Tractability of Quantified Temporal Constraints To The Max

TL;DR

This paper investigates the computational complexity of quantified temporal constraints, demonstrating that certain tractable classes remain tractable when extended with quantifiers, based on algebraic properties and syntactic characterizations.

Contribution

It extends the classification of tractable temporal constraint languages to the quantified setting, identifying preservation properties that ensure tractability.

Findings

Several maximally tractable temporal constraint languages remain tractable with quantifiers.

Characterizations of these languages are provided through syntactic and algebraic properties.

The results unify the understanding of tractability in both unquantified and quantified temporal constraints.

Abstract

A temporal constraint language is a set of relations that are first-order definable over (Q;<). We show that several temporal constraint languages whose constraint satisfaction problem is maximally tractable are also maximally tractable for the more expressive quantified constraint satisfaction problem. These constraint languages are defined in terms of preservation under certain binary polymorphisms. We also present syntactic characterizations of the relations in these languages.