NDLI: On Symmetric Circuits and Fixed-Point Logics

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On Symmetric Circuits and Fixed-Point Logics

Content Provider	Springer Nature Link
Author	Anderson, Matthew Dawar, Anuj
Copyright Year	2016
Abstract	We study properties of relational structures, such as graphs, that are decided by families of Boolean circuits. Circuits that decide such properties are necessarily invariant to permutations of the elements of the input structures. We focus on families of circuits that are symmetric, i.e., circuits whose invariance is witnessed by automorphisms of the circuit induced by the permutation of the input structure. We show that the expressive power of such families is closely tied to definability in logic. In particular, we show that the queries defined on structures by uniform families of symmetric Boolean circuits with majority gates are exactly those definable in fixed-point logic with counting. This shows that inexpressibility results in the latter logic lead to lower bounds against polynomial-size families of symmetric circuits.
Starting Page	521
Ending Page	551
Page Count	31
File Format	PDF
ISSN	14324350
Journal	Theory of Computing Systems
Volume Number	60
Issue Number	3
e-ISSN	14330490
Language	English
Publisher	Springer US
Publisher Date	2016-07-13
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Symmetric circuit Fixed-point logic Majority Counting Uniformity Theory of Computation Computational Mathematics and Numerical Analysis
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics

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