Abstract
In 2014, Jeandel proved that two dynamical properties regarding Turing machines can be computable with any desired error ϵ>0, the Turing machine Maximum Speed and Topological Entropy. Both problems were proved in parallel, using equivalent properties. Those results were unexpected, as most (if not all) dynamical properties are undecidable. Nevertheless, Topological Entropy positiveness for reversible and complete Turing machines was shortly proved to be undecidable, with a reduction of the halting problem with empty counters in 2-reversible Counter machines. Unfortunately, the same proof could not be used to prove undecidability of Speed Positiveness. In this research, we prove the undecidability of Homogeneous Tape Reachability Problem for aperiodic and reversible Turing machines, in order to use it to prove the undecidability of the Speed Positiveness Problem for complete and reversible Turing machines.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
