Abstract
We define the counting classes NC/sup 1/, GapNC/sup 1/ PNC/sup 1/ and C/sub =/NC/sup 1/. We prove that Boolean circuits, algebraic circuits, programs over nondeterministic finite automata, and programs over constant integer matrices yield equivalent definitions of the latter three classes. We investigate closure properties. We observe that NC/sup 1//spl sube/L and that C/sub =/NC/sup 1//spl sube/L. Then we exploit our finite automaton model and extend the padding techniques used to investigate leaf languages. Finally, we draw some consequences from the resulting body of leaf language characterizations of complexity classes, including the unconditional separation of ACC/sup 0/ from MOD-PH as well as that of TC/sup 0/ from the counting hierarchy. Moreover we obtain that dlogtime-uniformity and logspace-uniformity for AC/sup 0/ coincide if and only if the polynomial time hierarchy equals PSPACE.
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