Advertisement

Equational Systems on Posets and Their Applications

  • 2 Accesses

Abstract

In this paper, we introduce the notion of nonlinear equational systems. We consider some important results of equational systems on posets (partially ordered sets) and Banach lattices. Also we see their applications in data-flow analysis—a general theory to solve some special types of simultaneous nonlinear equations on complete lattices—and extend the Cournot oligopoly on Banach lattices. At the end, there are some new theoretical suggestions for decision makers, especially computer program designers, to shorten and optimize their calculations.

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

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

References

  1. Abramsky S, Jung A (1994) Domain theory in handbook of logic in computer science. Oxford University Press, Oxford, pp 1–168

  2. Agakov F, Bonilla E, Cavazos J, Franke B, Fursin G, OBoyle MFP, Thomson J, Toussaint M, Williams CKI (2004) Using machine learning to focus iterative optimization. In: Proceedings of the international symposium on code generation and optimization, San Jose, CA, USA, pp 20–24

  3. Bastoul C, Cohen A, Cavazos J, Pouchet LN (2008) Iterative optimization in the polyhedral model: part II, multidimensional time. In: Proceedings of the ACM SIGPLAN conference on programming language design and implementation (PLDI’08), Tucson, AZ, USA, pp 90–100

  4. Burden RL, Faires JD (2005) Numerical analysis, Chapt. 10, 9th edn. Thomson Brooks, Cole

  5. Chakrabarti SK (2010) Equilibrium in Cournot oligopolies with unknown costs. Int Econ Rev 51:1209–1238

  6. Davey BA, Priestley HA (2012) Introduction to lattices and order. Cambridge University Press, Cambridge

  7. Garin J, Lester R, Sims E (2018) Intermediate macro economics. University of Notre Dame Press, Notre Dame

  8. Goguen J, Thatcher J, Wagner E (1976) An initial algebra approach to the specification, correctness and implementation of abstract data types. IBM Thomas J. Watson Research Center, New York

  9. Hennessy M, Plotkin G (1979) Full abstraction for a simple parallel programming language. Math Found Comput Sci 74:108–120

  10. Karkare B, Khedker U, Sanyal A (2009) Data flow analysis: theory and practice. CRC Press, Boca Raton

  11. Kuhn K, Vives X (1994) Information exchanges among firms and their impact on competition. Institut dAnalisi Economica, Barcelona

  12. Larsen KS (2007) A note on lattices and fixed points. Department of Mathematics and Computer Science, University of Southern Denmark, Odense

  13. Li L (1985) Cournot oligopoly with information sharing. Rand J Econ 16:521–536

  14. Nalebuff BJ, Zeckhauser RJ (1986) Pensions and the retirement decision. University of Chicago Press, Chicago

  15. Plotkin G (2019) Pisa notes (on domain theory). http://homepages.inf.ed.ac.uk/gdp/publications/Domains_a4.ps

  16. Rasmusen E (2001) Games and information: an introduction to game theory, 3rd edn. Wiley-Blackwell, Hoboken

  17. Schaefer HH (1974) Banach lattices and positive operators. Springer, Berlin

  18. Schroder BSW (2002) Ordered sets: an introduction. Birkhauser, Boston

  19. Tarski A (1955) A lattice-theoretical fixed point theorem and its application. Pac J Math 5:285–309

Download references

Author information

Correspondence to Hamidreza Goudarzi.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Roointan, G., Goudarzi, H. Equational Systems on Posets and Their Applications. Iran J Sci Technol Trans Sci (2020) doi:10.1007/s40995-019-00808-z

Download citation

Keywords

  • Equational systems
  • Data-flow analysis
  • Partially ordered sets
  • Preserving maps
  • Monotone property
  • Iterative algorithm
  • Banach lattice
  • Cournot oligopoly