Abstract
Turing machines exposed to a small stochastic noise are considered. An exact characterisation of their (≈\({\it \Pi}\) \(_{\rm 2}^{\rm 0}\)) computational power (as noise level tends to 0) is obtained. From a probabilistic standpoint this is a theory of large deviations for Turing machines.
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McKee, W., Bergman, D., Nguyen, N., Aton, T., Block, L., Huynh, V., McAdams, H., Smith, E., McPherson, J., Janzen, J., Ondrusek, J., Hyslop, A., Russell, D., Coy, R.: Cosmic ray neutron induced upsets as a major contributor to the soft error rate of current and future generation DRAMs. In: Proceedings of the International Reliability Physics Symposium (1996)
Howard, J.J., Hardage, D.: Spacecraft environments interactions: Space radiation and its effects on electronic systems. Technical Report TP-1999-209373, NASA (1999), http://trs.nis.nasa.gov/archive/00000502/01/tp209373.pdf
Puri, A.: Dynamical properties of timed automata. Discrete Event Dynamic Systems 10, 87–113 (2000)
Fränzle, M.: Analysis of hybrid systems: An ounce of realism can save an infinity of states. In: Flum, J., Rodríguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 126–140. Springer, Heidelberg (1999)
Asarin, E., Bouajjani, A.: Perturbed Turing machines and hybrid systems. In: Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science, p. 269. IEEE Computer Society, Los Alamitos (2001)
Delyon, B., Maler, O.: On the effects of noise and speed on computations. Theoretical Computer Science 129, 279–291 (1994)
Maass, W., Orponen, P.: On the effect of analog noise in discrete-time analog computations. Neural Computation 10, 1071–1095 (1998)
Freidlin, M., Wentzell, A.: Random perturbations of dynamical systems. Springer, New York (1984)
Rogers, H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967)
Weihrauch, K.: Computable analysis. Springer, Berlin (2000)
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Asarin, E., Collins, P. (2005). Noisy Turing Machines. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds) Automata, Languages and Programming. ICALP 2005. Lecture Notes in Computer Science, vol 3580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11523468_83
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DOI: https://doi.org/10.1007/11523468_83
Publisher Name: Springer, Berlin, Heidelberg
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