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Towards applying computational complexity to foundations of physics
 Notes of Mathematical Seminars of St. Petersburg Department of Steklov Institute of Mathematics
, 2004
"... In one of his early papers, D. Grigoriev analyzed the decidability and computational complexity of different physical theories. This analysis was motivated by the hope that this analysis would help physicists. In this paper, we survey several similar ideas that may be of help to physicists. We hope ..."
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Cited by 17 (16 self)
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In one of his early papers, D. Grigoriev analyzed the decidability and computational complexity of different physical theories. This analysis was motivated by the hope that this analysis would help physicists. In this paper, we survey several similar ideas that may be of help to physicists. We hope that further research may lead to useful physical applications. 1
Fast Quantum Algorithms for Handling Probabilistic and Interval Uncertainty
, 2003
"... this paper, we show how the use of quantum computing can speed up some computations related to interval and probabilistic uncertainty. We end the paper with speculations on whether (and how) "hypothetic" physical devices can compute NPhard problems faster than in exponential time ..."
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Cited by 6 (6 self)
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this paper, we show how the use of quantum computing can speed up some computations related to interval and probabilistic uncertainty. We end the paper with speculations on whether (and how) "hypothetic" physical devices can compute NPhard problems faster than in exponential time
Towards Computers of Generation Omega  NonEquilibrium Thermodynamics, Granularity, and Acausal Processes: A Brief Survey
 Proceedings of the International Conference on Intelligent Systems and Semiotics (ISAS '97), Gaithersburg, MD: National Institute for Standards and Technology Publications
, 1997
"... Nowadays, we are using mainly computer of fourth generation, and we are designing fifthgeneration computers. It is reasonable to ask: what is the perspective? What will the computers of generation omega look like? ffl As the speed of data processing increases, we face a natural limitation of causa ..."
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Cited by 2 (1 self)
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Nowadays, we are using mainly computer of fourth generation, and we are designing fifthgeneration computers. It is reasonable to ask: what is the perspective? What will the computers of generation omega look like? ffl As the speed of data processing increases, we face a natural limitation of causality, according to which the speed of all processes is limited by the speed of light. ffl Lately, a new area of acausal (causality violating) processes has entered mainstream physics. This area has important astrophysical applications. In this paper, we show: ffl how nonequilibrium thermodynamics makes these processes consistent, ffl how these processes can be used in computations, and ffl how the very possibility of these processes lead to the granularity of the physical world. KEYWORDS: computer generations, granularity, nonequilibrium thermodynamics, quantum computing, acausal processes 1. GENERATIONS OF COMPUTERS: WE NEED FASTER AND FASTER COMPUTERS No matter how fast modern co...
Acausal Processes and Astrophysics: Case When Uncertainty is NonStatistical (Fuzzy?)
 Studies and Exchanges on Fuzziness and its AppLications (BUSEFAL
, 1996
"... In Newtonian physics, if we know the state of the world at some moment of time, then we can precisely predict the state of the world at all future times. In this sense, Newtonian physics is deterministic. In modern physics (starting with quantum mechanics), theories are usually nondeterministic ..."
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Cited by 2 (2 self)
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In Newtonian physics, if we know the state of the world at some moment of time, then we can precisely predict the state of the world at all future times. In this sense, Newtonian physics is deterministic. In modern physics (starting with quantum mechanics), theories are usually nondeterministic in the sense that even if we know exactly the initial state of the world, we cannot uniquely predict the future state of the world. In quantum mechanics (and in most modern quantumbased physical theories), the best we can get is probabilities of different future states.
Received (Day Month Year)
"... Accepted (Day Month Year) Communicated by (xxxxxxxxxx) In this paper, we explain why, in our opinion, logic and constructive mathematics are playing – and should play – an important role in the design, understanding, and analysis of unconventional computation. ..."
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Accepted (Day Month Year) Communicated by (xxxxxxxxxx) In this paper, we explain why, in our opinion, logic and constructive mathematics are playing – and should play – an important role in the design, understanding, and analysis of unconventional computation.
Designing, Understanding, and Analyzing Unconventional Computation: The Important Role of Logic and Constructive Mathematics
"... In this paper, we explain why, in our opinion, logic and constructive mathematics are playing – and should play – an important role in the design, understanding, and analysis of unconventional computation. ..."
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In this paper, we explain why, in our opinion, logic and constructive mathematics are playing – and should play – an important role in the design, understanding, and analysis of unconventional computation.