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Weight-reducing Turing machines by Bruno Guillon; Giovanni Pighizzini; Luca Prigioniero; Daniel Průša is a Computer Science article available to read on EtoBox.

What is Weight-reducing Turing machines about?

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.

Who reads Weight-reducing Turing machines?

Author

Bruno Guillon; Giovanni Pighizzini; Luca Prigioniero; Daniel Průša

Publisher

Elsevier BV

Published

2023

Language

EN

Field

Computer Science (Physical Sciences)