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International Conference on Information and Communication Technologies in Education, Research, and Industrial Applications

ICTERI 2019: Information and Communication Technologies in Education, Research, and Industrial Applications pp 50–67Cite as

Expressibility in the Kleene Algebra of Partial Predicates with the Complement Composition

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1175))

Abstract

In the paper we investigate the expressibility of partial predicates in the Kleene algebra extended with the composition of predicate complement and give a necessary and sufficient condition of this expressibility in terms of the existence of an optimal solution of an optimization problem. We also investigate the expressibility in the first-order Kleene algebra with predicate complement. The obtained results may be useful for software verification using an extension of the Floyd-Hoare logic for partial pre- and postconditions.

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Notes

  1. 1.

    The maximum cardinality of a subset such that any two of its distinct points are at the same distance.

  2. 2.

    If one interprets partiality in terms as possibility, minimization of ||f|| may be related to the principle of minimum specificity of D. Dubois et al. from possibility theory, or other similar principles.

References

  1. Wiik, J., Boström, P.: Contract-based verification of MATLAB and simulink matrix-manipulating code. In: Merz, S., Pang, J. (eds.) ICFEM 2014. LNCS, vol. 8829, pp. 396–412. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11737-9_26

    Chapter  Google Scholar 

  2. Floyd, R.: Assigning meanings to programs. Math. Aspects Comput. Sci. 19, 19–32 (1967)

    Article  MathSciNet  Google Scholar 

  3. Hoare, C.: An axiomatic basis for computer programming. Commun. ACM 12(10), 576–580 (1969)

    Article  Google Scholar 

  4. Ivanov, I., Korniłowicz, A., Nikitchenko, M.: Implementation of the composition-nominative approach to program formalization in Mizar. Comput. Sci. J. Moldova 26, 59–76 (2018)

    MathSciNet  MATH  Google Scholar 

  5. Ivanov, I., Korniłowicz, A., Nikitchenko, M.: Formalization of nominative data in Mizar. In: Proceedings of TAAPSD 2015, 23–26 December 2015, pp. 82–85. Taras Shevchenko National University of Kyiv, Ukraine (2015)

    Google Scholar 

  6. Ivanov, I.: An abstract block formalism for engineering systems. In: Ermolayev, V., et al. (eds.) Proceedings of the 9th International Conference on ICT in Education, Research and Industrial Applications: Integration, Harmonization and Knowledge Transfer, Kherson, Ukraine, June 19–22, 2013. CEUR Workshop Proceedings, vol. 1000, pp. 448–463. CEUR-WS.org (2013)

    Google Scholar 

  7. Ivanov, I.: On existence of total input-output pairs of abstract time systems. In: Ermolayev, V., Mayr, H.C., Nikitchenko, M., Spivakovsky, A., Zholtkevych, G. (eds.) ICTERI 2013. CCIS, vol. 412, pp. 308–331. Springer, Cham (2013). https://doi.org/10.1007/978-3-319-03998-5_16

    Chapter  Google Scholar 

  8. Ivanov, I.: On representations of abstract systems with partial inputs and outputs. In: Gopal, T.V., Agrawal, M., Li, A., Cooper, S.B. (eds.) TAMC 2014. LNCS, vol. 8402, pp. 104–123. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-06089-7_8

    Chapter  Google Scholar 

  9. Ivanov, I., Nikitchenko, M.: Inference rules for the partial floyd-hoare logic based on composition of predicate complement. In: Ermolayev, V., Suárez-Figueroa, M.C., Yakovyna, V., Mayr, H.C., Nikitchenko, M., Spivakovsky, A. (eds.) ICTERI 2018. CCIS, vol. 1007, pp. 71–88. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-13929-2_4

    Chapter  Google Scholar 

  10. Korniłowicz, A., Ivanov, I., Nikitchenko, M.: Kleene algebra of partial predicates. Formalized Math. 26, 11–20 (2018)

    Article  Google Scholar 

  11. Korniłowicz, A., Kryvolap, A., Nikitchenko, M., Ivanov, I.: An approach to formalization of an extension of Floyd-Hoare logic. In: Proceedings of the 13th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer, Kyiv, Ukraine, May 15–18, 2017, pp. 504–523 (2017)

    Google Scholar 

  12. Kornilowicz, A., Kryvolap, A., Nikitchenko, M., Ivanov, I.: Formalization of the algebra of nominative data in Mizar. In: Ganzha, M., Maciaszek, L.A., Paprzycki, M. (eds.) Proceedings of the 2017 Federated Conference on Computer Science and Information Systems. ACSIS, vol. 11, pp. 237–244 (2017)

    Google Scholar 

  13. Korniłowicz, A., Kryvolap, A., Nikitchenko, M., Ivanov, I.: Formalization of the nominative algorithmic algebra in Mizar. In: Świątek, J., Borzemski, L., Wilimowska, Z. (eds.) ISAT 2017. AISC, vol. 656, pp. 176–186. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-67229-8_16

    Chapter  Google Scholar 

  14. Kryvolap, A., Nikitchenko, M., Schreiner, W.: Extending floyd-hoare logic for partial pre- and postconditions. In: Ermolayev, V., Mayr, H.C., Nikitchenko, M., Spivakovsky, A., Zholtkevych, G. (eds.) ICTERI 2013. CCIS, vol. 412, pp. 355–378. Springer, Cham (2013). https://doi.org/10.1007/978-3-319-03998-5_18

    Chapter  Google Scholar 

  15. Nikitchenko, M., Kryvolap, A.: Properties of inference systems for Floyd-Hoare logic with partial predicates. Acta Electrotechnica et Informatica 13(4), 70–78 (2013)

    Article  Google Scholar 

  16. Nikitchenko, M., Ivanov, I., Korniłowicz, A., Kryvolap, A.: Extended floyd-hoare logic over relational nominative data. In: Bassiliades, N., et al. (eds.) ICTERI 2017. CCIS, vol. 826, pp. 41–64. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76168-8_3

    Chapter  Google Scholar 

  17. Nikitchenko, N.S.: A composition nominative approach to program semantics. Technical report, IT-TR 1998–020, Technical University of Denmark (1998)

    Google Scholar 

  18. Skobelev, V., Nikitchenko, M., Ivanov, I.: On algebraic properties of nominative data and functions. In: Ermolayev, V., Mayr, H., Nikitchenko, M., Spivakovsky, A., Zholtkevych, G. (eds.) ICTERI 2014. CCIS, vol. 469, pp. 117–138. Springer, Cham (2014)

    Chapter  Google Scholar 

  19. Yablonskii, S.: Functional constructions in a k-valued logic. Trudy Mat. Inst. Steklov. 51, 5–142 (1958)

    MathSciNet  Google Scholar 

  20. Nikitchenko, M., Shkilniak, O., Shkilniak, S., Mamedov, T.: Completeness of the logic of partial quasiary predicates with the complement composition. In: Proceedings of the Conference on Mathematical Foundations of Informatics MFOI 2019, July 3–6, 2019, Iasi, Romania (2019)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, 64/13, Volodymyrska Street, Kyiv, 01601, Ukraine

    Ievgen Ivanov & Mykola Nikitchenko

Authors
  1. Ievgen Ivanov
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  2. Mykola Nikitchenko
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Correspondence to Ievgen Ivanov .

Editor information

Editors and Affiliations

  1. Zaporizhzhia National University, Zaporizhzhia, Ukraine

    Vadim Ermolayev

  2. Université Cote d’Azur, Nice, France

    Frédéric Mallet

  3. University of Warmia and Mazury in Olsztyn, Olsztyn, Poland

    Vitaliy Yakovyna

  4. University of Klagenfurt, Klagenfurt am Wörthersee, Austria

    Heinrich C. Mayr

  5. Kherson State University, Kherson, Ukraine

    Aleksander Spivakovsky

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Ivanov, I., Nikitchenko, M. (2020). Expressibility in the Kleene Algebra of Partial Predicates with the Complement Composition. In: Ermolayev, V., Mallet, F., Yakovyna, V., Mayr, H., Spivakovsky, A. (eds) Information and Communication Technologies in Education, Research, and Industrial Applications. ICTERI 2019. Communications in Computer and Information Science, vol 1175. Springer, Cham. https://doi.org/10.1007/978-3-030-39459-2_3

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  • DOI: https://doi.org/10.1007/978-3-030-39459-2_3

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  • Online ISBN: 978-3-030-39459-2

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