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A Polynomial-Time Construction of a Hitting Set for Read-once Branching Programs of Width 3
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SYSNO ASEP 0367350 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A Polynomial-Time Construction of a Hitting Set for Read-once Branching Programs of Width 3 Author(s) Šíma, Jiří (UIVT-O) RID, SAI, ORCID
Žák, Stanislav (UIVT-O) SAI, RIDSource Title Fundamenta Informaticae. - : IOS Press - ISSN 0169-2968
Roč. 184, č. 4 (2021), s. 307-354Number of pages 48 s. Publication form Print - P Language eng - English Country NL - Netherlands Keywords derandomization ; hitting set ; read-once branching programs ; bounded width ; almost k-wise independent set Subject RIV IN - Informatics, Computer Science OECD category Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) R&D Projects GBP202/12/G061 GA ČR - Czech Science Foundation (CSF) GAP202/10/1333 GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support UIVT-O - RVO:67985807 UT WOS 000768542000003 EID SCOPUS 85127188809 DOI https://doi.org/10.3233/FI-2021-2101 Annotation Recently, an interest in constructing pseudorandom or hitting set generators for restricted branching programs has increased, which is motivated by the fundamental issue of derandomizing space-bounded computations. Such constructions have been known only in the case of width 2 and in very restricted cases of bounded width. In this paper, we characterize the hitting sets for read-once branching programs of width 3 by a so-called richness condition. Namely, we show that such sets hit the class of read-once conjunctions of DNF and CNF (i.e. the weak richness). Moreover, we prove that any rich set extended with all strings within Hamming distance of 3 is a hitting set for read-once branching programs of width 3. Then, we show that any almost O(log n)-wise independent set satisfies the richness condition. By using such a set due to Alon et al. (1992) our result provides an explicit polynomial-time construction of a hitting set for read-once branching programs of width 3 with acceptance probability epsilon>5/6. We announced this result at conferences more than ten years ago, including only proof sketches, which motivated a number of subsequent results on pseudorandom generators for restricted read-once branching programs. This paper contains our original detailed proof that has not been published yet. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2022 Electronic address http://dx.doi.org/10.3233/FI-2021-2101
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