Abstract
We study the complexity of circuit-based combinatorial problems (e.g., the circuit value problem and the satisfiability problem) defined by boolean circuits w ith gates from an arbitrary finite base of boolean functions. Special cases have been investigated in the literature. We give a complete characterization of their complexity depending on the base . For example, for the satisfiability problem for boolean circuits with gates from we present a complete collection of (decidable) criteria which tell us for which this problem is in , is complete for , is complete for , is complete for , or is complete for . Our proofs make substantial use of the characterization of all closed classes of boolean functions given by E.L. POST already in the twenties.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.