47 July 2000
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Proceedings 15th Annual IEEE Conference on Computational Complexity
Publication Year: 2000 PDF (178 KB) 
Timespace tradeoffs for nondeterministic computation
Publication Year: 2000, Page(s):2  13
Cited by: Papers (11)We show new tradeoffs for satisfiability and nondeterministic linear time. Satisfiability cannot be solved on general purpose randomaccess Turing machines in time n/sup 1.618/ and space n/sup o(1)/. This improves recent results of Fortnow and of Lipton and Viglas. In general, for any constant a less than the golden ratio, we prove that satisfiability cannot be solved in time n/sup a/ and space n/... View full abstract»

A lower bound for the shortest path problem
Publication Year: 2000, Page(s):14  21
Cited by: Papers (1)We show that the shortest path problem cannot be solved in o(log n) time on an unbounded fanin PRAM without bit operations using poly(n) processors even when the bitlengths of the weights on the edges are restricted to be of size O(log/sup 3/ n). This shows that the matrixbased repeated squaring algorithm for the shortest path problem is optimal in the unbounded fanin PRAM model without bit op... View full abstract»

Timespace lower bounds for SAT on uniform and nonuniform machines
Publication Year: 2000, Page(s):22  33
Cited by: Papers (3)The arguments used by R. Kannan (1984), L. Fortnow (1997), and LiptonViglas (1999) are generalized and combined with a new argument for diagonalizing over machines taking n bits of advice on inputs of length n to obtain the first nontrivial timespace lower bounds for SAT on nonuniform machines. In particular we show that for any a </spl radic/2 and any b<1, SAT cannot be computed by a ran... View full abstract»

BP(f)=O(L(f)/sup 1+/spl epsi//)
Publication Year: 2000, Page(s):36  43Any B/sub 2/formula of size /spl Lscr/ can be transformed into a branching program of size O(e/spl Lscr//sup 1+/spl epsi//)for arbitrary E>0. The presented proof is based on a technique due to R. Cleve (1991) to simulate balanced algebraic formulas of size s by algebraic straightline programs that employ a constant number of registers and have length O(s/sup 1+/spl epsi//). The best previousl... View full abstract»

The communication complexity of enumeration, elimination, and selection
Publication Year: 2000, Page(s):44  53
Cited by: Papers (1)Let f:{0, 1}/sup n//spl times/{0, 1}/sup n//spl rarr/{0, 1}. Assume Alice has x/sub 1/, ..., x/sub k//spl isin/{0, 1}/sup n/, Bob has y/sub 1/, ..., y/sub k//spl isin/{0, 1}/sup n/, and they want to compute f(x/sub 1/, y/sub 1/)/spl middot//spl middot//spl middot/f(x/sub k/, y/sub k/) communicating as few bits as possible. The Direct Sum Conjecture of Karchmer, Raz, and Wigderson, states that the ... View full abstract»

The query complexity of orderfinding
Publication Year: 2000, Page(s):54  59
Cited by: Papers (2)We consider the problem where /spl pi/ is an unknown permutation on (0, 1,..., 2/sup n/1), /spl gamma//sub 0//spl isin/(0, 1,..., 2/sup n/1), and the goal is to determine the minimum r>0 such that /spl pi//sup r/(y/sub 0/)=y/sub 0/. Information about /spl pi/ is available only via queries that yield /spl pi//sup x/(y) from any x/spl isin/(0, 1,..., 2/sup n/1) and /spl gamma//sub /spl isin//(... View full abstract»

On the complexity of some problems on groups input as multiplication tables
Publication Year: 2000, Page(s):62  69
Cited by: Papers (1)The Cayley group membership problem (CGM) is to input a groupoid (binary algebra) G given as a multiplication table, a subset X of G, and an element t of G, and to determine whether t can be expressed as a product of elements of X. For general groupoids CGM is Pcomplete, and for associative algebras (semigroups) it is NLcomplete. Here we investigate CGM for particular classes of groups. The prob... View full abstract»

The complexity of tensor calculus
Publication Year: 2000, Page(s):70  86Tensor calculus over semirings is shown relevant to complexity theory in unexpected ways. First, evaluating well formed tensor formulas with explicit tensor entries is shown complete for /spl oplus/P, for NP, and for #P as the semiring varies. Indeed the permanent of a matrix is shown expressible as the value of a tensor formula in much the same way that Berkowitz' theorem expresses its determinan... View full abstract»

The complexity of verifying the characteristic polynomial and testing similarity
Publication Year: 2000, Page(s):87  95
Cited by: Papers (1)We investigate the computational complexity of some important problems in linear algebra. 1. The problem of verifying the characteristic polynomial of a matrix is known to be in the complexity class C/sub =/L (Exact Counting in Logspace). We show that it is complete for C/sub =/L under logspace manyone reductions. 2. The problem of deciding whether two matrices are similar is known to be in the c... View full abstract»

A dual version of Reimer's inequality and a proof of Rudich's conjecture
Publication Year: 2000, Page(s):98  103
Cited by: Papers (10)We prove a dual version of the celebrated inequality of D. Reimer (a.k.a. the van den BergKesten conjecture). We use the dual inequality to prove a combinatorial conjecture of S. Rudich motivated by questions in cryptographic complexity. One consequence of Rudich's Conjecture is that there is an oracle relative to which oneway functions exist but oneway permutations do not. The dual inequality ... View full abstract»

Computational complexity and phase transitions
Publication Year: 2000, Page(s):104  115
Cited by: Papers (3)Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been addressed in statistical mechanics and artificial intelligence, but not studied rigorously. We take a first step in this direction by investigating the existence of s... View full abstract»

An application of matroid theory to the SAT problem
Publication Year: 2000, Page(s):116  124
Cited by: Papers (22)We consider the deficiency /spl delta/(F):=c(F)n(F) and the maximal deficiency /spl delta/*(F):=max/sub F'/spl sube/F//sup /spl delta//(F) of a clauseset F (a conjunctive normal form), where c(F) is the number of clauses in F and n(F) is the number of variables. Combining ideas from matching and matroid theory with techniques from the area of resolution refutations, we prove that for clausesets... View full abstract»

New bounds for the language compression problem
Publication Year: 2000, Page(s):126  130
Cited by: Papers (5)The CD complexity of a string x is the length of the shortest polynomial time program which accepts only the string x. The language compression problem consists of giving an upper bound on the CD(A/sup /spl les/n/) complexity of all strings x in some set A. The best known upper bound for this problem is 2log(/spl par/A/sup /spl les/n//spl par/)+O(log(n)), due to Buhrman and Fortnow. We show that t... View full abstract»

Combinatorial interpretation of Kolmogorov complexity
Publication Year: 2000, Page(s):131  137
Cited by: Papers (1)The very first Kolmogorov's paper on algorithmic information theory was entitled "Three approaches to the definition of the quantity of information". These three approaches were called combinatorial, probabilistic and algorithmic. Trying to establish formal connections between combinatorial and algorithmic approaches, we prove that every linear inequality including Kolmogorov complexities could be... View full abstract»

Independent minimum length programs to translate between given strings
Publication Year: 2000, Page(s):138  144
Cited by: Papers (2)A string p is called a program to compute y given x if U(p, x)=y, where U denotes universal programming language. Kolmogorov complexity K(yz) of y relative to x is defined as minimum length of a program to compute y given x. Let K(x) denote K(xempty string) (Kolmogorov complexity of x) and let I(x: y)=K(x)+K(y)K(<x, y>) (the amount of mutual information in x, y). In the present paper we a... View full abstract»

A survey of optimal PCP characterizations of NP
Publication Year: 2000, Page(s):146  148Probabilistically checkable proofs (PCPs) define a model of computation that is quite interesting in its own right, and that is an extremely powerful tool to study the complexity of finding approximate solutions for combinatorial optimization. Since U. Feige et al. (1996) suggested a connection between proofchecking and approximation, this connection has been generalized and exploited to an amazi... View full abstract»

Easiness assumptions and hardness tests: trading time for zero error
Publication Year: 2000, Page(s):150  157
Cited by: Papers (6)We propose a new approach towards derandomization in the uniform setting, where it is computationally hard to find possible mistakes in the simulation of a given probabilistic algorithm. The approach consists in combining both easiness and hardness complexity assumptions: if a derandomization method based on an easiness assumption fails, then we obtain a certain hardness test that can be used to r... View full abstract»

Dimension in complexity classes
Publication Year: 2000, Page(s):158  169
Cited by: Papers (7)A theory of resourcebounded dimension is developed using gales, which are natural generalizations of martingales. When the resource bound /spl Delta/(a parameter of the theory) is unrestricted, the resulting dimension is precisely the classical Haludolff dimension (sometimes called "fractal dimension"). Other choices of the parameter /spl Delta/ yield internal dimension theories in E, E/sub 2/, ... View full abstract»

Average case complexity of unbounded fanin circuits
Publication Year: 2000, Page(s):170  185Several authors have shown that the PARITYfunction cannot be computed by unbounded fanin circuits of small depth and polynomial size. Even more, constant depth k circuits of size exp(n/sup /spl ominus/(1/k)/) give wrong results for PARITY for almost half of all inputs. We generalize these results in two directions. First, we obtain similar tight lower bounds for the average case complexity of cir... View full abstract»

On the hardness of 4coloring a 3collorable graph
Publication Year: 2000, Page(s):188  197
Cited by: Papers (7)We give a new proof showing that it is NPhard to color a 3colorable graph using just four colors. This result is already known, but our proof is novel as it does not rely on the PCP theorem. This highlights a qualitative difference between the known hardness result for coloring 3colorable graphs and the factor n/sup /spl epsiv// hardness for approximating the chromatic number of general graphs,... View full abstract»

Deciding the kdimension is PSPACEcomplete
Publication Year: 2000, Page(s):198  203N. Littlestone (1998) introduced the optimal mistakebound learning model to learning theory. In this model the difficulty of learning a concept from a concept class is measured by the Kdimension of the concept class, which is a purely combinatorial notion. This is similar to the situation in PAClearning, where the difficulty of learning can be measured by the VapnikCervonenkis dimension. We sh... View full abstract»

Integer circuit evaluation is PSPACEcomplete
Publication Year: 2000, Page(s):204  211
Cited by: Papers (1)In this paper, we address the problem of evaluating the integer circuit (IC), or the {U,/spl times/,+}circuit over the set of natural numbers. The problem is a natural extension to the integer expression by L.J. Stockmeyer and A.R. Mayer (1973); and is also studied by P. Mckenzie et al. (1999) in their "Polynomial Replacement System". We show a polynomialtime algorithm that reduces QBP (quantifi... View full abstract»

A separation of determinism, Las Vegas and nondeterminism for picture recognition
Publication Year: 2000, Page(s):214  228The investigation of the computational power of randomized computations is one of the central tasks of current complexity and algorithm theory. In this paper for the first time a "strong" separation between the power of determinism, Las Vegas randomization, and nondeterminism for a computing model is proved. The computing models considered here are finite automata with twodimensional input tapes ... View full abstract»

On the complexity of intersecting finite state automata
Publication Year: 2000, Page(s):229  234
Cited by: Papers (1)We consider the problem of testing whether the intersection of a collection of k automata is empty. The straightforward algorithm for solving this problem runs in time /spl sigma//sup k/ where a is the size of the automata. In this work we prove that the assumption that there exists a better algorithm solving the FSA intersection emptiness problem implies that nondeterministic time is in subexpone... View full abstract»