eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-08-29
20:1
20:16
10.4230/LIPIcs.CSL.2018.20
article
Symmetric Circuits for Rank Logic
Dawar, Anuj
1
https://orcid.org/0000-0003-4014-8248
Wilsenach, Gregory
1
Department of Computer Science and Technology, University of Cambridge, UK
Fixed-point logic with rank (FPR) is an extension of fixed-point logic with counting (FPC) with operators for computing the rank of a matrix over a finite field. The expressive power of FPR properly extends that of FPC and is contained in P, but it is not known if that containment is proper. We give a circuit characterization for FPR in terms of families of symmetric circuits with rank gates, along the lines of that for FPC given by [Anderson and Dawar 2017]. This requires the development of a broad framework of circuits in which the individual gates compute functions that are not symmetric (i.e., invariant under all permutations of their inputs). This framework also necessitates the development of novel techniques to prove the equivalence of circuits and logic. Both the framework and the techniques are of greater generality than the main result.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol119-csl2018/LIPIcs.CSL.2018.20/LIPIcs.CSL.2018.20.pdf
fixed-point logic with rank
circuits
symmetric circuits
uniform families of circuits
circuit characterization
circuit framework
finite model theory
descriptive complexity