2026/06/25 by Henning Fernau, Benedek Nagy, R. Jennifer Rose +4 · 1 voice
Biochemistry, Genetics and Molecular Biology · Computer Science · #Abstract family of languages #Automata theory #Class (philosophy) #Closure (psychology) #DNA and Biological Computing #Deterministic pushdown automaton #Finite-state machine #Machine Learning and Algorithms #Nested word #Quantum finite automata #Regular language #cs.FL #semigroups and automata theory
paper · pdf · open access · doi:10.4204/eptcs.446.3
published in Electronic Proceedings in Theoretical Computer Science 446, 37-52 (Open Publishing Association)
openalex publication_date 2026/06/25 · arxiv published 2026/06/25 · arxiv updated 2026/06/25 · openalex created_date 2026/06/28 · openalex updated_date 2026/08/05
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.