Skip to main content
SpringerLink
Log in

Lattice-valued General Orthomodular Automata

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

In recent years, the rapid development of quantum computation has stimulated researchers to establish a theory of computation based on quantum logic. The present study therefore aims to introduce the notion of lattice-valued general orthomodular automaton, for simplicity, lattice-valued GOA. The class of languages, accepted by lattice-valued GOA, is also defined and explicated. Moreover, the acceptance abilities of lattice-valued GOA and their various modifications are compared. Finally, the closure properties of orthomodular languages as union, complement and product are consequently derived.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Abolpour, K., Zahedi, M.M.: Isomorphism between two BL-general fuzzy automata. Soft. Comput. 16729–736 (2012)

  2. Abolpour, K., Zahedi, M.M.: BL-General fuzzy automata and accept behavior. J. Appl. Math. Comput. 38, 103–118 (2012)

    Article  MATH  Google Scholar 

  3. Abolpour, K., Zahedi, M.M.: General fuzzy automata based on complete residuated Lattice-Valued. Iranian Journal of Fuzzy Systems 14, 103–121 (2017)

    MATH  Google Scholar 

  4. Abolpour, K. h., Zahedi, M.M., Shamsizadeh, M.: BL-general fuzzy automata and minimal realization: Based on the associated categories. Iranian Journal of Fuzzy Systems 17, 155–169 (2020)

    MATH  Google Scholar 

  5. Abolpour, K., Zahedi, M.M.: LB-valued general fuzzy automata. Fuzzy Set. Syst. 442, 288–308 (2022)

    Article  Google Scholar 

  6. Benioff, P.A.: The computer as a physical system: a microscopic quantum mechanical Hamiltonian model of computer s as represented by Turing machines. J. Statist. Phys. 22, 563–591 (1980)

    Article  ADS  MATH  Google Scholar 

  7. Beran, L.: Orthomodular Lattice (Algebraic Approach), D. Reidel Publishing Company, Dordrecht/Boston/Lancaster (1985)

  8. Birkhoff, G., von Neumann, J.: The logic of quantum mechanics. Ann. Math. 37, 823–843 (1936)

    Article  MATH  Google Scholar 

  9. Bruns, G., Harding, J.: Algebraic Aspects of Orthomodular Lattices. In: Coecke, B., Moore, D., Wilce, A. (eds.) Current Research in Operational Quantum Logic: Algebras, Categories, Languages., pp 37–65. Kluwer, Dordrecht (2000)

  10. Cirac, J.I., Zoller, P.: Quantum computation with cold trapped ions. Phys. Rev. Lett. 74, 4091–4094 (1995)

    Article  ADS  Google Scholar 

  11. Crutchfield, J.P., Moore, C.: Quantum automata and quantum grammar. Theoret. Comput. Sci. 237, 275–306 (2000)

    Article  MATH  Google Scholar 

  12. Deutsch, D.: Quantum theory, the Church–Turing principle and the universal quantum computer. Proc. Roy. Soc. Lond. A400, 97–117 (1985)

    ADS  MATH  Google Scholar 

  13. Deutsch, D.: Quantum computational networks. Proc. Roy. Soc. Lond. A425, 73–90 (1989)

    ADS  MATH  Google Scholar 

  14. Doostfatemeh, M., Kremer, S.C.: New directions in fuzzy automata. Int. J. Approx. Reason. 38, 175–214 (2005)

    Article  MATH  Google Scholar 

  15. Feynman, R.P.: Simulating physics with computers. Int. J. Theoret. Phys. 21, 467–488 (1982)

    Article  Google Scholar 

  16. Gudder, S.: Basic properties of quantum automata. Found. Phys. 30, 301–319 (2000)

    Article  Google Scholar 

  17. Kalmbach, G.: Orthomodular logic. Z. Math. Logik Grundlagen Math. 20, 395–406 (1974)

    Article  MATH  Google Scholar 

  18. Kalmbach, G.: Orthomodular Lattices. Academic Press, London (1983)

    MATH  Google Scholar 

  19. Kondacs, A., Watrous, J.: On the power of quantum finite state automata. In: Proceedings 38th Annual Symposium on Foundations of Computer Science, pp 65–75 (1997)

  20. Lloyd, S.: Apotentially realizable quantum computer. Science 261, 1569–1571 (1993)

    Article  ADS  Google Scholar 

  21. Takeuti, G.: Quantum Set Theory. In: Beltrametti, E., van Fraassen, B. C. (eds.) Current Issues in Quantum Logics, pp 303–322. Plenum, New York (1981)

  22. Yao, A.C.: Quantum circuit complexity. Proceedings 34th Annual IEEE Symposium on Foundations of Computer Science 352–361 (1993)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran

    Kh. Abolpour

  2. Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran

    M. M. Zahedi

  3. Department of Mathematics, Behbahan Khatam Alanbia University of Technology, Khouzestan, Iran

    M. Shamsizadeh

Authors
  1. Kh. Abolpour
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. M. Zahedi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Shamsizadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kh. Abolpour.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abolpour, K., Zahedi, M.M. & Shamsizadeh, M. Lattice-valued General Orthomodular Automata. Int J Theor Phys 62, 13 (2023). https://doi.org/10.1007/s10773-022-05242-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10773-022-05242-3

Keywords

Search

Navigation