66 May 1999
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Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)
Publication Year: 1999 PDF (187 KB) 
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»

On the complexity of diophantine geometry in low dimensions
Publication Year: 1999
Cited by: Papers (1)We 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 f/sub 1/,...,f/sub m//spl isin/Z[x/sub 1/,...,x/sub n/] defining a variety of dimension /spl les/0 in C/sup n/, find all solutions in Z/sup n/ of f/sub 1/=/spl middot//spl middot//spl middot/=f/... View full abstract»

Pseudorandom generators without the XOR lemma
Publication Year: 1999
Cited by: Papers (29)  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»

Linear gaps between degrees for the polynomial calculus modulo distinct primes
Publication Year: 1999
Cited by: Papers (4)Two important algebraic proof systems are the Nullstellensatz system and the polynomial calculus (also called the Grobner system). The Nullstellensatz system is a propositional proof system based on Hilbert's Nullstellensatz, and the polynomial calculus (PC) is a proof system which allows derivations of polynomials, over some field. The complexity of a proof in these systems is measured in terms o... 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»

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 V/sub A/ and V/sub B/ of size n each. Player A is given a function f/sub A/: VA/spl rarr/VB and player B is given a function f/sub B/: VB/spl rarr/VA. In the problem g/sub k/ the players have to determine the vertex reached... 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»

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 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 AC/sup 0/. This provides a striking contrast to the nonplanar case, where exactly NC/sup 1/ is computed. We show that the circuit value problem for monotone planar circuits, with inputs on... 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 /spl epsiv/ 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... 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/sup (2/3)+/spl epsi// 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/sup (1/2)+/spl epsi// bits of an Nbit witness. These pursuits are motivated by the wo... 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 (24)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»

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»

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 w/sub 1//spl middot/w/sub 2//spl middot//spl middot//spl middot//spl middot//spl middot/w/sub k/=id where each w/sub i/ 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 ... 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»

Stronger separations for randomselfreducibility, rounds, and advice
Publication Year: 1999, Page(s):98  104
Cited by: Papers (2)A function f is selfreducible if it can be computed given an oracle for f. In a randomselfreduction the queries must be made in such a way that the distribution of the ith query is independent of the input that gave rise to it. Randomselfreductions have many applications, including countless cryptographic protocols, probabilistically checkable proofs, averagecase complexity, and program chec... 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 /spl Delta/ such that n points lying in the unit disc necessarily contain a triangle of area at most /spl Delta/. Heilbronn initially conjectured /spl Delta/=O(1/n/sup 2/). As a result of concerted mathematical effort it is currently known that there are positive constants c and C such that c log n/n/sup 2//spl les//spl Delta//spl les/C/n/sup 8/7/sp... View full abstract»

Upper semilattice of binary strings with the relation "x is simple conditional to y"
Publication Year: 1999, Page(s):114  122In this paper we construct a structure R that is a "finite version" of the semilattice of Turing degrees. Its elements are strings (technically, sequences of strings) and x/spl les/y means that K(x)=(conditional Kolmogorov complexity of x relative to y) is small. We construct two elements in R that do not have greatest lower bound. We give a series of examples that show how natural algebraic cons... 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/sub (m+1)tt//sup SAT/=P/sub mtt//sup SAT//spl rArr/P/sub btt//sup SAT/=P/sub mtt//sup SAT/ and for all sets A/spl middot/FP/sub (m=1)tt//sup A/=FP/sub mtt//sup A//spl rArr/FP/sub btt//sup A/=FP/sub mtt//sup A//spl middot/P/sub (m+1)T//sup A/=P/sub mT//sup A/=P/sub bT//sup A//s... 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/spl I.oarr/=(D/sub 1/,...,D/sub k/) of decision problems is defined to be sequentially complete for NP if each D/sub i//spl isin/NP and every problem in NP can be decided in polynomial time with one query to each of D/sub 1/,...,D/sub k/ in this order. It is shown that, if NP contains a language that is pgeneric in the sen... 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»

Some recent progress on the complexity of lattice problems
Publication Year: 1999, Page(s):158  178
Cited by: Papers (2)We survey some recent developments in the study of the complexity of lattice problems. After a discussion of some problems on lattices which can be algorithmically solved efficiently, our main focus is the recent progress on complexity results of intractability. We discuss Ajtai's worstcase/averagecase connections, NPhardness and nonNPhardness, transference theorems between primal and dual la... View full abstract»

Quantum simulations of classical random walks and undirected graph connectivity
Publication Year: 1999, Page(s):180  187
Cited by: Papers (2)  Patents (1)There are a number of questions in quantum complexity that have been resolved in the timebounded setting, but remain open in the spacebounded setting. For example, it is not currently known if spacebounded probabilistic computations can be simulated by spacebounded quantum machines without allowing measurements during the computation, while it is known that an analogous statement holds in the ... 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»