# All-Instances Restricted Chase Termination

## TL;DR

This paper investigates the problem of whether the restricted chase procedure terminates for all databases given certain classes of dependencies, showing that for guarded and sticky single-head TGDs, this problem is decidable.

## Contribution

It proves that all-instances restricted chase termination is decidable for guarded and sticky single-head TGDs, extending understanding beyond the oblivious chase.

## Key findings

- Decidability of all-instances restricted chase termination for guarded TGDs
- Decidability of all-instances restricted chase termination for sticky TGDs
- Extension of chase termination results to the standard (restricted) chase

## Abstract

The chase procedure is a fundamental algorithmic tool in database theory with a variety of applications. A key problem concerning the chase procedure is all-instances termination: for a given set of tuple-generating dependencies (TGDs), is it the case that the chase terminates for every input database? In view of the fact that this problem is undecidable, it is natural to ask whether known well-behaved classes of TGDs ensure decidability. We consider here the main paradigms that led to robust TGD-based formalisms, that is, guardedness and stickiness. Although all-instances termination is well-understood for the oblivious version of the chase, the more subtle case of the restricted (a.k.a. the standard) chase is rather unexplored. We show that all-instances restricted chase termination for guarded and sticky single-head TGDs is decidable.