Synthesis of Temporal Causality

TL;DR

This paper introduces a complete automata-based algorithm for synthesizing omega-regular causes of omega-regular effects in reactive systems, advancing causal analysis beyond existing limited methods.

Contribution

It presents the first complete cause-synthesis algorithm for omega-regular effects, ensuring causes are also omega-regular and automata-computable.

Findings

Algorithm successfully synthesizes causes as omega-regular automata.

Prototype tool demonstrates practical feasibility and performance.

Method extends causal analysis capabilities in reactive systems.

Abstract

We present an automata-based algorithm to synthesize omega-regular causes for omega-regular effects on executions of a reactive system, such as counterexamples uncovered by a model checker. Our theory is a generalization of temporal causality, which has recently been proposed as a framework for drawing causal relationships between trace properties on a given trace. So far, algorithms exist only for verifying a single causal relationship and, as an extension, cause synthesis through enumeration, which is complete only for a small fragment of effect properties. This work presents the first complete cause-synthesis algorithm for the class of omega-regular effects. We show that in this case, causes are guaranteed to be omega-regular themselves and can be computed as, e.g., nondeterministic B\"uchi automata. We demonstrate the practical feasibility of this algorithm with a prototype tool and evaluate its performance for cause synthesis and cause checking.