Reverse Post Correspondence Problem and Undecidability of $5' \rightarrow 3'$ String Assembly Systems
本文定义并证明了反向Post对应问题的不可判定性，并基于此结果证明了5'->3'字符串组装系统空集问题的不可判定性。
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2-Head 2D Returning Finite Automata
This study investigates the computational power of two-head finite automata in two-dimensional picture language recognition and their relationship with context-free matrix grammars (CFMGs) and returning pushdown automata (RPDAs). It introduces two novel models of two-head returning finite automata operating on rectangular pictures: the 2-HRFA, which allows backward moves, and the B2-HRFA, which enforces synchronous head movement—a constraint newly introduced in this work. Through formal language-theoretic analysis and closure properties, the paper establishes that the class of languages recognized by 2-HRFA is a proper subset of those recognized by RPDAs and incomparable with CFMGs. Furthermore, it demonstrates that B2-HRFA strictly lies between RFA and 2-HRFA in recognition power, thereby establishing a strict hierarchy among these three models.
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On some Classes of Reversible 2-head Automata
This paper investigates the reversible computational power of deterministic two-head finite automata (2DFA-2H). Specifically, it addresses whether such automata can recognize linear languages—e.g., palindromes—and how their accepted language class relates to that generated by left-deterministic linear grammars (LDLGs). To this end, the authors introduce two restricted reversible variants: 1-limited and complete reversible 2DFA-2H, and establish a strict computational hierarchy among them. Using formal language theory, bidirectional computation trajectory analysis, and state classification techniques, they prove that reversible 2DFA-2H accept prototypical non-regular linear languages (e.g., palindromes) yet fail to recognize certain regular languages. Moreover, the class of languages accepted by reversible 2DFA-2H is strictly contained in the LDLG language class and strictly contains the regular language class. This work provides the first systematic characterization of the recognition boundaries and structural properties of two-head automata under reversibility constraints.
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A Myhill-Nerode Type Characterization of 2detLIN Languages
This paper addresses the lack of an algebraic characterization for the class of languages recognized by two-way deterministic linear automata (2detLIN). We introduce, for the first time, a Myhill–Nerode–type equivalence relation based on prefix–suffix pairs, requiring both cross-freeness and completeness to precisely capture the recognition mechanism of bidirectional read heads in deterministic linear computation. By integrating concepts from WK finite automata and linear automata models, we establish a rigorous characterization: a language belongs to 2detLIN if and only if it admits a finite, cross-free, and complete partition of prefix–suffix equivalence classes. This result provides the first algebraic decidability criterion for 2detLIN and furnishes a novel theoretical framework for analyzing the structural properties of languages accepted by bidirectional deterministic automata.
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Reverse Post Correspondence Problem and Undecidability of $5' \rightarrow 3'$ String Assembly Systems
本文定义并证明了反向Post对应问题的不可判定性，并基于此结果证明了5'->3'字符串组装系统空集问题的不可判定性。
0 citationsRead paper
2-Head 2D Returning Finite Automata
This study investigates the computational power of two-head finite automata in two-dimensional picture language recognition and their relationship with context-free matrix grammars (CFMGs) and returning pushdown automata (RPDAs). It introduces two novel models of two-head returning finite automata operating on rectangular pictures: the 2-HRFA, which allows backward moves, and the B2-HRFA, which enforces synchronous head movement—a constraint newly introduced in this work. Through formal language-theoretic analysis and closure properties, the paper establishes that the class of languages recognized by 2-HRFA is a proper subset of those recognized by RPDAs and incomparable with CFMGs. Furthermore, it demonstrates that B2-HRFA strictly lies between RFA and 2-HRFA in recognition power, thereby establishing a strict hierarchy among these three models.
0 citationsRead paper
On some Classes of Reversible 2-head Automata
This paper investigates the reversible computational power of deterministic two-head finite automata (2DFA-2H). Specifically, it addresses whether such automata can recognize linear languages—e.g., palindromes—and how their accepted language class relates to that generated by left-deterministic linear grammars (LDLGs). To this end, the authors introduce two restricted reversible variants: 1-limited and complete reversible 2DFA-2H, and establish a strict computational hierarchy among them. Using formal language theory, bidirectional computation trajectory analysis, and state classification techniques, they prove that reversible 2DFA-2H accept prototypical non-regular linear languages (e.g., palindromes) yet fail to recognize certain regular languages. Moreover, the class of languages accepted by reversible 2DFA-2H is strictly contained in the LDLG language class and strictly contains the regular language class. This work provides the first systematic characterization of the recognition boundaries and structural properties of two-head automata under reversibility constraints.
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A Myhill-Nerode Type Characterization of 2detLIN Languages
This paper addresses the lack of an algebraic characterization for the class of languages recognized by two-way deterministic linear automata (2detLIN). We introduce, for the first time, a Myhill–Nerode–type equivalence relation based on prefix–suffix pairs, requiring both cross-freeness and completeness to precisely capture the recognition mechanism of bidirectional read heads in deterministic linear computation. By integrating concepts from WK finite automata and linear automata models, we establish a rigorous characterization: a language belongs to 2detLIN if and only if it admits a finite, cross-free, and complete partition of prefix–suffix equivalence classes. This result provides the first algebraic decidability criterion for 2detLIN and furnishes a novel theoretical framework for analyzing the structural properties of languages accepted by bidirectional deterministic automata.
0 citationsRead paper