66 May 1999
Filter Results

Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)
Publication Year: 1999 PDF (187 KB) 
Pseudorandom generators without the XOR lemma
Publication Year: 1999
Cited by: Papers (28)  Patents (1)Summary form only given. R. Impagliazzo and A. Wigderson (1997) have recently shown that if there exists a decision problem solvable in time 2/sup O(n)/ and having circuit complexity 2/sup /spl Omega/(n)/ (for all but finitely many n) then P=BPP. This result is a culmination of a series of works showing connections between the existence of hard predicates and the existence of good pseudorandom gen... View full abstract»

Graph Ramsey theory and the polynomial hierarchy
Publication Year: 1999
Cited by: Papers (1)Summary form only given, as follows. In the Ramsey theory of graphs F/spl rarr/(G, H) means that for every way of coloring the edges of F red and blue F will contain either a red G or a blue H as a subgraph. The problem ARROWING of deciding whether F/spl rarr/(G, H) lies in /spl Pi//sub 2//sup P/=coNP/sup NP/ and it was shown to be coNPhard by S.A. Burr (1990). We prove that ARROWING is actually ... View full abstract»

Author index
Publication Year: 1999, Page(s): 241 PDF (92 KB) 
Nonautomatizability of boundeddepth Frege proofs
Publication Year: 1999, Page(s):15  23
Cited by: Papers (5)In this paper; we show how to extend the argument due to Bonet, Pitassi and Raz to show that boundeddepth Frege proofs do not have feasible interpolation, assuming that factoring of Blum integers or computing the DiffieHellman function is sufficiently hard. It follows as a corollary that boundeddepth Frege is not automatizable; in other words, there is no deterministic polynomialtime algorithm... View full abstract»

On the complexity of diophantine geometry in low dimensions
Publication Year: 1999We consider the averagecase complexity of some otherwise undecidable or open Diophantine problems. More precisely, we show that the following two problems can be solved within PSPACE: I. Given polynomials f1,…,fm∈Z[x1 ,…,xn] defining a variety of dimension ⩽0 in Cn, find all solutions in Z
View full abstract» 
Proofs, codes, and polynomialtime reducibilities
Publication Year: 1999, Page(s):46  53
Cited by: Papers (4)We show how to construct proof systems for NP languages where a deterministic polynomialtime verifier can check membership, given any N (2/3)+ε bits of an Nbit witness of membership. We also provide a slightly superpolynomial time proof system where the verifier can check membership, given only N(1/2)+ε bits of an Nbit witness. These pursuits are motivated by the... View full abstract»

Query order and NPcompleteness
Publication Year: 1999, Page(s):142  148
Cited by: Papers (1)The effect of query order on NPcompleteness is investigated. A sequence D&oarr;=(D1,…,Dk) of decision problems is defined to be sequentially complete for NP if each Di ∈NP and every problem in NP can be decided in polynomial time with one query to each of D1,…,Dk in this order. It is shown that, if NP contains a language th... View full abstract»

Circuit lower bounds collapse relativized complexity classes
Publication Year: 1999, Page(s):222  226Since the publication of M. Furst et al. (1984) seminal paper connecting AC0 with the polynomial hierarchy, it has been well known that circuit lower bounds allow you to construct oracles that separate complexity classes. We show that similar circuit lower bounds allow you to construct oracles that collapse complexity classes. For example, based on Hastad's parity lower bound, we constr... View full abstract»

A lower bound for primality
Publication Year: 1999, Page(s):10  14Recent work by Bernasconi, Damm and Shparlinski proved lower bounds on the circuit complexity of the squarefree numbers, and raised as an open question if similar (or stronger) lower bounds could be proved for the set of prime numbers. In this short note, we answer this question affirmatively, by showing that the set of prime numbers (represented in the usual binary notation) is not contained in ... View full abstract»

Short proofs are narrowresolution made simple
Publication Year: 1999
Cited by: Papers (10)We develop a general strategy for proving width lower bounds, which follows Haken's original proof technique but is now simple and clear. It reveals that large width is implied by certain natural expansion properties of the clauses (axioms) of the tautology in question. We show that in the classical examples of the Pigeonhole principle, Tseitin graph tautologies, and random kCNFs, these expansion... View full abstract»

Computing from partial solutions
Publication Year: 1999, Page(s):34  45
Cited by: Papers (4)We consider the question: Is finding just a part of a solution easier than finding the full solution? For example, is finding only an ε fraction of the bits in a satisfying assignment to a 3CNF formula easier than computing the whole assignment? For several important problems in NP we show that obtaining only a small fraction of the solution is as hard as finding the full solution. This can ... View full abstract»

Derandomizing BPP: the state of the art
Publication Year: 1999, Page(s):76  77The introduction of randomization into efficient computation has been one of the most fertile and useful ideas in computer science. In cryptography and asynchronous computing, randomization makes possible tasks that are impossible to perform deterministically. Even for function computation, many examples are known in which randomization allows considerable savings in resources like space and time ... View full abstract»

Complexity of kSAT
Publication Year: 1999, Page(s):237  240
Cited by: Papers (12)The problem of kSAT is to determine if the given kCNF has a satisfying solution. It is a celebrated open question as to whether it requires exponential time to solve kSAT for k⩾3. Define sk (for k⩾3) to be the infimum of {δ: there exists an O(2 δn) algorithm for solving kSAT}. Define ETH (ExponentialTime Hypothesis) for kSAT as follows: for k⩾3,... View full abstract»

The complexity of solving equations over finite groups
Publication Year: 1999, Page(s):80  86
Cited by: Papers (5)We study the computational complexity of solving systems of equations over a finite group. An equation over a group G is an expression of the form w1·w2 ·····wk=id where each wi is either a variable, an inverted variable, or group constant and id is the identity element of G. A solution to such an equation is an ... View full abstract»

Gaps in bounded query hierarchies
Publication Year: 1999, Page(s):124  141Prior results show that most bounded query hierarchies cannot contain finite gaps. For example, it is known that P(m+1)tt SAT=PmttSAT⇒Pbtt SAT=PmttSAT and for all sets A·FP(m=1)ttA=FPmttA ⇒FPbttA=FPmttA View full abstract»

The expected size of Heilbronn's triangles
Publication Year: 1999, Page(s):105  113
Cited by: Papers (1)Heilbronn's triangle problem asks for the least Δ such that n points lying in the unit disc necessarily contain a triangle of area at most Δ. Heilbronn initially conjectured Δ=O(1/n2 ). As a result of concerted mathematical effort it is currently known that there are positive constants c and C such that c log n/n2⩽Δ⩽C/n8/7ε for... View full abstract»

Learning DNF by approximating inclusionexclusion formulae
Publication Year: 1999, Page(s):215  220
Cited by: Papers (3)We analyze upper and lower bounds on size of Boolean conjunctions necessary and sufficient to approximate a given DNF formula by accuracy slightly better than 1/2 (here we define the size of a Boolean conjunction as the number of distinct variables on which it depends). Such an analysis determines the performance of a naive search algorithm that exhausts Boolean conjunctions in the order of their ... View full abstract»

The communication complexity of pointer chasing. Applications of entropy and sampling
Publication Year: 1999
Cited by: Papers (1)The following pointer chasing problem plays a central role in the study of bounded round communication complexity. There are two players A and B. There are two sets of vertices VA and VB of size n each. Player A is given a function fA: VA→VB and player B is given a function fB: VB→VA. In the problem g k the players have to determine ... View full abstract»

Deterministic amplification of spacebounded probabilistic algorithms
Publication Year: 1999, Page(s):188  198
Cited by: Papers (2)This paper initiates the study of deterministic amplification of spacebounded probabilistic algorithms. The straightforward implementations of known amplification methods cannot be used for such algorithms, since they consume too much space. We present a new implementation of the AjtaiKomlosSzemeredi method, that enables to amplify an Sspace algorithm that uses r random bits and errs with prob... View full abstract»

On monotone planar circuits
Publication Year: 1999, Page(s):24  31
Cited by: Papers (6)In this paper we show several results about monotone planar circuits. We show that monotone planar circuits of bounded width, with access to negated input variables, compute exactly the functions in nonuniform AC0. This provides a striking contrast to the nonplanar case, where exactly NC1 is computed. We show that the circuit value problem for monotone planar circuits, with... View full abstract»

Comparing entropies in statistical zero knowledge with applications to the structure of SZK
Publication Year: 1999, Page(s):54  73
Cited by: Papers (12)We consider the following (promise) problem, denoted ED (for Entropy Difference): The input is a pair of circuits, and YES instances (resp., NO instances) are such pairs in which the first (resp., second) circuit generates a distribution with noticeably higher entropy. On one hand we show that any language having a (honestverifier) statistical zeroknowledge proof is Karpreducible to ED. On the ... View full abstract»

Quantum bounded query complexity
Publication Year: 1999, Page(s):149  156We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query, complexity of decision problems. Under traditional complexity assumptions, we obtain an exponential speedup between the quantum and the classical query complexity of function clas... View full abstract»

Complicated complementations
Publication Year: 1999, Page(s):227  236Kolmogorov complexity has proven to be a very useful tool in simplifying and improving proofs that use complicated combinatorial arguments. Using Kolmogorov complexity for oracle construction, we obtain separation results that are much stronger than separations obtained previously even with the use of very complicated combinatorial arguments. Moreover the use of Kolmogorov arguments almost trivial... View full abstract»

Depth3 arithmetic formulae over fields of characteristic zero
Publication Year: 1999, Page(s):87  96
Cited by: Papers (4)In this paper we prove near quadratic lower bounds for depth3 arithmetic formulae over fields of characteristic zero. Such bounds are obtained for the elementary symmetric functions, the (trace of) iterated matrix multiplication, and the determinant. As corollaries we get the first nontrivial lower bounds for computing polynomials of constant degree, and a gap between the power depth3 arithmeti... View full abstract»