On some Classes of Reversible 2-head Automata

2025-07-21

AI Summary

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.

Technology Category

• Knowledge Representation and Reasoning: Knowledge Representation Languages
• Natural Language Processing: (Large) Language Models
• Machine Learning: Structured Learning

Application Category

• Search and Retrieval-Augmented AI: Multilingual and cross-lingual Web search
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Deterministic 2-head finite automata which are machines that process an input word from both ends are analyzed for their ability to perform reversible computations. This implies that the automata are backward deterministic, enabling unique forward and backward computation. We explore the computational power of such automata, discovering that, while some regular languages cannot be accepted by these machines, they are capable of accepting some characteristic linear languages, e.g., the language of palindromes. Additionally, we prove that restricted variants, i.e., both 1-limited reversible 2-head finite automata and complete reversible 2-head finite automata are less powerful and they form a proper hierarchy. In the former, in each computation step exactly one input letter is being processed, i.e., only one of the heads can read a letter. These automata are also characterized by putting their states to classes based on the head(s) used to reach and to leave the state. In the complete reversible 2-head finite automata, it is required that any input can be fully read by the automaton. The accepted families are also compared to the classes generated by left deterministic linear grammars.

Problem

• Analyzing reversible computations in 2-head finite automata
• Exploring computational power of reversible 2-head automata
• Comparing automata classes with linear grammar languages

Innovation

• Reversible 2-head automata enable bidirectional computation
• Automata classify states by head movement patterns
• Restricted variants form a computational hierarchy