Effective theories for circuits and automata

Chaos

Volumn 21, Issue 3, 2011, Pages

  DeDeo, Simon ^a  

^a SANTA FE INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80053414694     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3640747     Document Type: Article

References (48)

1. von Neumann J. Automata Studies 1956, C. E. Shannon, J. McCarthy, in edited by and (Princeton University, Princeton, NJ)
2. Glass L. Kauffman S.A. J. Theor. Biol. 1973, 39:103. 10.1016/0022-5193(73)90208-7
3. Anderson P.W. Science 1972, 177:393. 10.1126/science.177.4047.393.
4. Rhodes J. Applications of Automata Theory and Algebra 2010, C. L. Nehaniv, edited by (World Scientific, Singapore) edited and corrected edition of 1971 text.
5. Crutchfield J.P. Young K. Complexity, Entropy and the Physics of Information 1989, 223. W. H. Zurek, and edited by (Addison-Wesley, Redwood City, Calif.)
6. Bonn S. Furlong E.E. M. Curr. Opin. Genet. Dev. 2008, 18:513. 10.1016/j.gde.2008.09.005
7. Davidson E.H. Rast J.P. Oliveri P. Ransick A. Calestani C. Yuh C.-H. Minokawa T. Amore G. Hinman V. Arenas-Mena C. Otim O. Brown C.T. Livi C.B. Lee P.Y. Revilla R. Schilstra M.J. Clarke P.J. C. Rust A.G. Pan Z. Arnone M.I. Rowen L. Cameron R.A. McClay D.R. Hood L. Bolouri H. Dev .Biol. 2002, 246:162. 10.1006/dbio.2002.0635
8. Davidson E.H. Dev. Biol. 2011, 357:35. 10.1016/j.ydbio.2011.02.004, (1).
9. Macía J. Widder S. Solé R. J. Theor. Biol. 2009, 261:126. 10.1016/j.jtbi.2009.07.019
10. Post E.L. Bull. AMS 1920, 26:437.
11. Lau D. Function Algebras on Finite Sets: a Basic Course on Many-Valued Logic and Clone Theory 2006, Springer Monographs in Mathematics (Springer, New York)
12. Pearl J. Causality 2009, (Cambridge University Press, New York)
13. Dassow J. Structural Theory of Automata, Semigroups, and Universal Algebra 2005, 207:77-108. V. Kudryavtsev, I. Rosenberg, M. Goldstein, NATO Science Series, edited by and (Springer, Netherlands) pp.
14. Dassow J. Completeness Problems in the Structural Theory of Automata 1981, (Akademie-Verlag, Berlin)
15. Pippenger N. Theories of Computability 1996, (Cambridge University Press, New York)
16. We use the word deterministic in the automata sense-i.e., a deterministic system is such that a letter-state pair is associated with a unique transition, δ σ ×Q → Q as opposed to δ σ × Q → Powerset[Q]. We do not consider non-deterministic automata explicitly in this paper; well-known methods allow one to construct a deterministic automata corresponding to any non-deterministic one. We use the word probabilistic to refer to situations in which a deterministic transition is chosen from a set probabilistically.
17. As with non-deterministic and probabilistic, it is worth distinguishing irreversible and dissipative. Irreversibility need not be associated with any randomness, and can be a consequence of a completely non-probabilistic map, such as an irreversible computation that deletes input. Dissipation, by contrast, we associate with processes that can not be run backwards because different histories have been merged due to an ignorance of which randomly-chosen operation was performed. We return to this distinction at the end of Sec.
18. For clarity, we do not include the transitory 0 and 1 states in our automata pictures.
19. A related notion is that of one machine pre-processing the environment and handing off its output to the next machine-this turns out to be equivalent to the description we use here, but harder to formulate in terms of our finite state automata.
20. Krohn K. Rhodes J.L. Trans. Am. Math. Soc. 1965, 116:450. 10.1090/S0002-9947-1965-0188316-1
21. Homomorphic behavior means that there exists a map between the two semigroups that preserves multiplication. There is a homomorphic mapping - between two groups in the case that multiplication is preserved: -(a)· -(b). -(a· b). Homomorphic mappings need not one-to-one, and in general the cascade will be larger than the original machine; in particular, the mapping may need to be restricted to a subautomaton of the cascade, and some states within this subautomaton may need to be identified with each other.
22. Eilenberg S. Automata, Languages, and Machines 1976, B. Vol. (Academic Press, New York)
23. Holcombe W. Algebraic Automata Theory 1982, Cambridge Studies in Advanced Mathematics (Cambridge University Press, New York), Chap. 4.
24. Nehaniv C. Rhodes J. Artificial Life 2000, 6:45. 10.1162/106454600568311.
25. Maler O. On the Krohn-Rhodes Cascaded Decomposition Theorem. Time for Verification: Essays in Memory of Amir Pnueli 2010, 6200. Z. Manna, D. A. Peled, in edited by and Lecture Notes in Computer Science Vol. (Springer, Berlin), ISBN: 978-3-642-13753-2.
26. Egri-Nagy A. Nehaniv C.L. 2011, and sgpdec-software package for hierarchical coordinatization of groups and semigroups, implemented in the GAP computer algebra system, Version 0.5.34
27. Egri-Nagy A. Nehaniv C.L. Artificial Life 2008, 14:299. 10.1162/artl.2008.14.3.14305
28. Egri-Nagy A. Nehaniv C.L. 2009, and e-prints arXiv:0911.5433 [math.GR].
29. 2008, GAP-Groups, Algorithms, and Programming, Version 4.4.12, The GAP Group.
30. Maler O. Theor. Comput. Sci. 1995, 145:391. 10.1016/0304-3975(95)00004-G.
31. Pippenger N. J. ACM 1989, 36:531. 10.1145/65950.77248.
32. Krakauer D.C. Sasaki A. Proc. Biol. Sci. 2002, 269:2423. 10.1098/rspb.2002.2127
33. Rao C. Wolf D. Nature (London) 2002, 420:231. 10.1038/nature01258
34. Süel G. Kulkarni R. Dworkin J. Garcia-Ojalvo J. Science 2007, 315:1716. 10.1126/science.1137455
35. Lehner B. Mol. Syst.Biol. 2008, 4:170. 10.1038/msb.2008.11.
36. Bar-Even A. Paulsson J. Maheshri N. Carmi M. Nat. Genet. 2006, 38:636. 10.1038/ng1807
37. Hornung G. PLoS Comput. Biol. 2008, 4:e8. 10.1371/journal.pcbi.0040008.sd001.
38. Jia H. Rochefort N. Chen X. Konnerth A. Nature (London) 2010, 464:1307. 10.1038/nature08947
39. Priebe N.J. Ferster D. Nature (London) 2010, 464:1290. 10.1038/4641290b
40. Calvin W.H. Stevens C.F. Science 1967, 155:842. 10.1126/science.155.3764.842
41. Calvin W.H. Stevens C.F. J. Neurophysiol. 1968, 31:574.
42. Lampl I. Reichova I. Ferster D. Neuron 1999, 22:361. 10.1016/S0896-6273(00)81096-X.
43. Huggett N. Weingard R. Synthese 1995, 102:171. 10.1007/BF01063904
44. Weinberg S. Physica A 1979, 96:327. 10.1016/0378-4371(79)90223-1.
45. Polchinski J. Nucl. Phys. B 1984, 231:269. 10.1016/0550-3213(84)90287-6.
46. Georgi H. Annu. Rev. Nucl. Part. Sci. 1993, 43:209. 10.1146/annurev.ns.43.120193.001233.
47. Bennett C.H. Int. J. Theor. Phys. 1982, 21:905. 10.1007/BF02084158.
48. Schneier B. Applied Cryptography 1996, (John Wiley & Sons, New York), Chap. 16.