# Causality Analysis for Concurrent Reactive Systems (Extended Abstract)

## TL;DR

This paper introduces a formal language-theoretic framework for causality analysis in concurrent reactive systems, enabling explanation of safety violations and comparison of causality notions for debugging and system design.

## Contribution

It provides a unified formalization of causality notions, new definitions, and automata-based algorithms for causal analysis in concurrent reactive systems.

## Key findings

- Unified causality framework for concurrent systems
- Automata-based algorithms for causal set computation
- Analysis of causality notions for debugging and liability

## Abstract

We present a comprehensive language theoretic causality analysis framework for explaining safety property violations in the setting of concurrent reactive systems. Our framework allows us to uniformly express a number of causality notions studied in the areas of artificial intelligence and formal methods, as well as define new ones that are of potential interest in these areas. Furthermore, our formalization provides means for reasoning about the relationships between individual notions which have mostly been considered independently in prior work; and allows us to judge the appropriateness of the different definitions for various applications in system design. In particular, we consider causality analysis notions for debugging, error resilience, and liability resolution in concurrent reactive systems. Finally, we present automata-based algorithms for computing various causal sets based on our language-theoretic encoding, and derive the algorithmic complexities.