Physical portrayal of computational complexity

@article{Annila2009PhysicalPO,
  title={Physical portrayal of computational complexity},
  author={Arto Annila},
  journal={ArXiv},
  year={2009},
  volume={abs/0906.1084}
}
  • A. Annila
  • Published 5 June 2009
  • Computer Science
  • ArXiv
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because information requires physical representations and because many natural processes complete in nondeterministic polynomial time (NP). The irreversible process with three or more degrees of freedom is found intractable when, in terms of physics, flows of energy are inseparable from their driving forces… 

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References

SHOWING 1-10 OF 143 REFERENCES

Physical foundations of evolutionary theory

Abstract The theory of evolution by natural selection is herein subsumed by the 2nd law of thermodynamics. The mathematical form of evolutionary theory is based on a re-examination of the probability

Physics and Computation: The Status of Landauer's Principle

TLDR
Ladyman et al. (2007) offer a precisification and general proof Landauer's Principle and an analysis of what it is for a physical process to implement a logical transformation and its implications for realism about computation and the use of Land Bauer's Principle in foundational debates is assessed.

Natural games

The physical character of information

TLDR
The dichotomy between the formal definition and the practical perception of information are examined by the second law of thermodynamics, which shows that the physical representation of information is not inconsequential in generation, transmission and processing of information.

Emergent attractors and the law of maximum entropy production: Foundations to a theory of general evolution

By Boltzmann's widely accepted reduction of the second law to a stochastic collision function, transformations from an incoherent to a coherent state are ‘infinitely improbable’. Yet it is precisely

Irreversibility and heat generation in the computing process

TLDR
Two simple, but representative, models of bistable devices are subjected to a more detailed analysis of switching kinetics to yield the relationship between speed and energy dissipation, and to estimate the effects of errors induced by thermal fluctuations.

The computational complexity of Kauffman nets and the P versus NP problem

Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown

The complexity of theorem-proving procedures

  • S. Cook
  • Mathematics, Computer Science
    STOC
  • 1971
It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a
...