Systems of Graph Formulas and their Equivalence to Alternating Graph Automata
Abstract
Graph-based modeling plays a fundamental role in many areas of computer science. In this paper, we introduce systems of graph formulas with variables for specifying graph properties; this notion generalizes the graph formulas introduced in earlier work by incorporating recursion. We show that these formula systems have the same expressive power as alternating graph automata, a computational model that extends traditional finite-state automata to graphs, and allows both existential and universal states. In particular, we provide a bidirectional translation between formula systems and alternating graph automata, proving their equivalence in specifying graph languages. This result implies that alternating graph automata can be naturally represented using logic-based formulations, thus bridging the gap between automata-theoretic and logic-based approaches to graph language specification.
Keywords
Cite
@article{arxiv.2510.25260,
title = {Systems of Graph Formulas and their Equivalence to Alternating Graph Automata},
author = {Frank Drewes and Berthold Hoffmann and Mark Minas},
journal= {arXiv preprint arXiv:2510.25260},
year = {2026}
}
Comments
To appear in the post-proceedings of the International Workshop on Graph Computational Models (GCM 2025), to be published via EPTCS