Conference on Computational Complexity 

About: Conference on Computational Complexity is an academic conference. The conference publishes majorly in the area(s): Control theory & Upper and lower bounds. Over the lifetime, 1659 publications have been published by the conference receiving 24878 citations.

On the complexity of K -SAT

Abstract: The k-SAT problem is to determine if a given k-CNF has a satisfying assignment It is a celebrated open question as to whether it requires exponential time to solve k-SAT for k?3 Here exponential time means 2?n for some ?>0 In this paper, assuming that, for k?3, k-SAT requires exponential time complexity, we show that the complexity of k-SAT increases as k increases More precisely, for k?3, define sk=inf{?:there exists 2?n algorithm for solving k-SAT} Define ETH (Exponential-Time Hypothesis) for k-SAT as follows: for k?3, sk>0 In this paper, we show that sk is increasing infinitely often assuming ETH for k-SAT Let s∞ be the limit of sk We will in fact show that sk?(1?d/k)s∞ for some constant d>0 We prove this result by bringing together the ideas of critical clauses and the Sparsification Lemma to reduce the satisfiability of a k-CNF to the satisfiability of a disjunction of 2?nk?-CNFs in fewer variables for some k??k and arbitrarily small ?>0 We also show that such a disjunction can be computed in time 2?n for arbitrarily small ?>0

Pseudorandom generators without the XOR lemma

Abstract: 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 generators. The construction of Impagliazzo and Wigderson goes through three phases of "hardness amplification" (a multivariate polynomial encoding, a first derandomized XOR Lemma, and a second derandomized XOR Lemma) that are composed with the Nisan-Wigderson (1994) generator. In this paper we present two different approaches to proving the main result of Impagliazzo and Wigderson. In developing each approach, we introduce new techniques and prove new results that could be useful in future improvements and/or applications of hardness-randomness trade-offs.

Consequences and limits of nonlocal strategies

Abstract: This paper investigates various aspects of the nonlocal effects that can arise when entangled quantum information is shared between two parties. A natural framework for studying nonlocality is that of cooperative games with incomplete information, where two cooperating players may share entanglement. Here, nonlocality can be quantified in terms of the values of such games. We review some examples of non-locality and show that it can profoundly affect the soundness of two-prover interactive proof systems. We then establish limits on nonlocal behavior by upper-bounding the values of several of these games. These upper bounds can be regarded as generalizations of the so-called Tsirelson inequality. We also investigate the amount of entanglement required by optimal and nearly optimal quantum strategies.

Complexity of k-SAT

Abstract: The problem of k-SAT is to determine if the given k-CNF has a satisfying solution. It is a celebrated open question as to whether it requires exponential time to solve k-SAT for k/spl ges/3. Define s/sub k/ (for k/spl ges/3) to be the infimum of {/spl delta/: there exists an O(2/sup /spl delta/n/) algorithm for solving k-SAT}. Define ETH (Exponential-Time Hypothesis) for k-SAT as follows: for k/spl ges/3, s/sub k/>0. In other words, for k/spl ges/3, k-SA does not have a subexponential-time algorithm. In this paper we show that s/sub k/ is an increasing sequence assuming ETH for k-SAT: Let s/sub /spl infin// be the limit of s/sub k/. We in fact show that s/sub k//spl les/(1-d/k) s/sub /spl infin// for some constant d>0.

The Learning with Errors Problem (Invited Survey)

Abstract: In this survey we describe the Learning with Errors (LWE) problem, discuss its properties, its hardness, and its cryptographic applications.