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The complexity of analog computation
 in Math. and Computers in Simulation 28(1986
"... We ask if analog computers can solve NPcomplete problems efficiently. Regarding this as unlikely, we formulate a strong version of Church’s Thesis: that any analog computer can be simulated efficiently (in polynomial time) by a digital computer. From this assumption and the assumption that P ≠ NP w ..."
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We ask if analog computers can solve NPcomplete problems efficiently. Regarding this as unlikely, we formulate a strong version of Church’s Thesis: that any analog computer can be simulated efficiently (in polynomial time) by a digital computer. From this assumption and the assumption that P ≠ NP we can draw conclusions about the operation of physical devices used for computation. An NPcomplete problem, 3SAT, is reduced to the problem of checking whether a feasible point is a local optimum of an optimization problem. A mechanical device is proposed for the solution of this problem. It encodes variables as shaft angles and uses gears and smooth cams. If we grant Strong Church’s Thesis, that P ≠ NP, and a certain ‘‘Downhill Principle’ ’ governing the physical behavior of the machine, we conclude that it cannot operate successfully while using only polynomial resources. We next prove Strong Church’s Thesis for a class of analog computers described by wellbehaved ordinary differential equations, which we can take as representing part of classical mechanics. We conclude with a comment on the recently discovered connection between spin glasses and combinatorial optimization. 1.
The Frozen Accident’ as an Evolutionary Adaptation: A Rate Distortion Theory Perspective on the Dynamics and Symmetries of Genetic Coding Mechanisms. Informatica 36:53–73
, 2012
"... We survey some interpretations and related issues concerning ‘the frozen accident ’ hypothesis proposed by Francis Crick and how it can be explained in terms of several natural mechanisms involving errorcorrection codes, spin glasses, symmetry breaking and the characteristic robustness of genetic ne ..."
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We survey some interpretations and related issues concerning ‘the frozen accident ’ hypothesis proposed by Francis Crick and how it can be explained in terms of several natural mechanisms involving errorcorrection codes, spin glasses, symmetry breaking and the characteristic robustness of genetic networks. The approach to most of these questions involves using elements of Shannon’s rate distortion theory incorporating a semantic system which is meaningful for the relevant alphabets and vocabulary implemented in transmission of the genetic code. We apply the fundamental homology between information source uncertainty with the free energy density of a thermodynamical system with respect to transcriptional regulators and the communication channels of sequence/structure in proteins. The collective outcome of these processes supports previous suggestions that ‘the frozen accident ’ may in fact have been a temporal evolutionary adaptation. Povzetek: Članek obravnava izvor genetskega kodiranja. 1