Visibly Recursive Automata

TL;DR

This paper introduces visibly recursive automata (VRAs), a new automaton model allowing automata to call each other, extending procedural automata, and explores their complexity and decision problems.

Contribution

The paper defines VRAs as a novel automaton model, analyzes their complexity, and introduces codeterminism to enable algorithmic properties like complementation.

Findings

VRAs are a strict extension of procedural automata.

Deterministic VRAs are less expressive than general VRAs.

Codeterminism enables algorithmic operations such as complementation.

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.