Small Turing machines and generalized busy beaver competition

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Small Turing machines and generalized busy beaver competition

Let TM(k, l) be the set of one-tape Turing machines with k states and l symbols. It is known that the halting problem is decidable for machines in TM(2, 3) and TM(3, 2). We prove that the decidability of machines in TM(2, 4) and TM(3, 3) will be difficult to settle, by giving machines in these sets for which the halting problem depends on an open problem in number theory. A machine in TM(5, 2) ...

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ژورنال

عنوان ژورنال: Theoretical Computer Science

سال: 2004

ISSN: 0304-3975

DOI: 10.1016/j.tcs.2004.05.008