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2-Head 2D Returning Finite Automata
[Submitted on 25 Jun 2026] · 2026-06-26 · via cs updates on arXiv.org

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Abstract:We introduce and study a family of two-head finite automata called two head returning finite automata (2-HRFA) operating on rectangular arrays of picture languages, in which both heads move in opposite directions. We show that the class of picture languages accepted by 2-HRFA is incomparable with the class of languages generated by context-free matrix grammars (CFMG), while it forms a proper subset of the class of languages accepted by returning pushdown automata (RPDA). In addition, we define a constrained variant, both head stepping two head returning finite automata (B2-HRFA), in which both heads are required to move in a synchronized, stepwise fashion. We prove that the class of languages accepted by returning finite automata (RFA) is a proper subset of the class of languages accepted by B2-HRFA, which in turn is a proper subset of the class of languages accepted by 2-HRFA. Closure properties for both the families of languages accepted by 2-HRFA and B2-HRFA are also investigated.

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Thu, 25 Jun 2026 07:13:34 UTC (25 KB)