Halting Problem for One-State Turing Machines
Yannick Saouter · 1995
: 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 probl`eme 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. Key-words: Turing Machines; Decidability (R'esum'e : tsvp) y email: [email protected] CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE Centre National de la Recherche Scientifique Institut National de Recherche en Informatique (URA 227) Universite de Rennes 1 -- Insa de Rennes et en Automatique -- unite de recherche de Rennes Probl`eme de l'arret pour machines de Turing `...