Automatic Structures of Bounded Degree Revisited

Abstract. It it shown that the first-order theory of an automatic structure, whose Gaifman graph has bounded degree, is decidable in doubly exponential space (for injective automatic presentations, this holds even uniformly). Presenting an automatic structure of bounded degree whose theory is hard for 2EXPSPACE, we also prove this result to be optimal. These findings close the gap left open in [14].

• Type: Conference
• Year: 2009
• Where: CSL
• Authors: Dietrich Kuske, Markus Lohrey
• Keywords: Artificial Intelligence, Automatic Structure, CSL 2009, Injective Automatic Presentations, first-order Theory