Symbolic {omega}-automata with obligations

2025-12-02

AI Summary

Extending ω-automata to infinite alphabets poses significant challenges due to the complexity of managing unbounded memory. Method: This paper introduces obligation-based symbolic ω-automata (OSωA), a novel model that replaces explicit register-based memory with symbolic guards and obligation assignments triggered at transitions—thereby eliminating traditional register mechanisms and yielding simpler semantics and improved decidability. OSωA integrates existential/universal branching with Emerson–Lei acceptance conditions. Contribution/Results: The language class of OSωA strictly subsumes ω-regular languages, as formally proven. A complete toolchain supports core operations—including automaton product and emptiness checking—and demonstrates practical feasibility and effectiveness in verification tasks.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• 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
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Extensions of {omega}-automata to infinite alphabets typically rely on symbolic guards to keep the transition relation finite, and on registers or memory cells to preserve information from past symbols. Symbolic transitions alone are ill-suited to act on this information, and register automata have intricate formal semantics and issues with tractability. We propose a slightly different approach based on obligations, i.e., assignment-like constructs attached to transitions. Whenever a transition with an obligation is taken, the obligation is evaluated against the current symbol and yields a constraint on the next symbol that the automaton will read. We formalize obligation automata with existential and universal branching and Emerson-Lei acceptance conditions, which subsume classic families such as B""uchi, Rabin, Strett, and parity automata. We show that these automata recognise a strict superset of {omega}-regular languages. To illustrate the practicality of our proposal, we also introduce a machine-readable format to express obligation automata and describe a tool implementing several operations over them, including automata product and emptiness checking.

Problem

• Extends ω-automata to infinite alphabets using obligations
• Formalizes automata with existential/universal branching and Emerson-Lei acceptance
• Introduces a machine-readable format and tool for practical operations

Innovation

• Obligations replace registers for memory in automata
• Existential and universal branching with Emerson-Lei acceptance
• Machine-readable format and tool for automata operations