Meena Mahajan
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Bibliometrics: Citation Count: 0 We provide a list of new natural V N P-intermediate polynomial families, based on basic (combinatorial) N P-complete 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, VNP-intermediate 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 Full text available: PDF The ground-breaking paper “Short Proofs Are Narrow -- Resolution Made Simple” by Ben-Sasson 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: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 0 Polynomial Identity Testing (PIT) algorithms have focussed on polynomials computed either by small alternation-depth arithmetic circuits, or by read-restricted formulas. Read-once polynomials (ROPs) are computed by read-once formulas (ROFs) and are the simplest of read-restricted polynomials. Building structures above these, we show the following: (1) a deterministic polynomial-time non-black-box 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 Full text available: PDF 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 Full text available: PDF S ubset S um is a well-known NP-complete 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: One-pass streaming algorithm, fully polynomial-time 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: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 0 An arithmetic read-once formula ROF is a formula circuit of fan-out 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: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 0 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 North-Holland, Inc. Bibliometrics: Citation Count: 0 We show that Level-ordered Q-resolution and Tree-like Q-resolution, two restrictions of the Q-resolution system for proving false QBFs false, are incomparable. While the � Exp + Res system is known to p-simulate Tree-like Q-resolution, we observe that it cannot p-simulate Level-ordered Q-resolution. We show that Level-ordered Q-resolution and Tree-like Q-resolution ... Keywords: Computational complexity, Quantified Boolean formulas (QBF), Proof complexity, Resolution 9 February 2016 Information Processing Letters: Volume 116 Issue 2, February 2016 Publisher: Elsevier North-Holland, Inc. Bibliometrics: Citation Count: 0 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 blow-up in size. In particular, multilinear-VNP equals multilinear-VP. 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. Bibliometrics: Citation Count: 1 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 read-twice or read-thrice 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. Bibliometrics: Citation Count: 0 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 read-twice or read-thrice 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: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 0 13 September 2013 Computational Complexity: Volume 22 Issue 3, September 2013 Publisher: Birkhauser Verlag Bibliometrics: Citation Count: 2 The class of polynomials computable by polynomial size log-depth 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: PDF 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 Bibliometrics: Citation Count: 2 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: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 0 We give a #NC 1 upper bound for the problem of counting accepting paths in any fixed visibly pushdown automaton. Our algorithm involves a non-trivial 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 ... 17 October 2012 Algorithmica - Special Issue: Computing and Combinatorics: Volume 64 Issue 2, October 2012 Publisher: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 0 We give a #NC 1 upper bound for the problem of counting accepting paths in any fixed visibly pushdown automaton. Our algorithm involves a non-trivial 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: Springer-Verlag Bibliometrics: Citation Count: 4 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 read-twice 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. Bibliometrics: Citation Count: 6 In the k-means 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: NP-hardness, Planar graphs, Clustering, k-means 20 February 2012 Theoretical Computer Science: Volume 417, February, 2012 Publisher: Elsevier Science Publishers Ltd. Bibliometrics: Citation Count: 1 The class NC^1 of problems solvable by bounded fan-in 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