Quantum Two-Way One-Counter Automata

Title: Quantum Two-Way One-Counter Automata

Research Question: Can quantum automata with two-way and one-counter capabilities recognize more complex languages compared to their classical counterparts?

Methodology: The researchers introduced a new model of automata called two-way quantum one-counter automata (2Q1CAs). These automata combine the features of two-way quantum finite state automata (2QFAs) and one-way quantum one-counter automata (1Q1CAs). They provided a formal definition for 2Q1CAs with well-formedness conditions.

Results: The researchers proved that 2Q1CAs are at least as powerful as two-way deterministic one-counter automata (2D1CAs), meaning they can recognize the same set of languages. They also showed that some non-context-free languages, such as {anbn2|n≥1} and {anb2n|n≥1}, can be recognized by 2Q1CAs with bounded error. This suggests that 2Q1CAs have more power than their classical counterparts.

Implications: The results of this study suggest that quantum automata with two-way and one-counter capabilities can recognize more complex languages than their classical counterparts. This could have implications for the field of quantum computing and the potential applications of quantum computers. The study also raises questions about the boundaries of what can be computed efficiently on a quantum computer.

Link to Article: https://arxiv.org/abs/0110005v1 Authors: arXiv ID: 0110005v1