The Complexity of Deciding if a Boolean Function Can Be Computed by Circuits over a Restricted Basis

We study the complexity of the following algorithmic problem: Given a Boolean function f and a finite set of Boolean functions B , decide if there is a circuit with basis B that computes  f . We show that if both f and all functions in B are given by their truth-table, the problem is in quasipolynom...

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Vydáno v:Theory of computing systems Ročník 44; číslo 1; s. 82 - 90
Hlavní autor: Vollmer, Heribert
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer-Verlag 01.01.2009
Springer Nature B.V
Témata:
Algebra
Algorithms
Boolean
Circuits
Codes
Computer Science
Mathematical analysis
Studies
Theory of Computation
Post’s lattice
Membership problem
Clones
Boolean circuit
Computational complexity
ISSN:1432-4350, 1433-0490
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Popis
Shrnutí:We study the complexity of the following algorithmic problem: Given a Boolean function f and a finite set of Boolean functions B , decide if there is a circuit with basis B that computes  f . We show that if both f and all functions in B are given by their truth-table, the problem is in quasipolynomial-size AC 0 , and thus cannot be hard for AC 0 (2) or any superclass like NC 1 , L, or NL. This answers an open question by Bergman and Slutzki (SIAM J. Comput., 2000 ). Furthermore we show that, if the input functions are not given by their truth-table but in a succinct way, i.e., by circuits (over any complete basis), the above problem becomes complete for the class coNP.
Bibliografie:SourceType-Scholarly Journals-1
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-007-9030-9