The Church-Turing Thesis: Breaking the Myth

Goldin, Dina; Wegner, Peter

doi:10.1007/11494645_20

Cited by 41 publications

(27 citation statements)

References 10 publications

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“…Many of the advocates of hypercomputation are well aware of the questions raised in this contribution (for example [13]) and deal with them in a different way. Firm believers in the obsolescence of the CTT such as Goldin and Wegner [22] agree with this author and others that the usual notion of computability is in fact mathematical and not physical. Opinions often diverge only as to the adequacy of the essentially mathematical definition.…”

Section: Resultssupporting

confidence: 69%

Zeno machines and hypercomputation

Potgieter

2006

Theoretical Computer Science

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This paper reviews the Church-Turing Thesis (or rather, theses) with reference to their origin and application and considers some models of "hypercomputation", concentrating on perhaps the most straight-forward option: Zeno machines (Turing machines with accelerating clock). The halting problem is briefly discussed in a general context and the suggestion that it is an inevitable companion of any reasonable computational model is emphasised. It is suggested that claims to have "broken the Turing barrier" could be toned down and that the important and well-founded rôle of Turing computability in the mathematical sciences stands unchallenged.

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Section: Resultssupporting

confidence: 69%

Zeno machines and hypercomputation

Potgieter

2006

Theoretical Computer Science

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“…They argue that this hypothesis, when combined with their result that PTMs are more expressive than classical TMs, provides a formal proof of Wegner's conjecture that "interaction is more powerful than algorithms" [22,24,25,26], and hence refutes what they call the Strong Church-Turing Thesis -different from the original Church-Turing Thesis -, stating any possible computation can be captured by some Turing machine, or in other words, that "models of computation more expressive than TMs are impossible" [24,26].…”

Section: Historical Backgroundmentioning

confidence: 93%

“…All these consideration led Goldin and Wegner to formulate the so-called Sequential Interaction Thesis, a generalization of the Church-Turing Thesis in the realm of interactive computation, claiming that "any sequential interactive computation can be performed by a persistent Turing machine" [22,24,25,26]. They argue that this hypothesis, when combined with their result that PTMs are more expressive than classical TMs, provides a formal proof of Wegner's conjecture that "interaction is more powerful than algorithms" [22,24,25,26], and hence refutes what they call the Strong Church-Turing Thesis -different from the original Church-Turing Thesis -, stating any possible computation can be captured by some Turing machine, or in other words, that "models of computation more expressive than TMs are impossible" [24,26].…”

Section: Historical Backgroundmentioning

confidence: 99%

Recurrent Neural Networks and Super-Turing Interactive Computation

Cabessa

Villa

2015

Springer Series in Bio-/Neuroinformatics

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Abstract. We present a complete overview of the computational power of recurrent neural networks involved in an interactive bio-inspired computational paradigm. More precisely, we recall the results stating that interactive rational-and realweighted neural networks are Turing-equivalent and super-Turing, respectively. We further prove that interactive evolving neural networks are super-Turing, irrespective of whether their synaptic weights are modeled by rational or real numbers. These results show that the computational powers of neural nets involved in a classical or in an interactive computational framework follow similar patterns of characterization. They suggest that some intrinsic computational capabilities of the brain might lie beyond the scope of Turing-equivalent models of computation, hence surpass the potentialities every current standard artificial models of computation.

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“…For interactive (see [20,30]), concurrent (see [15]), distributed, real-time computations the notion of Turing-computability is not directly applicable and less well understood (see [16][17][18]). Concepts like infinite non-terminating computations and fairness bring in new questions (see [3]).…”

Section: Motivationmentioning

confidence: 99%

Computability and realizability for interactive computations

Broy

2015

Information and Computation

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The Church-Turing Thesis: Breaking the Myth

Cited by 41 publications

References 10 publications

Zeno machines and hypercomputation

Zeno machines and hypercomputation

Recurrent Neural Networks and Super-Turing Interactive Computation

Computability and realizability for interactive computations

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