Proceedings 15th Annual IEEE Conference on Computational Complexity

4-7 July 2000

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  • Proceedings 15th Annual IEEE Conference on Computational Complexity

    Publication Year: 2000
    Request permission for commercial reuse | PDF file iconPDF (178 KB)
    Freely Available from IEEE
  • The complexity of tensor calculus

    Publication Year: 2000, Page(s):70 - 86
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (495 KB)

    Tensor 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»

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  • Average case complexity of unbounded fanin circuits

    Publication Year: 2000, Page(s):170 - 185
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (537 KB)

    Several authors have shown that the PARITY-function 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»

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  • Author index

    Publication Year: 2000, Page(s): 279
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    Freely Available from IEEE
  • On the complexity of intersecting finite state automata

    Publication Year: 2000, Page(s):229 - 234
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (224 KB)

    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 σk 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 subexpon... View full abstract»

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  • A separation of determinism, Las Vegas and nondeterminism for picture recognition

    Publication Year: 2000, Page(s):214 - 228
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (444 KB)

    The 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 two-dimensional ... View full abstract»

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  • Integer circuit evaluation is PSPACE-complete

    Publication Year: 2000, Page(s):204 - 211
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (300 KB)

    In this paper, we address the problem of evaluating the integer circuit (IC), or the {U,×,+}-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 polynomial-time algorithm that reduces QBP (... View full abstract»

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  • BP(f)=O(L(f)1+ε)

    Publication Year: 2000, Page(s):36 - 43
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (276 KB)

    Any B2-formula of size L can be transformed into a branching program of size O(eL1+ε)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 straight-line programs that employ a constant number of registers and have length O(s1+ε). The best previously known sim... View full abstract»

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  • Deciding the k-dimension is PSPACE-complete

    Publication Year: 2000, Page(s):198 - 203
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (256 KB)

    N. Littlestone (1998) introduced the optimal mistake-bound learning model to learning theory. In this model the difficulty of learning a concept from a concept class is measured by the K-dimension of the concept class, which is a purely combinatorial notion. This is similar to the situation in PAC-learning, where the difficulty of learning can be measured by the Vapnik-Cervonenkis dimension. We sh... View full abstract»

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  • Time-space lower bounds for SAT on uniform and non-uniform machines

    Publication Year: 2000, Page(s):22 - 33
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (412 KB)

    The arguments used by R. Kannan (1984), L. Fortnow (1997), and Lipton-Viglas (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 time-space lower bounds for SAT on non-uniform machines. In particular we show that for any a <√2 and any b<1, SAT cannot be computed by a random-... View full abstract»

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  • On the hardness of 4-coloring a 3-collorable graph

    Publication Year: 2000, Page(s):188 - 197
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (284 KB)

    We give a new proof showing that it is NP-hard to color a 3-colorable 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 3-colorable graphs and the factor nε hardness for approximating the chromatic number of general graphs,... View full abstract»

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  • A dual version of Reimer's inequality and a proof of Rudich's conjecture

    Publication Year: 2000, Page(s):98 - 103
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (196 KB)

    We prove a dual version of the celebrated inequality of D. Reimer (a.k.a. the van den Berg-Kesten 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 one-way functions exist but one-way permutations do not. The dual inequality ... View full abstract»

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  • A survey of optimal PCP characterizations of NP

    Publication Year: 2000, Page(s):146 - 148
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (156 KB)

    Probabilistically 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 proof-checking and approximation, this connection has been generalized and exploited to an amazi... View full abstract»

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  • A lower bound for the shortest path problem

    Publication Year: 2000, Page(s):14 - 21
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (280 KB)

    We show that the shortest path problem cannot be solved in o(log n) time on an unbounded fan-in PRAM without bit operations using poly(n) processors even when the bit-lengths of the weights on the edges are restricted to be of size O(log3 n). This shows that the matrix-based repeated squaring algorithm for the shortest path problem is optimal in the unbounded fan-in PRAM model without b... View full abstract»

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  • Combinatorial interpretation of Kolmogorov complexity

    Publication Year: 2000, Page(s):131 - 137
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (268 KB)

    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 complexit... View full abstract»

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  • Characterization of non-deterministic quantum query and quantum communication complexity

    Publication Year: 2000, Page(s):271 - 278
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (312 KB)

    It is known that the classical and quantum query complexities of a total Boolean function f are polynomially related to the degree of its representing polynomial, but the optimal exponents in these relations are unknown. We show that the non-deterministic quantum query complexity of f is linearly related to the degree of a “non-deterministic” polynomial for f. We also prove a quantum-c... View full abstract»

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  • On the complexity of the monotonicity verification

    Publication Year: 2000, Page(s):235 - 238
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (236 KB)

    We present a sequence {Sn} of circuits of functional elements that check the monotonicity of input discrete functions depending on n variables and represented as value column vectors. The complexity of circuits equals O(N√log log N). This is the lowest asymptotical current complexity View full abstract»

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  • The communication complexity of enumeration, elimination, and selection

    Publication Year: 2000, Page(s):44 - 53
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (436 KB)

    Let f:{0, 1}n×{0, 1}n→{0, 1}. Assume Alice has x1, ..., xk∈{0, 1}n , Bob has y1, ..., yk∈{0, 1}n, and they want to compute f(x1, y1)···f(xk, yk) communicating as few bits as possible. The Direct Sum Conjecture of Karchmer, Raz... View full abstract»

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  • Computational complexity and phase transitions

    Publication Year: 2000, Page(s):104 - 115
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (380 KB)

    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 ex... View full abstract»

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  • Easiness assumptions and hardness tests: trading time for zero error

    Publication Year: 2000, Page(s):150 - 157
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (268 KB)

    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»

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  • The complexity of verifying the characteristic polynomial and testing similarity

    Publication Year: 2000, Page(s):87 - 95
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (320 KB)

    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=L (Exact Counting in Logspace). We show that it is complete for C=L under logspace many-one reductions. 2. The problem of deciding whether two matrices are similar is known to b... View full abstract»

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  • Independent minimum length programs to translate between given strings

    Publication Year: 2000, Page(s):138 - 144
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (260 KB)

    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(y|z) of y relative to x is defined as minimum length of a program to compute y given x. Let K(x) denote K(x|empty 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 ... View full abstract»

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  • Quantum Kolmogorov complexity

    Publication Year: 2000, Page(s):240 - 249
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (328 KB)

    In this paper we give a definition for quantum Kolmogorov complexity. In the classical setting, the Kolmogorov complexity of a string is the length of the shortest program that can produce this string as its output. It is a measure of the amount of innate randomness (or information) contained in the string. We define the quantum Kolmogorov complexity of a qubit string as the length of the shortest... View full abstract»

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  • The query complexity of order-finding

    Publication Year: 2000, Page(s):54 - 59
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (240 KB)

    We consider the problem where π is an unknown permutation on (0, 1,..., 2n-1), γ0∈(0, 1,..., 2n -1), and the goal is to determine the minimum r>0 such that πr(y0)=y0. Information about π is available only via queries that yield πx(y) from any x∈(0, 1,..., 2n-1) and γ&is... View full abstract»

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  • Time-space tradeoffs for nondeterministic computation

    Publication Year: 2000, Page(s):2 - 13
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (344 KB)

    We show new tradeoffs for satisfiability and nondeterministic linear time. Satisfiability cannot be solved on general purpose random-access Turing machines in time n1.618 and space no(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 na View full abstract»

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