One Tape Linear Time Turing Machines

Title: One Tape Linear Time Turing Machines

Research Question: How can one-tape linear-time Turing machines be used to study computational complexity, and what are the implications of these findings?

Methodology: The researchers used a one-tape Turing machine model, which consists of a single input/work tape that stretches indefinitely in both directions. The machine has a finite number of states and reads and writes symbols on the tape. The researchers considered various types of machines, such as deterministic, nondeterministic, reversible, alternating, probabilistic, counting, and quantum Turing machines. They defined a "running time" for these machines, which is the height of the computation tree produced by the execution of the machine on a given input.

Results: The researchers found that one-tape linear-time Turing machines can recognize non-regular languages, which is a significant result in computational complexity theory. They also established a close connection between one-tape linear-time Turing machines and finite state automata.

Implications: The findings have implications for the study of computational complexity, as they provide a new way to analyze the power and limitations of Turing machines. The results also have practical applications in fields such as computer science, artificial intelligence, and cryptography.

Link to Article: https://arxiv.org/abs/0310046v1 Authors: arXiv ID: 0310046v1