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The Complexity of the Comparator Circuit Value Problem [article]

Stephen A. Cook, Yuval Filmus, Dai Tri Man Le
2013 arXiv   pre-print
In 1990 Subramanian defined 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.  ... 
arXiv:1208.2721v3 fatcat:xq5dhydghrb4xaikamyputsmxa

The complexity of the comparator circuit value problem

Stephen A. Cook, Yuval Filmus, Dai Tri Man Lê
2014 ACM Transactions on Computation Theory  
In 1990 Subramanian defined 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.  ... 
doi:10.1145/2635822 fatcat:koqu6ezg5zgtfogjiqtki56vgu

The complexity of circuit value and network stability

Ernst W. Mayr, Ashok Subramanian
1992 Journal of computer and system sciences (Print)  
We develop a method for nontrivially restricting fanout in a 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}.  ... 
doi:10.1016/0022-0000(92)90024-d fatcat:m6t6ddbkabgc3mqzyz42cs7zp4

A Formal Theory for the Complexity Class Associated with the Stable Marriage Problem

Dai Tri Man Lê, Stephen A. Cook, Yuli Ye, Marc Herbstritt
2011 Annual Conference for Computer Science Logic  
Motivation Classify theorems according to 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. . .  ... 
doi:10.4230/lipics.csl.2011.381 dblp:conf/csl/LeCY11 fatcat:nqcy6nxozfd5ljmc74ezle7lii

Comparator Circuits over Finite Bounded Posets [article]

Balagopal Komarath, Jayalal Sarma, K.S. Sunil
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.  ... 
arXiv:1503.00275v2 fatcat:vxmi6fopvbgvvksyew4ftuunea

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

Yushi Wang, Marek Perkowski
2011 2011 41st IEEE International Symposium on Multiple-Valued Logic  
Can be reused Binary Inequality Comparator circuitCompare 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  ... 
doi:10.1109/ismvl.2011.42 dblp:conf/ismvl/WangP11 fatcat:hnhxc2hugjgvlknkihzkeyyo3y

Complexity of the Exact Solution to the Test Sequencing Problem

Wenhao Liu, Ross D. Shachter
2015 Conference on Uncertainty in Artificial Intelligence  
We prove that this decision 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.  ... 
dblp:conf/uai/LiuS15 fatcat:23bzgh7itzf2xnrfe4iqg2fyyu

Minimization of the Complexity of the digital Circuit using Genetic Algorithm
IJARCCE - Computer and Communication Engineering

Amit Pandey, Sudha Nair
2015 IJARCCE  
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.  ... 
doi:10.17148/ijarcce.2015.4393 fatcat:q3ythimgevarrj4zvwksk42lkq

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

Stephen A. Cook, Dai Tri Man Le, Yuli Ye
2011 arXiv   pre-print
Subramanian defined 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.  ... 
arXiv:1106.4142v2 fatcat:dpewd4po2nfnnoe6obigbloc2a

Logic restructuring for delay balancing in wave-pipelined circuits: an integer programming approach

S. Sethupathy, N. Park, M. Paprzycki
2005 Seventh International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC'05)  
We also 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] .  ... 
doi:10.1109/synasc.2005.42 dblp:conf/synasc/SethupathyPP05 fatcat:fyvqamp6ybadjbdfllfubnlhhm

Bureaucratic protocols for secure two-party sorting, selection, and permuting

Guan Wang, Tongbo Luo, Michael T. Goodrich, Wenliang Du, Zutao Zhu
2010 Proceedings of the 5th ACM Symposium on Information, Computer and Communications Security - ASIACCS '10  
In a nutshell, 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).  ... 
doi:10.1145/1755688.1755716 dblp:conf/ccs/WangLGDZ10 fatcat:o7cvqtufpnhntouqama672n2s4

Variational Quantum Circuit-Based Reinforcement Learning for POMDP and Experimental Implementation

Tomoaki Kimura, Kodai Shiba, Chih-Chieh Chen, Masaru Sogabe, Katsuyoshi Sakamoto, Tomah Sogabe, Erivelton Geraldo Nepomuceno
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  ... 
doi:10.1155/2021/3511029 fatcat:areeonp6mvda3nealqp6m6uixu

High-Level vs. RTL Combinational Equivalence: An Introduction

Alan J. Hu
2006 Computer Design (ICCD '99), IEEE International Conference on  
Other papers in this invited session discuss techniques for dealing with 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.  ... 
doi:10.1109/iccd.2006.4380828 dblp:conf/iccd/Hu06 fatcat:33jdicviszcardg2wknzaffnkm

A Solution of the P versus NP Problem based on specific property of clique function [article]

Boyu Sima
2020 arXiv   pre-print
lower bound 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  ... 
arXiv:1911.00722v2 fatcat:5x2gu7hw2ffr5hanirhz3etwq4

Improving the average delay of sorting

Andreas Jakoby, Maciej Liśkiewicz, Rüdiger Reischuk, Christian Schindelhauer
2009 Theoretical Computer Science  
In previous work we have introduced an average case measure for 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  ... 
doi:10.1016/j.tcs.2008.10.028 fatcat:xz4ti4llejg77okuictpzkxulm
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