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1
April 2018
Theory of Computing Systems: Volume 62 Issue 3, April 2018
Publisher: SpringerVerlag New York, Inc.
We provide a list of new natural V N Pintermediate polynomial families, based on basic (combinatorial) N Pcomplete problems that are complete under parsimonious reductions. Over finite fields, these families are in V N P, and under the plausible hypothesis M o d p P źź P / p o ...
Keywords:
Extension complexity, Homomorphisms, Monotone projections, Tree decomposition, VBP, VP, Completeness, Lower bounds, VNPintermediate
2
December 2017
ACM Transactions on Computational Logic (TOCL): Volume 19 Issue 1, February 2018
Publisher: ACM
Bibliometrics:
Citation Count: 0
Downloads (6 Weeks): 8, Downloads (12 Months): 93, Downloads (Overall): 93
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The groundbreaking paper “Short Proofs Are Narrow  Resolution Made Simple” by BenSasson and Wigderson (J. ACM 2001) introduces what is today arguably the main technique to obtain resolution lower bounds: to show a lower bound for the width of proofs. Another important measure for resolution is space, and in ...
Keywords:
QBF, simulations, Proof complexity, lower bound techniques, resolution
3
December 2016
Algorithmica: Volume 76 Issue 4, December 2016
Publisher: SpringerVerlag New York, Inc.
Polynomial Identity Testing (PIT) algorithms have focussed on polynomials computed either by small alternationdepth arithmetic circuits, or by readrestricted formulas. Readonce polynomials (ROPs) are computed by readonce formulas (ROFs) and are the simplest of readrestricted polynomials. Building structures above these, we show the following: (1) a deterministic polynomialtime nonblackbox PIT ...
Keywords:
Polynomial Identity Testing, Arithmetic circuits, Algebraic algorithms
4
October 2016
ACM Transactions on Computation Theory (TOCT): Volume 9 Issue 1, December 2016
Publisher: ACM
Bibliometrics:
Citation Count: 0
Downloads (6 Weeks): 3, Downloads (12 Months): 16, Downloads (Overall): 85
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A proof system for a language L is a function f such that Range( f ) is exactly L . In this article, we look at proof systems from a circuit complexity point of view and study proof systems that are computationally very restricted. The restriction we study is proof ...
Keywords:
Proof complexity, circuit complexity, proof circuits, small depth proofs
5
June 2016
ACM Transactions on Computation Theory (TOCT): Volume 8 Issue 4, July 2016
Publisher: ACM
Bibliometrics:
Citation Count: 0
Downloads (6 Weeks): 4, Downloads (12 Months): 37, Downloads (Overall): 109
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S ubset S um is a wellknown NPcomplete problem: given t ∈ Z + and a set S of m positive integers, output YES if and only if there is a subset S ′⊆ S such that the sum of all numbers in S ′ equals t . The problem ...
Keywords:
Onepass streaming algorithm, fully polynomialtime approximations chemes FPTAS, knapsack problem, monotone circuits
6
June 2016
CSR 2016: Proceedings of the 11th International Computer Science Symposium on Computer Science  Theory and Applications  Volume 9691
Publisher: SpringerVerlag New York, Inc.
An arithmetic readonce formula ROF is a formula circuit of fanout 1 over $$+, \times $$ where each variable labels at most one leaf. Every multilinear polynomial can be expressed as the sum of ROFs. In this work, we prove, for certain multilinear polynomials, a tight lower bound on the ...
7
June 2016
CSR 2016: Proceedings of the 11th International Computer Science Symposium on Computer Science  Theory and Applications  Volume 9691
Publisher: SpringerVerlag New York, Inc.
We provide a list of new natural $$\mathsf {VNP}$$Intermediate polynomial families, based on basic combinatorial $$\mathsf {NP}$$Complete problems that are complete under parsimonious reductions. Over finite fields, these families are in $$\mathsf {VNP}$$, and under the plausible hypothesis $$\mathsf {Mod}_p\mathsf {P}\not \subseteq \mathsf {P/poly}$$, are neither $$\mathsf {VNP}$$hard even under ...
8
March 2016
Information Processing Letters: Volume 116 Issue 3, March 2016
Publisher: Elsevier NorthHolland, Inc.
We show that Levelordered Qresolution and Treelike Qresolution, two restrictions of the Qresolution system for proving false QBFs false, are incomparable. While the � Exp + Res system is known to psimulate Treelike Qresolution, we observe that it cannot psimulate Levelordered Qresolution. We show that Levelordered Qresolution and Treelike Qresolution ...
Keywords:
Computational complexity, Quantified Boolean formulas (QBF), Proof complexity, Resolution
9
February 2016
Information Processing Letters: Volume 116 Issue 2, February 2016
Publisher: Elsevier NorthHolland, Inc.
In this note, we show that over fields of any characteristic, exponential sums of Boolean instantiations of polynomials computed by multilinear circuits can be computed by multilinear circuits with polynomial blowup in size. In particular, multilinearVNP equals multilinearVP. Our result showing closure under exponential sums also holds for other restricted ...
Keywords:
Circuits, Multilinearity, Computational complexity, Algebraic complexity, Branching programs
10
March 2014
Theoretical Computer Science: Volume 524 Issue C, March 2014
Publisher: Elsevier Science Publishers Ltd.
We study the problem of testing if the polynomial computed by an arithmetic circuit is identically zero. We give a deterministic polynomial time algorithm for this problem when the inputs are readtwice or readthrice formulas. In the process, these algorithms also test if the input circuit is computing a multilinear ...
Keywords:
Arithmetic circuits, Computational complexity
11
March 2014
Theoretical Computer Science: Volume 524, March, 2014
Publisher: Elsevier Science Publishers Ltd.
We study the problem of testing if the polynomial computed by an arithmetic circuit is identically zero. We give a deterministic polynomial time algorithm for this problem when the inputs are readtwice or readthrice formulas. In the process, these algorithms also test if the input circuit is computing a multilinear ...
Keywords:
Arithmetic circuits, Computational complexity
12
October 2013
Theory of Computing Systems: Volume 53 Issue 3, October 2013
Publisher: SpringerVerlag New York, Inc.
13
September 2013
Computational Complexity: Volume 22 Issue 3, September 2013
Publisher: Birkhauser Verlag
The class of polynomials computable by polynomial size logdepth arithmetic circuits (VNC 1 ) is known to be computable by constant width polynomial degree circuits (VsSC 0 ), but whether the converse containment holds is an open problem. As a partial answer to this question, we give a construction which ...
Keywords:
algebraic branching programs, 68Q15, circuit width, Valiant's classes, 03D15, 68Q05, Arithmetic circuits, syntactic multilinearity
14
May 2013
ACM Transactions on Computation Theory (TOCT): Volume 5 Issue 1, May 2013
Publisher: ACM
Bibliometrics:
Citation Count: 1
Downloads (6 Weeks): 3, Downloads (12 Months): 14, Downloads (Overall): 137
Full text available:
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In this paper we initiate the study of proof systems where verification of proofs proceeds by NC 0 circuits. We investigate the question which languages admit proof systems in this very restricted model. Formulated alternatively, we ask which languages can be enumerated by NC 0 functions. Our results show that ...
Keywords:
Proof circuits, Proof complexity, small depth proofs, circuit complexity
15
March 2013
Computational Complexity: Volume 22 Issue 1, March 2013
Publisher: Birkhauser Verlag
In the uniform circuit model of computation, the width of a boolean circuit exactly characterizes the "space" complexity of the computed function. Looking for a similar relationship in Valiant's algebraic model of computation, we propose width of an arithmetic circuit as a possible measure of space. In the uniform setting, ...
Keywords:
03D15, 68Q05, Arithmetic circuits, algebraic branching programs, 68Q15, circuit width, space complexity, Valiant's classes
16
October 2012
Algorithmica: Volume 64 Issue 2, October 2012
Publisher: SpringerVerlag New York, Inc.
We give a #NC 1 upper bound for the problem of counting accepting paths in any fixed visibly pushdown automaton. Our algorithm involves a nontrivial adaptation of the arithmetic formula evaluation algorithm of Buss, Cook, Gupta and Ramachandran (SIAM J. Comput. 21:755780, 1992). We also show that the problem is ...
17
October 2012
Algorithmica  Special Issue: Computing and Combinatorics: Volume 64 Issue 2, October 2012
Publisher: SpringerVerlag New York, Inc.
We give a #NC 1 upper bound for the problem of counting accepting paths in any fixed visibly pushdown automaton. Our algorithm involves a nontrivial adaptation of the arithmetic formula evaluation algorithm of Buss, Cook, Gupta and Ramachandran (SIAM J. Comput. 21:755–780, 1992). We also show that the problem is ...
18
August 2012
MFCS'12: Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Publisher: SpringerVerlag
We study the problem of testing if the polynomial computed by an arithmetic circuit is identically zero (ACIT). We give a deterministic polynomial time algorithm for this problem when the inputs are readtwice formulas. This algorithm also computes the MLIN predicate, testing if the input circuit computes a multilinear polynomial. ...
19
July 2012
Theoretical Computer Science: Volume 442, July, 2012
Publisher: Elsevier Science Publishers Ltd.
In the kmeans problem, we are given a finite set S of points in @?^m, and integer k>=1, and we want to find k points (centers) so as to minimize the sum of the square of the Euclidean distance of each point in S to its nearest center. We show ...
Keywords:
NPhardness, Planar graphs, Clustering, kmeans
20
February 2012
Theoretical Computer Science: Volume 417, February, 2012
Publisher: Elsevier Science Publishers Ltd.
The class NC^1 of problems solvable by bounded fanin circuit families of logarithmic depth is known to be contained in logarithmic space L, but not much about the converse is known. In this paper we examine the structure of classes in between NC^1 and L based on counting functions or, ...
Keywords:
Arithmetic circuits, Exact counting classes, NC1, Oracle hierarchy, Threshold classes, Complexity classes

