One-Tape Linear-Time Turing Machines: A New Perspective on Computational Complexity

Title: One-Tape Linear-Time Turing Machines: A New Perspective on Computational Complexity

Research Question: How do the resources of one-tape linear-time Turing machines affect their computational patterns and power?

Methodology: The researchers explored the structural properties of one-tape linear-time Turing machines and clarified how their resources, such as the number of tapes and execution time, impact their computational capabilities. They used mathematical models and proofs to analyze and compare the power of these machines to other types of Turing machines.

Results: The study found that one-tape linear-time Turing machines are closely related to finite state automata, which significantly simplifies their structure. Despite their simplicity, these machines still offer complex structures. The researchers were able to prove that no one-tape linear-time deterministic Turing machine can be more powerful than deterministic finite state automata. They also demonstrated that any language accepted by a machine with short crossing sequences has constantly-bounded non-regularity.

Implications: This research provides a new perspective on computational complexity by focusing on the resources and capabilities of one-tape linear-time Turing machines. The findings suggest that these machines offer a different model of computation compared to multiple-tape and polynomial-time models. The study also has practical implications for the design and analysis of computer systems and algorithms, as it helps to understand the limitations and possibilities of different computational resources.

Link to Article: https://arxiv.org/abs/0310046v3 Authors: arXiv ID: 0310046v3