Depth Lower Bounds for Monotone Semi-Unbounded Fan-in Circuits

Depth Lower Bounds for Monotone Semi-Unbounded Fan-in Circuits

The depth hierarchy results for monotone circuits of Raz and McKenzie [5] are extended to the case of monotone circuits of semiunbounded fan-in. It follows that the inclusions NC ⊆ SAC ⊆ AC are proper in the monotone setting, for every i ≥ 1. Mathematics Subject Classification. 68Q17, 68Q15.

Depth Lower Bounds for Monotone Semi-Unbounded Fan-in Cir uits

Depth Reduction for Circuits of Unbounded Fan-In

We prove that constant depth circuits of size n log O(1) n over the basis AND, OR, PARITY are no more powerful than circuits of this size with depth four. Similar techniques are used to obtain several other depth reduction theorems; in particular, we show every set in AC 0 can be recognized by a family of depththree threshold circuits of size n log O(1) n . The size bound n log O(1) n is optima...

Lower Bounds for Monotone Counting Circuits

A {+,×}-circuit counts a given multivariate polynomial f , if its values on 0-1 inputs are the same as those of f ; on other inputs the circuit may output arbitrary values. Such a circuit counts the number of monomials of f evaluated to 1 by a given 0-1 input vector (with multiplicities given by their coefficients). A circuit decides f if it has the same 0-1 roots as f . We first show that some...

Unambiguous Auxiliary Pushdown Automata and Semi-unbounded Fan-in Circuits

Notions of unambiguity for uniform circuits and AuxPDAs are studied and related to each other. In particular, a coincidence for counting and unambiguous versions of AuxPDAs and semi-unbounded fan-in circuits is shown. Moreover, an improved simulation of LOGUCFL (the class of languages logspace many-one reducible to unambiguous context-free languages) by unambiguous circuits and AuxPDAs is devel...