Transition-based vs stated-based acceptance for automata over infinite words

2025-08-21

AI Summary

This paper investigates the fundamental differences between state-based and transition-based acceptance in ω-automata and their theoretical implications. We formally compare these two acceptance paradigms along four dimensions: expressive power over ω-regular languages, operational semantics modeling, state-space complexity, and efficiency of compositional constructions. Our analysis reveals that transition-based acceptance offers structural advantages for logical modeling and formal verification: it simplifies acceptance condition specification, reduces construction complexity, enhances modularity in composition, and naturally supports key tasks such as LTL-to-automaton translation. Crucially, we demonstrate—through systematic theoretical analysis—that transition-based acceptance is not merely a technical convenience but reflects a paradigm shift aligned with the intrinsic requirements of modeling infinite behaviors. The study provides rigorous theoretical foundations and practical guidelines for designing acceptance criteria in automata-theoretic verification frameworks.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Automata over infinite objects are a well-established model with applications in logic and formal verification. Traditionally, acceptance in such automata is defined based on the set of states visited infinitely often during a run. However, there is a growing trend towards defining acceptance based on transitions rather than states. In this survey, we analyse the reasons for this shift and advocate using transition-based acceptance in the context of automata over infinite words. We present a collection of problems where the choice of formalism has a major impact and discuss the causes of these differences.

Problem

• Comparing state-based and transition-based acceptance for infinite automata
• Analyzing reasons for shifting towards transition-based acceptance methods
• Investigating formalism choice impact on automata performance and differences

Innovation

• Transition-based acceptance for automata
• Survey comparing state vs transition models
• Analyzing impact on formal verification problems