A Formal Framework for the Explanation of Finite Automata Decisions

2026-02-12

AI Summary

This work addresses the problem of explaining why a finite automaton makes a specific decision on a given input word and how its output can be altered through minimal modifications. We formally define the notion of a minimal feature explanation for automaton decisions as the smallest set of critical input symbols responsible for the current acceptance or rejection outcome. To compute all such minimal explanations exactly, we propose an efficient algorithm that integrates formal methods, automata theory, and combinatorial optimization. Experimental evaluation demonstrates that our approach scales well in complex scenarios and consistently produces unbiased, accurate minimal explanations, thereby providing rigorous interpretability guarantees for automaton-based decisions.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Machine Learning: Feature Construction/Reformulation

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Finite automata (FA) are a fundamental computational abstraction that is widely used in practice for various tasks in computer science, linguistics, biology, electrical engineering, and artificial intelligence. Given an input word, an FA maps the word to a result, in the simple case"accept"or"reject", but in general to one of a finite set of results. A question that then arises is: why? Another question is: how can we modify the input word so that it is no longer accepted? One may think that the automaton itself is an adequate explanation of its behaviour, but automata can be very complex and difficult to make sense of directly. In this work, we investigate how to explain the behaviour of an FA on an input word in terms of the word's characters. In particular, we are interested in minimal explanations: what is the minimal set of input characters that explains the result, and what are the minimal changes needed to alter the result? In this paper, we propose an efficient method to determine all minimal explanations for the behaviour of an FA on a particular word. This allows us to give unbiased explanations about which input features are responsible for the result. Experiments show that our approach scales well, even when the underlying problem is challenging.

Problem

• finite automata
• explanation
• minimal explanation
• input word
• decision reasoning

Innovation

• finite automata
• minimal explanation
• input attribution
• formal explainability
• automata behavior