Skip to main content
SpringerLink
Log in

Algorithmen – Berechenbarkeit und Komplexität

  • Chapter
  • First Online:
Grundkurs Informatik

  • 17k Accesses

Zusammenfassung

In den vorigen Kapiteln wurde gezeigt, dass die durch einen Computer zu bearbeitenden Aufgaben durch eine endliche Folge elementarer Anweisungen beschrieben werden müssen, und zwar letztlich in Maschinensprache. Eine solche Beschreibung, wie eine Aufgabe auszuführen ist, bezeichnet man als Algorithmus. Der Begriff Algorithmus leitet sich vom Namen des arabischen Gelehrten Al Chwarizmi ab, der um 820 lebte.

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

Access this chapter

Log in via an institution
eBook
USD 24.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  • [Abe96] H. Abelson und G. Sussman. Structure and Interpretation of Computer Programs. MIT Press, 2. Aufl., 1996.

    Google Scholar 

  • [Ack28] W. Ackermann. Zum Hilbertschen Aufbau der reellen Zahlen. Mathematische Annalen, 99:118–133, 1928.

    Google Scholar 

  • [Agr04] M. Agrawal, N. Kayal und N. Saxena. Primes is in P. Annals of Mathematics, 160(2):781–793, 2004.

    Google Scholar 

  • [Aho13] A. Aho, M. Lam und R. Sethi. Compilers. Addison-Wesley Longman, 2013.

    Google Scholar 

  • [App76] K. Appel und W. Haken. Every Planar Map is Four Colorable. Bulletin of the American Mathematical Society, 82(5):711–712, Sept. 1976.

    Google Scholar 

  • [App77] K. Appel und W. Haken. Every Planar Map is Four Colorable. Illinois Journal of Mathematics, 21(3):429–567, Sept. 1977.

    Google Scholar 

  • [App07] D. L. Applegate, R. E. Bixby, V. Chvátal und W. J. Cook. The Traveling Salesman Problem: A Computational Study. Princeton Series in Applied Mathematics. Princeton University Press, Princeton, NJ, USA, 2007.

    Google Scholar 

  • [Bac94] P. Bachmann. Die analytische Zahlentheorie. Teubner, 1894.

    Google Scholar 

  • [Box58] G. E. P. Box und M. E. Muller. A Note on the Generation of Random Normal Deviates. The Annals of Mathematical Statistics, 29:610–611, 1958.

    Google Scholar 

  • [Bra13] S. Brandt. Datenanalyse für Naturwissenschaftler und Ingenieure. Springer Spektrum, 5. Aufl., 2013.

    Google Scholar 

  • [Cha66] G. J. Chaitin. On the Length of Programs for Computing Finite Binary Sequences. J. ACM, 13(4):547–569, 1966.

    Google Scholar 

  • [Coo71] S. A. Cook. The Complexity of Theorem-proving Procedures. In Proceedings of the Third Annual ACM Symposium on Theory of Computing, STOC ’71, S. 151–158. ACM, New York, NY, USA, 1971.

    Google Scholar 

  • [Cor09] T. H. Cormen, C. E. Leiserson, R. L. Rivest und C. Stein. Introduction to Algorithms. The MIT Press, 3. Aufl., 2009.

    Google Scholar 

  • [Cra05] R. Crandall und C. B. Pomerance. Prime Numbers: A Computational Perspective. Springer, 2. Aufl., 2005.

    Google Scholar 

  • [Erk09] K. Erk und L. Priese. Theoretische Informatik. Eine umfassende Einführung. Springer, 3. Aufl., 2009.

    Google Scholar 

  • [Fra81] A. S. Fraenkel und D. Lichtenstein. Computing a Perfect Strategy for n × n Chess Requires Time Exponential in n. J. Comb. Theory, Ser. A, 31(2):199–214, 1981.

    Google Scholar 

  • [Für07] M. Fürer. Faster integer multiplication. In D. S. Johnson und U. Feige, Hg., STOC, S. 57–66. ACM, 2007.

    Google Scholar 

  • [Für09] M. Fürer. Faster Integer Multiplication. SIAM J. Comput., 39(3):979–1005, 2009.

    Google Scholar 

  • [Göd31] K. Gödel. Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik, 38:173–198, 1931.

    Google Scholar 

  • [Gon08a] G. Gonthier. Formal Proof – The Four-Color Theorem. Notices of the American Mathematical Society, 55(11):1382–1393, Dez. 2008.

    Google Scholar 

  • [Gon08b] G. Gonthier. The Four Colour Theorem: Engineering of a Formal Proof. In D. Kapur, Hg., Computer Mathematics, S. 333–333. Springer-Verlag, Berlin, Heidelberg, 2008.

    Google Scholar 

  • [Her65] H. Hermes. Enumerability, Decidability, Computability. Springer, 1965.

    Google Scholar 

  • [Her07] A. M. Herzberg und M. Murty. Sudoku Squares and Chromatic Polynomials. Int. Math. Nachr., Wien, 206:1–19, 2007.

    Google Scholar 

  • [Hof11] D. Hoffmann. Theoretische Informatik. Hanser, 2. Aufl., 2011.

    Google Scholar 

  • [Kar63] A. Karatsuba und Y. Ofman. Multiplication of Many-Digital Numbers by Automatic Computers. Soviet Physics-Doklady, 7:595–596, 1963. Übersetzung des russischen Originals aus Doklady Akad. Nauk SSSR. Vol. 145, 1962, S. 293–294.

    Google Scholar 

  • [Kar72] R. M. Karp. Reducibility Among Combinatorial Problems. In R. E. Miller und J. W. Thatcher, Hg., Complexity of Computer Computations, The IBM Research Symposia Series, S. 85–103. Plenum Press, New York, 1972.

    Google Scholar 

  • [Knu97a] D. E. Knuth. The Art of Computer Programming, Volume 1: Fundamental Algorithms. Addison-Wesley, 3. Aufl., 1997.

    Google Scholar 

  • [Knu97b] D. E. Knuth. The Art of Computer Programming, Volume 2: Seminumerical Algorithms. Addison-Wesley, 3. Aufl., 1997.

    Google Scholar 

  • [Kol65] A. N. Kolmogorov. Three Approaches to the Quantitative Definition of Information. Problems of Information Transmission, 1(1):3–11, 1965.

    Google Scholar 

  • [Leh49] D. H. Lehmer. Mathematical Methods in Large-scale Computing Units. In Proc. of a Second Symposium on Large-Scale Digital Calculating Machinery, S. 141–146. 1949.

    Google Scholar 

  • [Lic78] D. Lichtenstein und M. Sipser. GO Is PSPACE Hard. In FOCS, S. 48–54. IEEE Computer Society, 1978.

    Google Scholar 

  • [Lin68] A. Lindenmayer. Mathematical Models for Cellular Interaction in Development: Parts I and II. Journal of Theoretical Biology, 18:280–315, 1968.

    Google Scholar 

  • [Lud98] R. Ludwig. Kant für Anfänger: Die Kritik der reinen Vernunft. Deutscher Taschenbuch Verlag, 1998.

    Google Scholar 

  • [Man87] B. Mandelbrot. Die fraktale Geometrie der Natur. Birkhäuser, 1987.

    Google Scholar 

  • [Mar64] G. Marsaglia und T. Bray. A Convenient Method for Generating Normal Variables. SIAM Review, 6(3):260–264, 1964.

    Google Scholar 

  • [MB95] R. Morales-Bueno. Noncomputability is easy to understand. Communications of the ACM, 38(8):116–117, 1995.

    Google Scholar 

  • [Mey67] A. R. Meyer und D. M. Ritchie. The Complexity of Loop Programs. In Proceedings of the 1967 22 nd National Conference, ACM ’67, S. 465–469. ACM, 1967.

    Google Scholar 

  • [Mil] Millennium Problems. http://www.claymath.org/millenniumproblems.

  • [Mil75] G. L. Miller. Riemann’s Hypothesis and Tests for Primality. In Proceedings of Seventh Annual ACM Symposium on Theory of Computing, STOC ’75, S. 234–239. ACM, New York, NY, USA, 1975.

    Google Scholar 

  • [Mil76] G. L. Miller. Riemann’s Hypothesis and Tests for Primality. Journal of Computer and System Sciences, 13(3):300–317, Dez. 1976.

    Google Scholar 

  • [Pre07] W. H. Press, S. A. Teukolsky, W. T. Vetterling und B. P. Flannery. Numerical Recipes 3rd Edition: The Art of Scientific Computing. Cambridge University Press, New York, NY, USA, 3. Aufl., 2007.

    Google Scholar 

  • [Pri98] I. Prigogine. Die Gesetze des Chaos. Insel Verlag, 1998.

    Google Scholar 

  • [Pru96] P. Prusinkiewicz und A. Lindenmayer. The Algorithmic Beauty of Plants. Springer, New York, NY, USA, 1996.

    Google Scholar 

  • [Rab80] M. O. Rabin. Probabilistic Algorithm for Testing Primality. Journal of Number Theory, 12(1):128–138, 1980.

    Google Scholar 

  • [Rad62] T. Radó. On non-computable functions. The Bell System Technical Journal, 41(3):877–884, 1962.

    Google Scholar 

  • [Ric53] H. G. Rice. Classes of Recursively Enumerable Sets and Their Decision Problems. Transactions of the American Mathematical Society, 74:358–366, 1953.

    Google Scholar 

  • [Rob83] J. Robson. The Complexity of Go. In IFIP Congress, S. 413–417. 1983.

    Google Scholar 

  • [Rob84] J. Robson. N by N Checkers is Exptime Complete. SIAM Journal on Computing, 13(2):252–267, 1984.

    Google Scholar 

  • [San95] P. Sander, W. Stucky und R. Herschel. Grundkurs Angewandte Informatik IV: Automaten, Sprachen, Berechenbarkeit. Vieweg+Teubner, 2. Aufl., 1995.

    Google Scholar 

  • [Sch71] A. Schönhage und V. Strassen. Schnelle Multiplikation großer Zahlen. Computing, 7:281–292, 1971.

    Google Scholar 

  • [Sch08] U. Schöning. Theoretische Informatik – kurz gefasst. Spektrum Akad. Verlag, 5. Aufl., 2008.

    Google Scholar 

  • [Sed11] R. Sedgewick und K. Wayne. Algorithms. Addison-Wesley, 4. Aufl., 2011.

    Google Scholar 

  • [Sed13] R. Sedgewick und P. Flajolet. An Introduction to the Analysis of Algorithms. Addison Wesley, 2. Aufl., 2013.

    Google Scholar 

  • [Tur36] A. M. Turing. On Computable Numbers, with an Application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, 2(42):230–265, 1936.

    Google Scholar 

  • [Woe03] G. J. Woeginger. Exact Algorithms for NP-Hard Problems: A Survey. In M. Jünger, G. Reinelt und G. Rinaldi, Hg., Combinatorial Optimization – Eureka, You Shrink!, Bd. 2570 von Lecture Notes in Computer Science, S. 185–207. Springer, 2003.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FB Informatik, Hochschule Rosenheim FB Informatik, Rosenheim, Deutschland

    Hartmut Ernst

  2. Hochschule Rosenheim, Rosenheim, Deutschland

    Jochen Schmidt & Gerd Beneken

Authors
  1. Hartmut Ernst
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jochen Schmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gerd Beneken
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hartmut Ernst .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Fachmedien Wiesbaden

About this chapter

Cite this chapter

Ernst, H., Schmidt, J., Beneken, G. (2016). Algorithmen – Berechenbarkeit und Komplexität. In: Grundkurs Informatik. Springer Vieweg, Wiesbaden. https://doi.org/10.1007/978-3-658-14634-4_11

Download citation

Publish with us

Policies and ethics

Search

Navigation