Skip to main content
Log in

Characterizing sets of data structures by the connectivity relation

  • Published:
International Journal of Computer & Information Sciences Aims and scope Submit manuscript

Abstract

A formalism based on the directed graph connectivity relation is presented, in which a first-order predicate calculus notation is used with the purpose of defining sets of data structures and characterizing the structural operations on them. The formalism is designed so as to facilitate the proof that the intended operations on instances of a given set of data structures are correct, in the sense that they do not violate the structural form of the data.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. M. Burstall, “Some Techniques for Proving Correctness of Programs Which Alter Data Structures,” inMachine Intelligence 7 (Edinburgh University Press, Edinburgh, 1972).

    Google Scholar 

  2. C. Hoare, “Notes on Data Structuring,” inStructured Programming (Academic Press, New York, 1972).

    Google Scholar 

  3. T. Standish, “Data Structures — An Axiomatic Approach,” TR2639 (Bolt, Beranek and Newman, 1973).

    Google Scholar 

  4. C. C. Gotlieb and A. L. Furtado, “Data Schemata Based on Directed Graphs,” Technical Report 70, University of Toronto, Toronto (1974).

    Google Scholar 

  5. J. Earley, Toward an Understanding of Data Structures,Commun. ACM 14(10), 617–627 (October 1971).

    Google Scholar 

  6. A. Rosenberg, Data Graphs and Addressable Schemes,J. Comput. Syst. Sci. 5(6), 193–238 (1971).

    Google Scholar 

  7. C. Bachman, Data Structure Diagrams,Data Base — ACM/SIGBDP 1, 2 (1969).

    Google Scholar 

  8. P. Suppes,Axiomatic Set Theory (Van Nostrand, 1967).

  9. T. L. Booth,Sequential Machines and Automata Theory (John Wiley, New York, 1967).

    Google Scholar 

  10. E. F. Codd, A Relational Model for Large Shared Data Banks,Commun. ACM 13(6), 377–387 (1970).

    Google Scholar 

  11. D. Knuth,The Art of Computer Programming, Vol. 1 (Addison-Wesley, Reading, Massachusetts, 1968).

    Google Scholar 

  12. N. J. Nilsson,Problem-Solving Methods in Artificial Intelligence (McGraw-Hill, New York, 1971).

    Google Scholar 

  13. C. J. P. Lucena, “On the Synthesis of Reliable Programs,” Ph.D. thesis, UCLA, Los Angeles (1975).

    Google Scholar 

  14. O. Dahl, “Hierarchical Program Structures,” inStructured Programming (Academic Press, New York, 1972).

    Google Scholar 

  15. B. Liskov and S. Zilles, Programming with Abstract Data Types,Proc. Symp. Very High Level Languages, ACM/SIGPLAN, 50–59 (1974).

  16. J. Pfaltz and A. Rosenfeld, “Web Grammars,” Technical Report 69–84, University of Maryland (1969).

  17. J. Mylopoulos, On the Relation of Graph Grammars and Graph Automata,Proc. 13th SWAT 108–120 (1972).

  18. D. G. Corneil, “The Analysis of Graph Theoretical Algorithms,” Technical Report 65, University of Toronto, Toronto (1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Furtado, A.L. Characterizing sets of data structures by the connectivity relation. International Journal of Computer and Information Sciences 5, 89–109 (1976). https://doi.org/10.1007/BF00975627

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00975627

Key words

Navigation