizers*of*ICCD 2006 for*the*opportunity to prepare this introductory paper. ...##
###
A Solution of the P versus NP Problem based on specific property of clique function
[article]

2020
*
arXiv
*
pre-print

lower bound

arXiv:1911.00722v2
fatcat:5x2gu7hw2ffr5hanirhz3etwq4
*compared*to*the*monotone one for computing*the*clique function. ... This indicates that*the*non-monotone network*complexity**of**the*clique function is super-polynomial which implies that P!=NP. ... We show that by replacement*of*each “Not” gates into constant “1” equivalently in standard*circuit*for clique*problem*, it can be proved that non-monotone network has*the*same or higher lower bound*compared*...##
###
Improving the average delay of sorting

2009
*
Theoretical Computer Science
*

In previous work we have introduced an average case measure for

doi:10.1016/j.tcs.2008.10.028
fatcat:xz4ti4llejg77okuictpzkxulm
*the*time*complexity**of*Boolean*circuits*. ... Thus,*compared*to C ,*the*depth*of*C will be larger by a factor up to*the*depth*of*CM. Our goal is to minimize*the*average delay*of*bit*comparator*sorting*circuits*. ... This implies that*the*average time*complexity**of**the*bit-*comparator**circuit*is at most a constant factor larger than*the*worst-case time*complexity**of**the*word*comparator**circuit*independent*of**the*length ...
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