Linear Datalog and Bounded Path Duality of Relational Structures

TL;DR

This paper explores the relationship between finite-variable logics, bounded pathwidth structures, and linear Datalog programs within CSPs, revealing a unified concept called bounded path duality that influences complexity classifications.

Contribution

It introduces bounded path duality as a unifying framework linking logic, structure, and Datalog in CSPs, and analyzes its impact on computational complexity.

Findings

CSPs with bounded path duality are solvable in NL

Bounded path duality explains all known NL CSP families

New NL problems are identified using the framework

Abstract

In this paper we systematically investigate the connections between logics with a finite number of variables, structures of bounded pathwidth, and linear Datalog Programs. We prove that, in the context of Constraint Satisfaction Problems, all these concepts correspond to different mathematical embodiments of a unique robust notion that we call bounded path duality. We also study the computational complexity implications of the notion of bounded path duality. We show that every constraint satisfaction problem $\csp(\best)$ with bounded path duality is solvable in NL and that this notion explains in a uniform way all families of CSPs known to be in NL. Finally, we use the results developed in the paper to identify new problems in NL.