Membrane Systems and Hypercomputation

Stannett, Mike

doi:10.1007/978-3-642-36751-9_6

“…Entire journals and series of conference proceedings are nowadays dedicated to the theme of 'unconventional' computing (International Journal of Unconventional Computing, Unconventional Models of Computation: International Conference Proceedings: Lecture Notes in Computer Science, Workshop Physics and Computation), whereby especially the possibility of 'hyper-computing' (da Costa & Doria, 2006;Hagar & Korolev, 2007;Loff & Costa, 2009;MacLennan, 2009;Teuscher & Sipper, 2002;Wegner & Goldin, 2003)-i.e., being able to decide the classically undecidable Halting Problem effectively and in general by new (whatever 'new' means) devices-has been (and is still being) much contested and debated (in some cases even by naming the opponents) (Cockshott, 2015;Cockshott & Michaelson, 2007;Cotogno, 2009;Kieu, 2006;Michaelson & Cockshott, 2006;Müller, 2011;Nayebi, 2014;Smith, 2006;Welch, 2004). Moreover, whenever any new 'models' of computation-for example: 'membrane' computing (Gheorghe & Stannett, 2012;Stannett, 2012Stannett, , 2014-were proposed, their own new complexity theories (Blakey, 2011) and/or 'power' of computability theories (Beggs & Tucker, 2007aCosta, 2017;Shang, Lu, & Lu, 2015Wüthrich, 2015;Ziegler, 2005) had to follow en-suite with many subtle technical details. Some papers have also appeared in which questions concerning the 'scientific-ness' (Bringsjord & Zenzen, 2002;Stannett, 2001;Ziegler, 2009) of all those various ideas have been asked from a higher-level science-philosophical vantage point-e.g., are the claims and hypotheses of this discourse empirically refutable?-etc.…”

Section: Brief Literature Overviewmentioning

confidence: 99%

On More or Less Appropriate Notions of ‘Computation’

Gravell¹,

Grüner²

2018

SACJ

0

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Half a century after the emergence of computer science (a.k.a. informatics) as an academic discipline, the notion of “computation” is not yet “settled”. On the contrary: recent developments in the natural sciences, in mathematics, as well as in computer hardware engineering have also shaken the belief in the sufficiency of the “classical” notion of “computation” from the tradition of the Church-Turing-Hypothesis. In this paper we review the recent discourse on what is “computation”, and we clarify our own position within this discourse. Although we present some arguments about which notions of “computation” may be considered “reasonably acceptable” for our own historic era, we also emphasize that every science-philosophical notion (including the notion of “computation”) has its own long-term historical semantics which cannot be fixed once and forever. At this point in time, however, no compelling assertion can yet be made about the possibility of “hypercomputation” as proper computation.

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“…In fact, the consequences of using a "desk machine" cannot be so readily dismissed, because this implies that the computation may involve coordination between two physically separated agents (the human and the machine) [22]. Being physically separated, the two agents may be subject to different forces and accelerations, and this can affect the rate at which they perceive each other's clocks to be running.…”

Section: Wider Relevance To Computability Theorymentioning

confidence: 99%

Using Isabelle/HOL to Verify First-Order Relativity Theory

Stannett

¹

,

Németi

²

2013

Self Cite

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Logicians at the Rényi Mathematical Institute in Budapest have spent several years developing versions of relativity theory (special, general, and other variants) based wholly on first-order logic, and have argued in favour of the physical decidability, via exploitation of cosmological phenomena, of formally unsolvable questions such as the Halting Problem and the consistency of set theory. As part of a joint project, researchers at Sheffield have recently started generating rigorous machine-verified versions of the Hungarian proofs, so as to demonstrate the soundness of their work. In this paper, we explain the background to the project and demonstrate a first-order proof in Isabelle/HOL of the theorem "no inertial observer can travel faster than light". This approach to physical theories and physical computability has several pay-offs, because the precision with which physical theories need to be formalised within automated proof systems forces us to recognise subtly hidden assumptions.

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“…In fact, the consequences of using a "desk machine" cannot be so readily dismissed, because this implies that the computation may involve coordination between two physically separated agents (the human and the machine) [Sta13]. Being physically separated, the two agents may be subject to different forces and accelerations, and this can affect the rate at which they perceive each other's clocks to be running.…”

Section: Circumventing Turing's Analysismentioning

confidence: 99%

“…Subsequent theoretical investigation by various researchers suggests, however, that physical systems may exist which can in fact decide HP by exploiting cosmological phenomena [Hog92, EN93, EN02, Hog04, Man10, ANS12]. This claim is, of course, highly controversial; we therefore begin by explaining the loophole in Turing's analysis which allows 'hypercomputational' systems of this kind to be designed [Sta06,Sta13].…”

Section: Introductionmentioning

confidence: 96%

Using Isabelle to verify special relativity, with application to hypercomputation theory

Stannett,

Németi

2012

Preprint

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0

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Logicians at the Rényi Mathematical Institute in Budapest have spent several years developing versions of relativity theory (special, general, and other variants) based wholly on first order logic, and have argued in favour of the physical decidability, via exploitation of cosmological phenomena, of formally undecidable questions such as the Halting Problem and the consistency of set theory.The Hungarian theories are very extensive, and their associated proofs are intuitively very satisfying, but this brings its own risks since intuition can sometimes be misleading. As part of a joint project, researchers at Sheffield have recently started generating rigorous machineverified versions of the Hungarian proofs, so as to demonstrate the soundness of their work. In this paper, we explain the background to the project and demonstrate an Isabelle proof of the theorem "No inertial observer can travel faster than light". This approach to physical theories and physical computability has several pay-offs: (a) we can be certain our intuition hasn't led us astray (or if it has, we can identify where this has happened); (b) we can identify which axioms are specifically required in the proof of each theorem and to what extent those axioms can be weakened (the fewer assumptions we make up-front, the stronger the results); and (c) we can identify whether new formal proof techniques and tactics are needed when tackling physical as opposed to mathematical theories.

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Membrane Systems and Hypercomputation

Cited by 5 publications

References 15 publications

On More or Less Appropriate Notions of ‘Computation’

On More or Less Appropriate Notions of ‘Computation’

Using Isabelle/HOL to Verify First-Order Relativity Theory

Using Isabelle to verify special relativity, with application to hypercomputation theory

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