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A programming language for the inductive sets, and applications

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Automata, Languages and Programming (ICALP 1982)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 140))

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Abstract

We introduce a programming language IND that generalizes alternating Turing machines to arbitrary first-order structures. We show that IND programs (respectively, everywhere-halting IND programs, loop-free IND programs) accept precisely the inductively definable (respectively, hyperelementary, elementary) relations. We give several examples showing how the language provides a robust and computational approach to the theory of first-order inductive definability. We then show: (1) on all acceptable structures (in the sense of Moschovakis [Mo]), r.e. Dynamic Logic is more expressive than finite-test Dynamic Logic. This refines a separation result of Meyer and Parikh [MP]; (2) IND provides a natural query language for the set of fixpoint queries over a relational database, answering a question of Chandra and Harel [CH2].

Research supported in part by a Bath-Sheva fellowship.

Work done in part at IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA.

On leave from IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA.

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References

  1. Aho, A.V. and J.D. Ullman, Universality of data retrieval languages. Proc. 6th ACM Symp. on Principles of Programming Languages, Jan. 1979, 110–117.

    Google Scholar 

  2. Apt, K. and G. Plotkin, A Cook's Tour of Countable Nondeterminism, ICALP '81.

    Google Scholar 

  3. Barwise, J. Admissible Sets & Structures. Springer-Verlag 1975.

    Google Scholar 

  4. Chandra, A.K. and D. Harel, Computable queries for relational data bases. JCSS 21; 2, Oct. 1980.

    Google Scholar 

  5. Chandra, A.K. and D. Harel, Structure and Complexity of Relational Queries, Proc. 21st IEEE Symp. on Foundations of Computer Science, Oct. 1980, 333–347.

    Google Scholar 

  6. Chandra, A.K. and D. Harel, Horn clauses and the fixpoint query hierarchy. SIGACT-SIGMOD Symp. on Principles of Data Base Systems, March, 1982.

    Google Scholar 

  7. Chandra, A.K., D. Kozen and L. Stockmeyer, Alternation, J. ACM, Jan. 1981.

    Google Scholar 

  8. Codd, E.F., A relational model for large shared data bases. CACM 13; 6, June 1970.

    Google Scholar 

  9. Codd, E.F., Relational completeness of data base sublanguages. In Data Base Systems (Rustin, ed.), Prentice Hall, 1972.

    Google Scholar 

  10. Cook, S.A. Soundness and Completeness of an Axiom System for Program Verification, SIAM J. on Computing 7; 1, (1978).

    Article  MathSciNet  Google Scholar 

  11. Gallaire, H. and J. Minker (eds.), Logic and Data Bases, Plenum, New York (1978).

    MATH  Google Scholar 

  12. Grumberg, Francez, Makowsky and de Roever, A Proof Rule for fair Termination of Guarded Commands, Technion Tech. Report #197, Feb. 1981.

    Google Scholar 

  13. Harel, D. First-Order Dynamic Logic. Lecture Notes in Computer Science 68, Springer-Verlag 1979.

    Google Scholar 

  14. Immerman, N. Relational queries computable in polynomial ti, e. 14th ACM Symp. on Theory of Computing, May 1982.

    Google Scholar 

  15. Kowalski, R.A. Predicate logic as a programming language. Proc. IFIP74, North-Holland 1974, 556–574.

    Google Scholar 

  16. Lehman, D., A. Pnueli and J. Stavi, Impartiality, Justice and Fairness: The Ethics of Concurrent Termination, ICALP '81.

    Google Scholar 

  17. Meyer, A.R. and J. Tiuryn, A Note of Equivalences Among Logics of Programs. Proc. Workshop on Logics of Programs 1981, Lecture Notes in Computer Science 131, Springer-Verlag, 282–299.

    Google Scholar 

  18. Meyer, A.R. and R. Parikh, Definability in Dynamic Logic, Proc. 12th ACM Symp. on Theory of Computing (1980), 1–8.

    Google Scholar 

  19. Meyer, A.R. and K. Winkelmann, On the Expressive Power of Dynamic Logic, Proc. 12th ACM Symp. on Theory of Computing (1979), 167–175.

    Google Scholar 

  20. Mirkowska, G. On Formalized Systems of Algorithmic Logic, Bull. Acad. Pol. Sci., Ser. Math. Astr. Phys. 22 (1974), 421–428.

    MathSciNet  MATH  Google Scholar 

  21. Moschovakis, Y.N. Elementary Induction on Abstract Structure, North-Holland, 1974.

    Google Scholar 

  22. Pratt, V. Semantical Considerations on Floyd-Hoare Logic. Proc. 17th IEEE Symp. on Found, of Comp. Science, (1976), 109–121.

    Google Scholar 

  23. Tiuryn, J. Unbounded Program Memory adds to the Expressive Power of First-Order Dynamic Logic, Proc. 22nd IEEE Symp. on Found. of Comp. Science (1981).

    Google Scholar 

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Author information

Authors and Affiliations

  1. The Weizmann Institute, Rehovot, Israel

    David Harel

  2. Aarhus University, Aarhus, Denmark

    Dexter Kozen

Authors
  1. David Harel
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  2. Dexter Kozen
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Editor information

Mogens Nielsen Erik Meineche Schmidt

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© 1982 Springer-Verlag Berlin Heidelberg

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Harel, D., Kozen, D. (1982). A programming language for the inductive sets, and applications. In: Nielsen, M., Schmidt, E.M. (eds) Automata, Languages and Programming. ICALP 1982. Lecture Notes in Computer Science, vol 140. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0012779

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  • DOI: https://doi.org/10.1007/BFb0012779

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11576-2

  • Online ISBN: 978-3-540-39308-5

  • eBook Packages: Springer Book Archive

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