Tractability Frontier for Dually-Closed Temporal Quantified Constraint Satisfaction Problems

TL;DR

This paper establishes a clear complexity classification for QCSPs over dually-closed temporal languages, showing they are either polynomial-time solvable or NP/coNP-hard, thus advancing understanding of temporal constraint problems.

Contribution

It provides the first dichotomy theorem for QCSPs over dually-closed temporal languages, extending previous results from equality languages.

Findings

QCSP over dually-closed temporal languages is either in P or NP/coNP-hard.

The dichotomy generalizes previous results on equality languages.

The classification aids in understanding the computational complexity of temporal constraint satisfaction.

Abstract

A temporal (constraint) language is a relational structure with a first-order definition in the rational numbers with the order. We study here the complexity of the Quantified Constraint Satisfaction Problem (QCSP) for temporal constraint languages. Our main contribution is a dichotomy for the restricted class of dually-closed temporal languages. We prove that QCSP for such a language is either solvable in polynomial time or it is hard for NP or coNP. Our result generalizes a similar dichotomy of QCSPs for equality languages, which are relational structures definable by Boolean combinations of equalities.