Extremal Separation Problems for Temporal Instance Queries

TL;DR

This paper studies the extremal separation problem for temporal queries in linear temporal logic, providing complexity bounds and algorithms to identify the most specific and general separating queries for positive and negative data examples.

Contribution

It introduces the extremal separation problem for LTL-based instance queries and offers complexity analysis and algorithms for computing extremal separators.

Findings

Tight complexity bounds for verification and counting of extremal separators.

Algorithms for computing the most specific and general separators.

Insights into the structure of separating queries in temporal logic.

Abstract

The separation problem for a class Q of database queries is to find a query in Q that distinguishes between a given set of `positive' and `negative' data examples. Separation provides explanations of examples and underpins the query-by-example paradigm to support database users in constructing and refining queries. As the space of all separating queries can be large, it is helpful to succinctly represent this space by means of its most specific (logically strongest) and general (weakest) members. We investigate this extremal separation problem for classes of instance queries formulated in linear temporal logic LTL with the operators conjunction, next, and eventually. Our results range from tight complexity bounds for verifying and counting extremal separators to algorithms computing them.