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
  • 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 (339 KB)

    We show new tradeoffs for satisfiability and nondeterministic linear time. Satisfiability cannot be solved on general purpose random-access 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»

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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 (272 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(log/sup 3/ 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 bit op... 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 (405 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 </spl radic/2 and any b<1, SAT cannot be computed by a ran... View full abstract»

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  • BP(f)=O(L(f)/sup 1+/spl epsi//)

    Publication Year: 2000, Page(s):36 - 43
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (269 KB)

    Any 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 straight-line programs that employ a constant number of registers and have length O(s/sup 1+/spl epsi//). The best previousl... 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 (431 KB)

    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»

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  • The query complexity of order-finding

    Publication Year: 2000, Page(s):54 - 59
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (232 KB)

    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»

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  • On the complexity of some problems on groups input as multiplication tables

    Publication Year: 2000, Page(s):62 - 69
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (245 KB)

    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 P-complete, and for associative algebras (semigroups) it is NL-complete. Here we investigate CGM for particular classes of groups. The prob... View full abstract»

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  • 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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  • 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 (314 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/sub =/L (Exact Counting in Logspace). We show that it is complete for C/sub =/L under logspace many-one reductions. 2. The problem of deciding whether two matrices are similar is known to be in the c... 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 (190 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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  • 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 (375 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 existence of s... View full abstract»

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  • An application of matroid theory to the SAT problem

    Publication Year: 2000, Page(s):116 - 124
    Cited by:  Papers (20)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (308 KB)

    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 clause-set 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 clause-sets... View full abstract»

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  • New bounds for the language compression problem

    Publication Year: 2000, Page(s):126 - 130
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (215 KB)

    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»

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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 (263 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 complexities could be... 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 (254 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 we a... 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 (149 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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  • 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 (262 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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  • Dimension in complexity classes

    Publication Year: 2000, Page(s):158 - 169
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (384 KB)

    A theory of resource-bounded dimension is developed using gales, which are natural generalizations of martin-gales. 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»

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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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  • 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 (277 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 n/sup /spl epsiv// hardness for approximating the chromatic number of general graphs,... 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 (251 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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  • 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 (295 KB)

    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 polynomial-time algorithm that reduces QBP (quantifi... 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 (436 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 input tapes ... View full abstract»

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  • 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 (219 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 /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»

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