Visibly Recursive Automata

2026-03-12

AI Summary

This work addresses the limited expressiveness of traditional visibly pushdown automata by proposing a novel model called Visibly Recursive Automata (VRA), which extends procedural automata systems through mutually recursive classical automata. Introducing the new notion of “co-determinism,” the paper replaces conventional determinism constraints while preserving expressive power, thereby enabling efficient algorithms for crucial operations such as complementation. By integrating formal language theory, automata composition, and complexity analysis, the study rigorously demonstrates that VRA strictly subsumes existing models in expressiveness. Furthermore, it establishes that co-determinism enjoys favorable algorithmic properties, providing a solid foundation for efficient practical implementations.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Computer Vision: Language and Vision
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• 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
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures

Abstract

As an alternative to visibly pushdown automata, we introduce visibly recursive automata (VRAs), composed of a set of classical automata that can call each other. VRAs are a strict extension of so-called systems of procedural automata, a model proposed by Frohme and Steffen. We study the complexity of standard language-theoretic operations and classical decision problems for VRAs. Since the class of deterministic VRAs forms a strict subclass in terms of expressiveness, we propose a (weaker) notion that does not restrict expressive power and which we call codeterminism. Codeterminism comes with many desirable algorithmic properties that we demonstrate by using it, e.g., as a stepping stone towards implementing complementation of VRAs.

Problem

• visibly recursive automata
• language-theoretic operations
• decision problems
• codeterminism
• expressiveness

Innovation

• visibly recursive automata
• codeterminism
• procedural automata
• complementation
• expressiveness