Affiliation:
1. IBM Research, San Jose, CA
2. Univ. of Michigan, Ann Arbor
Abstract
In connection with the least fixed point operator the following question was raised: Suppose that a first-order formula
P
(
P
) is (semantically) monotone in a predicate symbol
P
on finite structures. Is
P
(
P
) necessarily equivalent on finite structures to a first-order formula with only positive occurrences of
P
? In this paper, this question is answered negatively. Moreover, the counterexample naturally gives a uniform sequence of constant-depth, polynomial-size, monotone Boolean circuits that is not equivalent to any (however nonuniform) sequence of constant-depth, polynomial-size, positive Boolean circuits.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
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