$n$-permutability and linear Datalog implies symmetric Datalog

TL;DR

The paper proves that for certain relational structures, if their CSP is solvable by linear Datalog and they are n-permutable, then the CSP is also solvable by symmetric Datalog, placing it in deterministic logspace.

Contribution

It establishes that n-permutability combined with linear Datalog solvability implies symmetric Datalog solvability for CSPs.

Findings

CSPs with n-permutable structures solvable by linear Datalog are also solvable by symmetric Datalog.

Such CSPs are in deterministic logspace.

The result links linear and symmetric Datalog through algebraic properties.

Abstract

We show that if $\mathbb A$ is a core relational structure such that CSP($\mathbb A$) can be solved by a linear Datalog program, and $\mathbb A$ is $n$-permutable for some $n$, then CSP($\mathbb A$) can be solved by a symmetric Datalog program (and thus CSP($\mathbb A$) lies in deterministic logspace). At the moment, it is not known for which structures $\mathbb A$ will CSP($\mathbb A$) be solvable by a linear Datalog program. However, once somebody obtains a characterization of linear Datalog, our result immediately gives a characterization of symmetric Datalog.