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January 2006
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140 Reads
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25 Citations
Proceedings of the Annual IEEE Conference on Computational Complexity
In this paper we prove that the class of functions expressible by first order formulas with only two variables coincides with the class of functions computable by AC0 circuits with a linear number of gates. We then investigate the feasibility of using Ehrenfeucht-Fraisse games to prove lower bounds for that class of circuits, as well as for general AC0 circuits
... In fact, our ability is so restricted that we cannot define more than a linear number of wires: 2 [reg]-this denotes that φ may have one free variable, and that it is x. The proof is done by induction on the structure of φ and follows the steps in the proof of [11,Theorem 2]. We will build a circuit C for φ(x) that has n inputs and n outputs (the output gates need not all be distinct). ...
January 2006
Proceedings of the Annual IEEE Conference on Computational Complexity
