Some Improvements in Fuzzy Turing Machines

TL;DR

This paper advances fuzzy Turing machine theory by redefining acceptance and rejection, introducing extended machines with indeterminacy states, and demonstrating their computational equivalences and capabilities.

Contribution

It redefines fuzzy Turing machines, introduces extended models with indeterminacy states, and explores their computational power and relation to classical and fuzzy languages.

Findings

Fuzzy, generalized fuzzy, and classical Turing machines are computationally equivalent.

Extended fuzzy Turing machines can capture certain loops of classical Turing machines.

A fuzzy language can be indeterminable by an extended fuzzy Turing machine.

Abstract

In this paper, we modify some previous definitions of fuzzy Turing machines to define the notions of accepting and rejecting degrees of inputs, computationally. We use a BFS-based search method and obtain an upper level bound to guarantee the existence of accepting and rejecting degrees. We show that fuzzy, generalized fuzzy and classical Turing machines have the same computational power. Next, we introduce the class of Extended Fuzzy Turing Machines equipped with indeterminacy states. These machines are used to catch some types of loops of the classical Turing machines. Moreover, to each r.e. or co-r.e language, we correspond a fuzzy language which is indeterminable by an extended fuzzy Turing machine.