A Polynomial-Time Construction of a Hitting Set for Read-once Branching Programs of Width 3

0367350 - ÚI 2022 RIV NL eng J - Článek v odborném periodiku
Šíma, Jiří - Žák, Stanislav
A Polynomial-Time Construction of a Hitting Set for Read-once Branching Programs of Width 3.
Fundamenta Informaticae. Roč. 184, č. 4 (2021), s. 307-354. ISSN 0169-2968. E-ISSN 1875-8681
Grant CEP: GA ČR GBP202/12/G061; GA ČR GAP202/10/1333
Institucionální podpora: RVO:67985807
Klíčová slova: derandomization * hitting set * read-once branching programs * bounded width * almost k-wise independent set
Obor OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impakt faktor: 1.166, rok: 2021
Způsob publikování: Omezený přístup
http://dx.doi.org/10.3233/FI-2021-2101

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.
Trvalý link: http://hdl.handle.net/11104/0202062