Succinct permanent is NEXP-hard with many hard instances (extended abstract)

Shlomi Dolev, Nova Fandina, Dan Gutfreund

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

The main motivation of this work is to study the average case hardness of the problems which belong to high complexity classes. In more detail, we are interested in provable hard problems which have a big set of hard instances. Moreover, we consider efficient generators of these hard instances of the problems. Our investigation has possible applications in cryptography. As a first step, we consider computational problems from the NEXP class. We extend techniques presented in [7] in order to develop efficient generation of hard instances of exponentially hard problems. Particularly, for any given polynomial time (deterministic/probabilistic) heuristic claiming to solve NEXP hard problem our procedure finds instances on which the heuristic errs. Then we present techniques for generating hard instances for (super polynomial but) sub exponential time heuristics. As a concrete example the Succinct Permanent problem is chosen. First, we prove the NEXP hardness of this problem (via randomized polynomial time reduction). Next, for any given polynomial time heuristic we construct hard instance. Finally, an efficient technique which expands one hard instance to exponential set (in the number of additional bits added to the found instance) of hard instances of the Succinct Permanent problem is provided.

Original languageEnglish
Title of host publicationAlgorithms and Complexity - 8th International Conference, CIAC 2013, Proceedings
Pages183-196
Number of pages14
DOIs
StatePublished - 9 Sep 2013
Event8th International Conference on Algorithms and Complexity, CIAC 2013 - Barcelona, Spain
Duration: 22 May 201324 May 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7878 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference8th International Conference on Algorithms and Complexity, CIAC 2013
Country/TerritorySpain
CityBarcelona
Period22/05/1324/05/13

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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