## Parallel Turing Machines (1984)

Citations: | 7 - 0 self |

### BibTeX

@MISC{Wiedermann84parallelturing,

author = {Juraj Wiedermann and Juraj Wiedermann and Juraj Wiedermann},

title = {Parallel Turing Machines},

year = {1984}

}

### OpenURL

### Abstract

A new model of parallel computation - a so called Parallel Turing Machine (PTM) - is proposed. It is shown that the PTM does not belong to the two machine classes suggested recently by van Emde Boas, i.e., the PTM belongs neither to the first machine class consisting of the machines which are polynomial-time and linear-space equivalent to the sequential Turing Machine, nor to the second machine class which consists of the machines which satisfy the parallel computation thesis. Further the notion of a pipelined PTM is introduced and the "period" is defied as a complexity measure suitable for evaluating the efficiency of pipelined computations. It is shown that to within...

### Citations

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Citation Context ...ely enumerable languages, i.e., languages with a noncomputable characteristic function. Note that in the case when ( ) = 1 for all ∈ the classical Fuzzy-NTM equals the standard NTM as de ned, e.g. in =-=[6]-=-. Such a machine is also called a crisp Turing machine. The languages accepted by the crisp machines are called crisp languages. 3. The power of classical fuzzy Turing machines Now we aim at a charact... |

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Citation Context ...rved. doi:10.1016/j.tcs.2003.12.004s62 J. Wiedermann / Theoretical Computer Science 317 (2004) 61 – 69 has been invoked by models of computations that make use of new physical principles (cf. quantum =-=[3]-=-, relativistic [13] or in nite time computations [5]), of di erent computational scenarios (cf. super-recursive [2] or interactive non-uniform evolutionary computing [10]) and, last but not least, of ... |

382 |
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Citation Context ...progress on the side of the respective computational theory. Recently, building mostly on the original results by Zadeh and Lee from 1970s and on the modern approach to the theory of fuzzy logic (cf. =-=[4]-=-) the present author devised a formal model of fuzzy computations and investigated its recursion-theoretical properties. This model is represented by the fuzzy Turing machine that is a generalization ... |

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Citation Context ... / Theoretical Computer Science 317 (2004) 61 – 69 has been invoked by models of computations that make use of new physical principles (cf. quantum [3], relativistic [13] or in nite time computations =-=[5]-=-), of di erent computational scenarios (cf. super-recursive [2] or interactive non-uniform evolutionary computing [10]) and, last but not least, of a di erent kind of the underlying logic of computati... |

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Citation Context .... [14]). In those days fuzzy variants of Turing machines, Markov algorithms, and nite automata (cf. [9,14]) have been proposed and also fundamentals of the fuzzy language theory have been established =-=[7]-=- but, unfortunately, without much attention being paid to the respective computability and complexity aspects. Since then fuzzy logic has made a tremendous progress towards its rigor mathematical foun... |

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Citation Context ...ysical principles (cf. quantum [3], relativistic [13] or in nite time computations [5]), of di erent computational scenarios (cf. super-recursive [2] or interactive non-uniform evolutionary computing =-=[10]-=-) and, last but not least, of a di erent kind of the underlying logic of computation. Among the lastly mentioned models attention has also been paid to formal models of fuzzy computations. The history... |

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Citation Context ...oked by models of computations that make use of new physical principles (cf. quantum [3], relativistic [13] or in nite time computations [5]), of di erent computational scenarios (cf. super-recursive =-=[2]-=- or interactive non-uniform evolutionary computing [10]) and, last but not least, of a di erent kind of the underlying logic of computation. Among the lastly mentioned models attention has also been p... |

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Citation Context ... of this subject goes back to the late 1960s when Zadeh came with his notion of fuzzy algorithms (cf. [14]). In those days fuzzy variants of Turing machines, Markov algorithms, and nite automata (cf. =-=[9,14]-=-) have been proposed and also fundamentals of the fuzzy language theory have been established [7] but, unfortunately, without much attention being paid to the respective computability and complexity a... |

9 |
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Citation Context ...j.tcs.2003.12.004s62 J. Wiedermann / Theoretical Computer Science 317 (2004) 61 – 69 has been invoked by models of computations that make use of new physical principles (cf. quantum [3], relativistic =-=[13]-=- or in nite time computations [5]), of di erent computational scenarios (cf. super-recursive [2] or interactive non-uniform evolutionary computing [10]) and, last but not least, of a di erent kind of ... |

8 |
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Citation Context ... properties. This model is represented by the fuzzy Turing machine that is a generalization of the original Lee’s and Zadeh’s model that corresponds to the present state-of-the-art of fuzzy logic. In =-=[12]-=- the fuzzy Turing machine has been presented in two variants: one with a so-called classical acceptance criterion, and the other with a so-called partially computable acceptance criterion. Surprisingl... |

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Citation Context ...tisfy the Church–Turing thesis and hence they were seen as a further evidence of the invariance of the thesis w.r.t. the machine architecture with a potential for the practice of fuzzy computing (cf. =-=[11]-=-) Nevertheless, with the revived interest in super-Turing computing the case of fuzzy Turing machines with the classical acceptance criterion reappeared: what is the true computational power of such m... |