A Purely Logical Characterization of Circuit Uniformity
نویسنده
چکیده
Utilizing the connection between uniform constantdepth circuits and first-order logic with numerical predicates, we are able to provide a purely logical characterization of uniformity based on the intrinsic properties of these predicates. By requiring a numerical predicate R to satisfy a natural extensibility condition — that it can be translated to a polynomially magnified domain based on tuple constructions — we show that R must already be elementarily definable from < and bit (both of which satisfy the extensibility condition). Our answer is motivated by, and coincides with, DLOGTIME uniformity.
منابع مشابه
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