Searching for authors named "Valentine Kabanets" – sorted by Relevance.
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Nonuniform Hard Boolean Functions and Uniform Complexity Classes
- …and Uniform Complexity Classes Valentine Kabanets Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2001 Uniform complexity classes are typically de ned in terms of resource-bounded Turing machines, while nonuniform complexity classes in terms of families of …
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Almost k-Wise Independence and Hard Boolean Functions
- …Andreev et al. [ABCR97] gave constructions of Boolean functions (computable by polynomialsize circuits) with large lower bounds for read-once branching program (1-b.p.'s): a function in P with the lower bound 2 n\Gammapolylog(n) , a function in quasipolynomial time with the lower bound 2 n\Gam…
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Easiness Assumptions and Hardness Tests: Trading Time for Zero Error
- …We propose a new approach towards derandomization in the uniform setting, where it is computationally hard to nd possible mistakes in the simulation of a given probabilistic algorithm. The approach consists in combining both easiness and hardness complexity assumptions: if a derandomization metho…
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Hardness amplification via space-efficient direct products
- …Abstract. We prove a version of the derandomized Direct Product lemma for deterministic space-bounded algorithms. Suppose a Boolean function g: {0, 1} n → {0, 1} cannot be computed on more than a fraction 1 − δ of inputs by any deterministic time T and space S algorithm, where δ � 1/t for some t. Th…
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Uniform hardness amplification in NP via monotone codes. ECCC
- …We consider the problem of amplifying uniform average-case hardness of languages in NP, where hardness is with respect to BPP algorithms. We introduce the notion of monotone errorcorrecting codes, and show that hardness amplification for NP is essentially equivalent to constructing efficiently local…
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Circuit Minimization Problem
- …We study the complexity of the circuit minimization problem: given the truth table of a Boolean function f and a parameter s, decide whether f can be realized by a Boolean circuit of size at most s. We argue why this problem is unlikely to be in P (or even in P=poly) by giving a number of surpris…
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Abstract
- …For any given Boolean formula φ(x1,..., xn), one can efficiently construct (using arithmetization) a low-degree polynomial p(x1,..., xn) that agrees with φ over all points in the Boolean cube {0, 1} n; the constructed polynomial p can be interpreted as a polynomial over an arbitrary field F. The pro…
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On the complexity of succinct zero-sum games
- …We study the complexity of solving succinct zero-sum games, i.e., the games whose payoff matrix M is given implicitly by a Boolean circuit C such that M(i, j) = C(i, j). We complement the known EXP-hardness of computing the exact value of a succinct zero-sum game by several results on approximating…
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In Search of an Easy Witness: Exponential Time vs. Probabilistic Polynomial Time
- …Restricting the search space f0; 1g to the set of truth tables of "easy" Boolean functions on log n variables, as well as using some known hardness-randomness tradeoffs, we establish a number of results relating the complexity of exponential-time and probabilistic polynomialtime complexity cla…
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Approximately list-decoding direct product codes and uniform hardness amplification
- …We consider the problem of approximately locally listdecoding direct product codes. For a parameter k, the kwise direct product encoding of an N-bit message msg is an N k-length string over the alphabet {0, 1} k indexed by ktuples (i1,..., ik) ∈ {1,..., N} k so that the symbol at position (i1,..., …
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