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Weight-reducing Turing machines

Guillon, Bruno ; Pighizzini, Giovanni ; Prigioniero, Luca ; Průša, Daniel

Information and computation, 2023-06, Vol.292, p.105030, Article 105030 [Periódico revisado por pares]

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Título:
Weight-reducing Turing machines
Autor: Guillon, Bruno ; Pighizzini, Giovanni ; Prigioniero, Luca ; Průša, Daniel
Assuntos: Computer Science ; Descriptional complexity ; Hennie machines ; One-tape Turing machines
É parte de: Information and computation, 2023-06, Vol.292, p.105030, Article 105030
Descrição: It is well known that one-tape Turing machines running in linear time are no more powerful than finite automata; namely they recognize exactly the class of regular languages. We prove that it is not decidable if a one-tape machine runs in linear time, even if it is deterministic and restricted to use only the portion of the tape that initially contains the input. This motivates the introduction of a constructive variant of one-tape machines, called a weight-reducing machine, and the investigation of its properties. We focus on the deterministic case. In particular, we show that, paying a polynomial size increase only, each weight-reducing machine can be turned into a halting one that runs in linear time. Furthermore each weight-reducing machine can be converted into equivalent nondeterministic and deterministic finite automata by paying an exponential and doubly-exponential increase in size, respectively. These costs cannot be reduced in the worst case.
Editor: Elsevier Inc
Idioma: Inglês

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