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Papers by Anna Gal

Research paper thumbnail of Hadamard Tensors and Lower Bounds on Multiparty Communication Complexity

Research paper thumbnail of Boolean complexity classes vs. their arithmetic analogs

Random Structures and Algorithms, 1996

Page 1. Boolean complexity classes vs. their arithmetic analogs Anna Gál∗ Avi Wigderson† Abstract... more Page 1. Boolean complexity classes vs. their arithmetic analogs Anna Gál∗ Avi Wigderson† Abstract ... Pr[|MIN(F,w)| > 1] ≤ 1/k In this paper we need a version of the Isolation Lemma that holds for multisets as well, ie for sets possibly containing some elements with mul-tiplicities. ...

Research paper thumbnail of Hadamard Tensors and Lower Bounds on Multiparty Communication Complexity

Research paper thumbnail of The cell probe complexity of succinct data structures

Theoretical Computer Science, 2007

Research paper thumbnail of Superpolynomial Lower Bounds for Monotone Span Programs

Combinatorica, 1999

computing explicit functions. The best previous lower bound was by Beimel, Gál, Paterson [7]; our... more computing explicit functions. The best previous lower bound was by Beimel, Gál, Paterson [7]; our proof exploits a general combinatorial lower bound criterion from that paper. Our lower bounds are based on an analysis of Paley-type bipartite graphs via Weil's character sum estimates. We prove an lower bound for the size of monotone span programs for the clique problem. Our results give the first superpolynomial lower bounds for linear secret sharing schemes. We demonstrate the surprising power of monotone span programs by exhibiting a function computable in this model in linear size while requiring superpolynomial size monotone circuits and exponential size monotone formulae. We also show that the perfect matching function can be computed by polynomial size (non-monotone) span programs over arbitrary fields.

Research paper thumbnail of Boolean Complexity Classes vs. Their Arithmetic Analogs

Electronic Colloquium on Computational Complexity, 1995

Page 1. Boolean complexity classes vs. their arithmetic analogs Anna Gál∗ Avi Wigderson† Abstract... more Page 1. Boolean complexity classes vs. their arithmetic analogs Anna Gál∗ Avi Wigderson† Abstract ... Pr[|MIN(F,w)| > 1] ≤ 1/k In this paper we need a version of the Isolation Lemma that holds for multisets as well, ie for sets possibly containing some elements with mul-tiplicities. ...

Research paper thumbnail of A characterization of span program size and improved lower bounds for monotone span programs

Computational Complexity, 2001

Abstract. We give a characterization of span program size by a combinatorial-algebraic measure. T... more Abstract. We give a characterization of span program size by a combinatorial-algebraic measure. The measure we consider is a gen-eralization of a measure on covers which has been used to prove lower bounds on formula size and has also been studied with respect to ...

Research paper thumbnail of Extremal bipartite graphs and superpolynomial lower bounds for monotone span programs

... R6nyai, Szab6 on the Zarankiewicz problem [KRS], and a subsequent paper by Babai, Gil, and Wi... more ... R6nyai, Szab6 on the Zarankiewicz problem [KRS], and a subsequent paper by Babai, Gil, and Wigderson on span programs [BGW]. The ... mulae are well known (eg Razborov [Ral, Ra2, Ra3], Haken [Ha] for circuits, Karchmer-Wigderson [KW1], Raz-...

Research paper thumbnail of Combinatorial Methods In Boolean Function Complexity

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Chapter 1. INTRODUCTION... more . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Chapter 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1. Complexity of Boolean functions . . . . . . . . . . . . . . . . . . 1 1.1.1. The basic model: Boolean circuits . . . . . . . . . . . . . . 1 1.1.2. The complexity classes NC and AC . . . . . . ...

Research paper thumbnail of Communication Complexity of Simultaneous Messages

Siam Journal on Computing, 2003

Research paper thumbnail of The Cell Probe Complexity of Succinct Data Structures

Research paper thumbnail of Hadamard Tensors and Lower Bounds on Multiparty Communication Complexity

Research paper thumbnail of Boolean complexity classes vs. their arithmetic analogs

Random Structures and Algorithms, 1996

Page 1. Boolean complexity classes vs. their arithmetic analogs Anna Gál∗ Avi Wigderson† Abstract... more Page 1. Boolean complexity classes vs. their arithmetic analogs Anna Gál∗ Avi Wigderson† Abstract ... Pr[|MIN(F,w)| > 1] ≤ 1/k In this paper we need a version of the Isolation Lemma that holds for multisets as well, ie for sets possibly containing some elements with mul-tiplicities. ...

Research paper thumbnail of Hadamard Tensors and Lower Bounds on Multiparty Communication Complexity

Research paper thumbnail of The cell probe complexity of succinct data structures

Theoretical Computer Science, 2007

Research paper thumbnail of Superpolynomial Lower Bounds for Monotone Span Programs

Combinatorica, 1999

computing explicit functions. The best previous lower bound was by Beimel, Gál, Paterson [7]; our... more computing explicit functions. The best previous lower bound was by Beimel, Gál, Paterson [7]; our proof exploits a general combinatorial lower bound criterion from that paper. Our lower bounds are based on an analysis of Paley-type bipartite graphs via Weil's character sum estimates. We prove an lower bound for the size of monotone span programs for the clique problem. Our results give the first superpolynomial lower bounds for linear secret sharing schemes. We demonstrate the surprising power of monotone span programs by exhibiting a function computable in this model in linear size while requiring superpolynomial size monotone circuits and exponential size monotone formulae. We also show that the perfect matching function can be computed by polynomial size (non-monotone) span programs over arbitrary fields.

Research paper thumbnail of Boolean Complexity Classes vs. Their Arithmetic Analogs

Electronic Colloquium on Computational Complexity, 1995

Page 1. Boolean complexity classes vs. their arithmetic analogs Anna Gál∗ Avi Wigderson† Abstract... more Page 1. Boolean complexity classes vs. their arithmetic analogs Anna Gál∗ Avi Wigderson† Abstract ... Pr[|MIN(F,w)| > 1] ≤ 1/k In this paper we need a version of the Isolation Lemma that holds for multisets as well, ie for sets possibly containing some elements with mul-tiplicities. ...

Research paper thumbnail of A characterization of span program size and improved lower bounds for monotone span programs

Computational Complexity, 2001

Abstract. We give a characterization of span program size by a combinatorial-algebraic measure. T... more Abstract. We give a characterization of span program size by a combinatorial-algebraic measure. The measure we consider is a gen-eralization of a measure on covers which has been used to prove lower bounds on formula size and has also been studied with respect to ...

Research paper thumbnail of Extremal bipartite graphs and superpolynomial lower bounds for monotone span programs

... R6nyai, Szab6 on the Zarankiewicz problem [KRS], and a subsequent paper by Babai, Gil, and Wi... more ... R6nyai, Szab6 on the Zarankiewicz problem [KRS], and a subsequent paper by Babai, Gil, and Wigderson on span programs [BGW]. The ... mulae are well known (eg Razborov [Ral, Ra2, Ra3], Haken [Ha] for circuits, Karchmer-Wigderson [KW1], Raz-...

Research paper thumbnail of Combinatorial Methods In Boolean Function Complexity

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Chapter 1. INTRODUCTION... more . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Chapter 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1. Complexity of Boolean functions . . . . . . . . . . . . . . . . . . 1 1.1.1. The basic model: Boolean circuits . . . . . . . . . . . . . . 1 1.1.2. The complexity classes NC and AC . . . . . . ...

Research paper thumbnail of Communication Complexity of Simultaneous Messages

Siam Journal on Computing, 2003

Research paper thumbnail of The Cell Probe Complexity of Succinct Data Structures

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