Glossary
The processor of a computer is that component in charge of executing the operations of an algorithm.
A time unit is the length of time required by a processor to perform a step of its computation, consisting of three elementary operations: a read operation in which it receives a constant number of fixed-size data as input, a calculate operation in which it performs a fixed number of constant-time arithmetic and logical calculations (such as adding two numbers, comparing two numbers, and so on), and a write operation in which it returns a constant number of fixed-size data as output.
A sequential computer, consists of a single processor. A parallel computer has n processors, numbered 1 to n, where n ≥ 2. Both computers use the same type of processor, and that processor is the fastest possible (Akl 1997). The assumption that the computers on hand, whether sequential or parallel, use the fastest conceivable processor is an important one. This is because the speed of the...
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Bibliography
(A) Primary Literature
Abramsky S et al (1992) Handbook of logic in computer science. Clarendon Press, Oxford
Akl SG (1997) Parallel computation: models and methods. Prentice Hall, Upper Saddle River
Akl SG (2005) The myth of universal computation. In: Trobec R, Zinterhof P, Vajtersic M, Uhl A (eds) Parallel numerics. University of Salzburg/Jozef Stefan Institute, Salzburg/Ljubljana, pp 211–236
Akl SG (2006a) Three counterexamples to dispel the myth of the universal computer. Parallel Proc Lett 16:381–403
Akl SG (2006b) Conventional or unconventional: is any computer universal? In: Adamatzky A, Teuscher C (eds) From utopian to genuine unconventional computers. Luniver Press, Frome, pp 101–136
Akl SG (2007a) Godel’s incompleteness theorem and nonuniversality in computing. In: Nagy M, Nagy N (eds) Proceedings of the workshop on unconventional computational problems. Sixth International Conference on Unconventional Computation, Kingston, pp 1–23
Akl SG (2007b) Even accelerating machines are not universal. Int J Unconv Comput 3:105–121
Akl SG (2008a) Unconventional computational problems with consequences to universality. Int J Unconv Comput 4:89–98
Akl SG (2008b) Evolving computational systems. In: Rajasekaran S, Reif JH (eds) Parallel computing: models, algorithms, and applications. Taylor and Francis, Boca Raton, pp 1–22
Akl SG (2009) Ubiquity and simultaneity: the science and philosophy of space and time in unconventional computation. Keynote address, Conference on the Science and Philosophy of Unconventional Computing, The University of Cambridge, Cambridge
Akl SG (2010) Time travel: a new hypercomputational paradigm. Int J Unconv Comput 6:329–351
Akl SG (2014) What is computation? Int J Parallel Emergent Distrib Syst 29:337–345
Akl SG (2016) Nonuniversality explained. Int J Parallel Emergent Distrib Syst 31:201–219
Akl SG (2017) Nonuniversality in computation: fifteen misconceptions rectified. In: Adamatzky A (ed) Advances in unconventional computing. Springer, Cham, pp 1–31
Akl SG Universality in computation: some quotes of interest. Technical report no 2006–511, School of Computing, Queen’s University. http://www.cs.queensu.ca/home/akl/techreports/quotes.pdf
Akl SG, Nagy M (2009a) Introduction to parallel computation. In: Trobec R, Vajtersic M, Zinterhof P (eds) Parallel computing: numerics, applications, and trends. Springer, London, pp 43–80
Akl SG, Nagy M (2009b) The future of parallel computation. In: Trobec R, Vajtersic M, Zinterhof P (eds) Parallel computing: numerics, applications, and trends. Springer, London, pp 471–510
Akl SG, Salay N (2015) On computable numbers, nonuniversality, and the genuine power of parallelism. Int J Unconv Comput 11:283–297
Bringsjord S (2017) Is universal computation a myth? In: Adamatzky A (ed) Emergent computation: a festschrift for Selim G. Akl. Springer, Cham, pp 19–37
Burgin M (2005) Super-recursive algorithms. Springer, New York
Calude CS, Paun G (2004) Bio-steps beyond Turing. Biosystems 77:175–194
Copeland BJ (1998) Super Turing-machines. Complexity 4:30–32
Davies EB (2001) Building infinite machines. Br J Philos Sci 52:671–682
Davis M (2000) The universal computer. W.W. Norton, New York
Denning PJ (2012) Reflections on a symposium on computation. Comput J 55:799–802
Denning PJ, Dennis JB, Qualitz JE (1978) Machines, languages, and computation. Prentice-Hall, Englewood Cliffs
Deutsch D (1997) The fabric of reality. Penguin Books, London
Earman J, Norton JD (1996) Infinite pains: the trouble with supertasks. In: Morton A, Stich SP (eds) Benacerraf and his critics. Blackwell, Cambridge, pp 231–261
Etesi G, Nemeti I (2002) Non-Turing computations via Malament-Hogarth space-times. Int J Theor Phys 41:341–370
Fraser R, Akl SG (2008) Accelerating machines: a review. Int J Parallel Emergent Distrib Syst 23:81–104
Goldin D, Wegner P (2005) The church-Turing thesis: breaking the myth. In: Cooper BS, Lowe B (eds) New computational paradigms. Springer, Berlin, pp 152–168
Harel D (1992) Algorithmics: the spirit of computing. Addison-Wesley, Reading
Hillis D (1998) The pattern on the stone. Basic Books, New York
Hopcroft JE, Ullman JD (1969) Formal languages and their relations to automata. Addison-Wesley, Reading
Lewis HR, Papadimitriou CH (1981) Elements of the theory of computation. Prentice Hall, Englewood Cliffs
Mandrioli D, Ghezzi C (1987) Theoretical foundations of computer science. Wiley, New York
Minsky ML (1967) Computation: finite and infinite machines. Prentice-Hall, Englewood Cliffs
Nagy M, Akl SG (2005) On the importance of parallelism for quantum computation and the concept of a universal computer. In: Calude CS, Dinneen MJ, Paun G, de Perez-Jimenez, M. J, Rozenberg G (eds) Unconventional computation. Springer, Heildelberg, pp 176–190
Nagy M, Akl SG (2006) Quantum measurements and universal computation. Int J Unconv Comput 2:73–88
Nagy M, Akl SG (2007a) Quantum computing: beyond the limits of conventional computation. Int J Parallel Emergent Distrib Syst 22:123–135
Nagy M, Akl SG (2007b) Parallelism in quantum information processing defeats the universal computer. Par Proc Lett 17:233–262
Nagy N, Akl SG (2011) Computations with uncertain time constraints: effects on parallelism and universality. In: Calude CS, Kari J, Petre I, Rozenberg G (eds) Unconventional computation. Springer, Heidelberg, pp 152–163
Nagy N, Akl SG (2012) Computing with uncertainty and its implications to universality. Int J Parallel Emergent Distrib Syst 27:169–192
Savage JE (1998) Models of computation. Addison-Wesley, Reading
Siegelmann HT (1999) Neural networks and analog computation: beyond the Turing limit. Birkhauser, Boston
Sipser M (1997) Introduction to the theory of computation. PWS Publishing Company, Boston
Steinhart E (2007) Infinitely complex machines. In: Schuster A (ed) Intelligent computing everywhere. Springer, New York, pp 25–43
Stepney S (2004) The neglected pillar of material computation. Physica D 237 :1157–1164
Toffoli T (1982) Physics and computation. Int J Theor Phys 21:165–175
(B) Books and Reviews
Akl SG (2004) Superlinear performance in real-time parallel computation. J Supercomput 29:89–111
Akl SG Non-universality in computation: the myth of the universal computer. School of Computing, Queen’s University. http://research.cs.queensu.ca/Parallel/projects.html
Akl SG A computational challenge. School of computing, Queen’s University http://www.cs.queensu.ca/home/akl/CHALLENGE/A_Computational_Challenge.htm
Akl SG, Yao W (2005) Parallel computation and measurement uncertainty in nonlinear dynamical systems. J Math Model Alg 4:5–15
Durand-Lose J (2004) Abstract geometrical computation for black hole computation. Research report no 2004–15, Laboratoire de l'lnformatique du Parallelisme, Ecole Nor-male Superieure de Lyon, Lyon
Einstein A (2009) Letter to Erwin Schrodinger. In: Gilder L (ed) The age of entanglement. Vintage Books, New York, p 170
Fortnow L The enduring legacy of the Turing machine. http://ubiquity.acm.org/article.cfm?id=1921573
Gleick J (2011) The information: a history, a theory, a flood. HarperCollins, London
Hypercomputation. http://en.wikipedia.org/wiki/Hypercomputation
Kelly K (2002) God is the machine. Wired 10. https://www.wired.com/2002/12/holytech/
Kleene SC (1952) Introduction to metamathematics. North Holland, Amsterdam
Lloyd S (2006) Programming the universe. Knopf, New York
Lloyd S, Ng YJ (2004) Black hole computers. Sci Am 291:53–61
Rucker R (2005) The lifebox, the seashell, and the soul. Thunder’s Mouth Press, New York
Seife C (2006) Decoding the universe. Viking Penguin, New York
Siegfried T (2000) The bit and the pendulum. Wiley, New York
Stepney S (2004) Journeys in non-classical computation. In: Hoare T, Milner R (eds) Grand challenges in computing research. BCS, Swindon, pp 29–32
Tipler FJ (1995) The physics of immortality: modern cosmology, God and the resurrection of the dead. Macmillan, London
Turing AM (1939) Systems of logic based on ordinals. Proc London Math Soc 2 45:161–228
Vedral V (2010) Decoding reality. Oxford University Press, Oxford
Wegner P, Goldin D (1997) Computation beyond Turing machines. Comm ACM 46:100–102
Wheeler JA (1989) Information, physics, quanta: The search for links. In: Proceedings of the third international symposium on foundations of quantum mechanics in light of new technology,Tokyo, pp 354–368
Wheeler JA (1990) Information, physics, quantum: the search for links. In: Zurek W (ed) Complexity, entropy, and the physics of information. Addison-Wesley, Redwood City
Wheeler JA (1994) At home in the universe. American Institute of Physics Press, Wood-bury
Wolfram S (2002) A new kind of science. Wolfram Media, Champaign
Zuse K (1970) Calculating space. MIT Technical Translation AZT-70-164-GEMIT, Massachusetts Institute of Technology (Project MAC), Cambridge
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Akl, S.G. (2017). Unconventional Computational Problems. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_680-1
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