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Halting Problem for One-State Turing Machines

Yannick Saouter 1
1 API - Parallel VLSI Architectures
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : In [1], Turing has established the well-known result of the indecidability of the general halting problem of Turing machines. It is also well known that there exists entire classes of Turing machines whose halting is decidable (machines operating on an alphabet of one symbol, machines with finite tapes etc ...). In this article we are paying attention on Turing machines with a single state for which we prove that the halting is decidable. The interest of this problème is that it settles exactly with other works the limit between decidable and undecidable in regard of the number of internal states of the machine.
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Submitted on : Wednesday, May 24, 2006 - 2:32:09 PM
Last modification on : Friday, February 4, 2022 - 3:08:55 AM
Long-term archiving on: : Monday, April 5, 2010 - 12:05:10 AM


  • HAL Id : inria-00074105, version 1


Yannick Saouter. Halting Problem for One-State Turing Machines. [Research Report] RR-2577, INRIA. 1995. ⟨inria-00074105⟩



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