Skip to main content
SpringerLink
Log in

Unconventional Computational Problems

  • Living reference work entry
  • First Online:
Encyclopedia of Complexity and Systems Science

  • 95 Accesses

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...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Bibliography

(A) Primary Literature

  • Abramsky S et al (1992) Handbook of logic in computer science. Clarendon Press, Oxford

    MATH  Google Scholar 

  • Akl SG (1997) Parallel computation: models and methods. Prentice Hall, Upper Saddle River

    Google Scholar 

  • 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

    Google Scholar 

  • Akl SG (2006a) Three counterexamples to dispel the myth of the universal computer. Parallel Proc Lett 16:381–403

    Article  MathSciNet  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Chapter  Google Scholar 

  • Akl SG (2007b) Even accelerating machines are not universal. Int J Unconv Comput 3:105–121

    Google Scholar 

  • Akl SG (2008a) Unconventional computational problems with consequences to universality. Int J Unconv Comput 4:89–98

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Akl SG (2010) Time travel: a new hypercomputational paradigm. Int J Unconv Comput 6:329–351

    Google Scholar 

  • Akl SG (2014) What is computation? Int J Parallel Emergent Distrib Syst 29:337–345

    Article  Google Scholar 

  • Akl SG (2016) Nonuniversality explained. Int J Parallel Emergent Distrib Syst 31:201–219

    Article  Google Scholar 

  • Akl SG (2017) Nonuniversality in computation: fifteen misconceptions rectified. In: Adamatzky A (ed) Advances in unconventional computing. Springer, Cham, pp 1–31

    Chapter  Google Scholar 

  • 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

    Chapter  Google Scholar 

  • 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

    Chapter  Google Scholar 

  • Akl SG, Salay N (2015) On computable numbers, nonuniversality, and the genuine power of parallelism. Int J Unconv Comput 11:283–297

    Google Scholar 

  • 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

    Chapter  Google Scholar 

  • Burgin M (2005) Super-recursive algorithms. Springer, New York

    MATH  Google Scholar 

  • Calude CS, Paun G (2004) Bio-steps beyond Turing. Biosystems 77:175–194

    Article  Google Scholar 

  • Copeland BJ (1998) Super Turing-machines. Complexity 4:30–32

    Article  MathSciNet  Google Scholar 

  • Davies EB (2001) Building infinite machines. Br J Philos Sci 52:671–682

    Article  MathSciNet  MATH  Google Scholar 

  • Davis M (2000) The universal computer. W.W. Norton, New York

    MATH  Google Scholar 

  • Denning PJ (2012) Reflections on a symposium on computation. Comput J 55:799–802

    Article  Google Scholar 

  • Denning PJ, Dennis JB, Qualitz JE (1978) Machines, languages, and computation. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Deutsch D (1997) The fabric of reality. Penguin Books, London

    Google Scholar 

  • 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

    Google Scholar 

  • Etesi G, Nemeti I (2002) Non-Turing computations via Malament-Hogarth space-times. Int J Theor Phys 41:341–370

    Article  MathSciNet  MATH  Google Scholar 

  • Fraser R, Akl SG (2008) Accelerating machines: a review. Int J Parallel Emergent Distrib Syst 23:81–104

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Chapter  Google Scholar 

  • Harel D (1992) Algorithmics: the spirit of computing. Addison-Wesley, Reading

    MATH  Google Scholar 

  • Hillis D (1998) The pattern on the stone. Basic Books, New York

    Google Scholar 

  • Hopcroft JE, Ullman JD (1969) Formal languages and their relations to automata. Addison-Wesley, Reading

    MATH  Google Scholar 

  • Lewis HR, Papadimitriou CH (1981) Elements of the theory of computation. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Mandrioli D, Ghezzi C (1987) Theoretical foundations of computer science. Wiley, New York

    MATH  Google Scholar 

  • Minsky ML (1967) Computation: finite and infinite machines. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  • 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

    Chapter  Google Scholar 

  • Nagy M, Akl SG (2006) Quantum measurements and universal computation. Int J Unconv Comput 2:73–88

    Google Scholar 

  • Nagy M, Akl SG (2007a) Quantum computing: beyond the limits of conventional computation. Int J Parallel Emergent Distrib Syst 22:123–135

    Article  MathSciNet  MATH  Google Scholar 

  • Nagy M, Akl SG (2007b) Parallelism in quantum information processing defeats the universal computer. Par Proc Lett 17:233–262

    Article  MathSciNet  Google Scholar 

  • 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

    Chapter  Google Scholar 

  • Nagy N, Akl SG (2012) Computing with uncertainty and its implications to universality. Int J Parallel Emergent Distrib Syst 27:169–192

    Article  Google Scholar 

  • Savage JE (1998) Models of computation. Addison-Wesley, Reading

    MATH  Google Scholar 

  • Siegelmann HT (1999) Neural networks and analog computation: beyond the Turing limit. Birkhauser, Boston

    Book  MATH  Google Scholar 

  • Sipser M (1997) Introduction to the theory of computation. PWS Publishing Company, Boston

    MATH  Google Scholar 

  • Steinhart E (2007) Infinitely complex machines. In: Schuster A (ed) Intelligent computing everywhere. Springer, New York, pp 25–43

    Chapter  Google Scholar 

  • Stepney S (2004) The neglected pillar of material computation. Physica D 237 :1157–1164

    Google Scholar 

  • Toffoli T (1982) Physics and computation. Int J Theor Phys 21:165–175

    Article  MathSciNet  Google Scholar 

(B) Books and Reviews

  • Akl SG (2004) Superlinear performance in real-time parallel computation. J Supercomput 29:89–111

    Article  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • Einstein A (2009) Letter to Erwin Schrodinger. In: Gilder L (ed) The age of entanglement. Vintage Books, New York, p 170

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    MATH  Google Scholar 

  • Lloyd S (2006) Programming the universe. Knopf, New York

    Google Scholar 

  • Lloyd S, Ng YJ (2004) Black hole computers. Sci Am 291:53–61

    Article  Google Scholar 

  • Rucker R (2005) The lifebox, the seashell, and the soul. Thunder’s Mouth Press, New York

    Google Scholar 

  • Seife C (2006) Decoding the universe. Viking Penguin, New York

    Google Scholar 

  • Siegfried T (2000) The bit and the pendulum. Wiley, New York

    Google Scholar 

  • Stepney S (2004) Journeys in non-classical computation. In: Hoare T, Milner R (eds) Grand challenges in computing research. BCS, Swindon, pp 29–32

    Google Scholar 

  • Tipler FJ (1995) The physics of immortality: modern cosmology, God and the resurrection of the dead. Macmillan, London

    Google Scholar 

  • Turing AM (1939) Systems of logic based on ordinals. Proc London Math Soc 2 45:161–228

    Article  MathSciNet  MATH  Google Scholar 

  • Vedral V (2010) Decoding reality. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Wegner P, Goldin D (1997) Computation beyond Turing machines. Comm ACM 46:100–102

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Wheeler JA (1994) At home in the universe. American Institute of Physics Press, Wood-bury

    Google Scholar 

  • Wolfram S (2002) A new kind of science. Wolfram Media, Champaign

    MATH  Google Scholar 

  • Zuse K (1970) Calculating space. MIT Technical Translation AZT-70-164-GEMIT, Massachusetts Institute of Technology (Project MAC), Cambridge

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computing and Department of Mathematics and Statistics, Queen’s University, Kingston, ON, K7L 3N6, Canada

    Selim G. Akl

Authors
  1. Selim G. Akl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Selim G. Akl .

Editor information

Editors and Affiliations

  1. Ramtech Ltd., Larkspur, California, USA

    Robert A. Meyers

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Science+Business Media LLC

About this entry

Cite this entry

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

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-27737-5_680-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27737-5

  • Online ISBN: 978-3-642-27737-5

  • eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics

Publish with us

Policies and ethics

Search

Navigation