Systems of Graph Formulas and their Equivalence to Alternating Graph Automata

📝 Original Info

• Title: Systems of Graph Formulas and their Equivalence to Alternating Graph Automata
• ArXiv ID: 2510.25260
• Date: 2025-10-29
• Authors: 정보 없음 (논문에 저자 정보가 제공되지 않음)

📝 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.

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