Hierarchies of Circuit Classes that are Closed Under Complement

Authors:
V Vinay
Affiliations:
-
Venue:
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Year:
1996

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Abstract

We examine three hierarchies of circuit classes and show they are closed under complementation. 1) The class of languages recognized by a family of polynomial size skew circuits with width O(w), are closed under complement. 2) The class of languages recognized by family of polynomial size circuits with width O(w) and polynomial tree-size, are closed under complement. 3) The class of languages recognized by a family of polynomial size, O(log (n)) depth, bounded AND fan-in with OR fan-in f (f is at least log (n)) circuits are closed under complement. These improve upon the results of (i) Immerman and Szelepcsenyi who show that NL is closed under complementation, and (ii) Borodin et al, who show that LOGCFL is closed under complement.