Incomputability at the foundations of physics (A study in the philosophy of science)

Costa, José Félix

doi:10.1093/logcom/ext048

Cited by 4 publications

(2 citation statements)

References 14 publications

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“…The strong incomputability of every sequence generated by the three-dimensional QRNGs studied in this paper contributes to the much-studied and debated problem of incomputability in physics [43–46]. This paper suggests that incomputability in physics is real and practically applicable, a fundamental phenomenon for understanding nature.…”

Section: Discussionmentioning

confidence: 81%

Photonic ternary quantum random number generators

Trejo

Calude

2023

Proc. R. Soc. A.

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We construct a class of three-dimensional photonic quantum random number generators (QRNGs) and prove that each of them generates maximally unpredictable digits via measurements that are robust to errors. This shows that every sequence generated is strongly incomputable; hence its quality is provably better than that of every pseudo-random sequence. These results suggest that incomputability in physics is real and practically applicable. Finally, we present photonic implementations of three-dimensional QRNGs and discuss device independence.

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Section: Discussionmentioning

confidence: 81%

Photonic ternary quantum random number generators

Trejo

Calude

2023

Proc. R. Soc. A.

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“…supposedly physical constants, may vary through time, adding incomputability to physical observations. This is a step further that we started considering in [84], following this assumption of Peirce:…”

Section: Accepted Manuscriptmentioning

confidence: 99%

East-West paths to unconventional computing

Adamatzky

Akl

Burgin³

et al. 2017

Progress in Biophysics and Molecular Biology

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Unconventional computing is about breaking boundaries in thinking, acting and computing. Typical topics of this non-typical field include, but are not limited to physics of computation, non-classical logics, new complexity measures, novel hardware, mechanical, chemical and quantum computing. Unconventional computing encourages a new style of thinking while practical applications are obtained from uncovering and exploiting principles and mechanisms of information processing in and functional properties of, physical, chemical and living systems; in particular, efficient algorithms are developed, (almost) optimal architectures are designed and working prototypes of future computing devices are manufactured. This article includes idiosyncratic accounts of 'unconventional computing' scientists reflecting on their personal experiences, what attracted them to the field, their inspirations and discoveries.

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A Hierarchy for $$ BPP //\log \!\star $$ B P P / / log ⋆ Based on Counting Calls to an Oracle

Beggs

Cortez

Costa

et al. 2016

Emergent Computation

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Algorithms whose computations involve making physical measurements can be modelled by Turing machines with oracles that are physical systems and oracle queries that obtain data from observation and measurement. The computational power of many of these physical oracles has been established using non-uniform complexity classes; in particular, for large classes of deterministic physical oracles, with fixed error margins constraining the exchange of data between algorithm and oracle, the computational power has been shown to be the non-uniform class BPP // log. In this paper, we consider non-deterministic oracles that can be modelled by random walks on the line. We show how to classify computations within BPP // log by making an infinite non-collapsing hierarchy between BPP // log and BPP. The hierarchy rests on the theorem that the number of calls to the physical oracle correlates with the size of the responses to queries.

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Incomputability at the foundations of physics (A study in the philosophy of science)

Cited by 4 publications

References 14 publications

Photonic ternary quantum random number generators

Photonic ternary quantum random number generators

East-West paths to unconventional computing

A Hierarchy for $$ BPP //\log \!\star $$ B P P / / log ⋆ Based on Counting Calls to an Oracle

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