Closure and Complexity of Temporal Causality

TL;DR

This paper investigates the closure properties and computational complexity of determining causes in temporal causality, revealing which properties are closed under causal inference and providing bounds for cause computation.

Contribution

It establishes closure properties for safety, reachability, and recurrence, and introduces complexity bounds for computing causes in temporal causality.

Findings

Safety, reachability, and recurrence are closed under causal inference.

Persistence and obligation are not closed under causal inference.

New upper and lower bounds for cause computation complexity.

Abstract

Temporal causality defines what property causes some observed temporal behavior (the effect) in a given computation, based on a counterfactual analysis of similar computations. In this paper, we study its closure properties and the complexity of computing causes. For the former, we establish that safety, reachability, and recurrence properties are all closed under causal inference: If the effect is from one of these property classes, then the cause for this effect is from the same class. We also show that persistence and obligation properties are not closed in this way. These results rest on a topological characterization of causes which makes them applicable to a wide range of similarity relations between computations. Finally, our complexity analysis establishes improved upper bounds for computing causes for safety, reachability, and recurrence properties. We also present the first lower bounds for all of the classes.