A programming language for the inductive sets, and applications

  • David Harel
  • Dexter Kozen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 140)


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].


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  1. [AU]
    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. [AP]
    Apt, K. and G. Plotkin, A Cook's Tour of Countable Nondeterminism, ICALP '81.Google Scholar
  3. [B]
    Barwise, J. Admissible Sets & Structures. Springer-Verlag 1975.Google Scholar
  4. [CH1]
    Chandra, A.K. and D. Harel, Computable queries for relational data bases. JCSS 21; 2, Oct. 1980.Google Scholar
  5. [CH2]
    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. [CH3]
    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. [CKS]
    Chandra, A.K., D. Kozen and L. Stockmeyer, Alternation, J. ACM, Jan. 1981.Google Scholar
  8. [C1]
    Codd, E.F., A relational model for large shared data bases. CACM 13; 6, June 1970.Google Scholar
  9. [C2]
    Codd, E.F., Relational completeness of data base sublanguages. In Data Base Systems (Rustin, ed.), Prentice Hall, 1972.Google Scholar
  10. [C]
    Cook, S.A. Soundness and Completeness of an Axiom System for Program Verification, SIAM J. on Computing 7; 1, (1978).Google Scholar
  11. [GM]
    Gallaire, H. and J. Minker (eds.), Logic and Data Bases, Plenum, New York (1978).Google Scholar
  12. [GFMR]
    Grumberg, Francez, Makowsky and de Roever, A Proof Rule for fair Termination of Guarded Commands, Technion Tech. Report #197, Feb. 1981.Google Scholar
  13. [H]
    Harel, D. First-Order Dynamic Logic. Lecture Notes in Computer Science 68, Springer-Verlag 1979.Google Scholar
  14. [I]
    Immerman, N. Relational queries computable in polynomial ti, e. 14th ACM Symp. on Theory of Computing, May 1982.Google Scholar
  15. [K]
    Kowalski, R.A. Predicate logic as a programming language. Proc. IFIP74, North-Holland 1974, 556–574.Google Scholar
  16. [LPS]
    Lehman, D., A. Pnueli and J. Stavi, Impartiality, Justice and Fairness: The Ethics of Concurrent Termination, ICALP '81.Google Scholar
  17. [MT]
    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. [MP]
    Meyer, A.R. and R. Parikh, Definability in Dynamic Logic, Proc. 12th ACM Symp. on Theory of Computing (1980), 1–8.Google Scholar
  19. [MW]
    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. [Mi]
    Mirkowska, G. On Formalized Systems of Algorithmic Logic, Bull. Acad. Pol. Sci., Ser. Math. Astr. Phys. 22 (1974), 421–428.Google Scholar
  21. [Mo]
    Moschovakis, Y.N. Elementary Induction on Abstract Structure, North-Holland, 1974.Google Scholar
  22. [Pr]
    Pratt, V. Semantical Considerations on Floyd-Hoare Logic. Proc. 17th IEEE Symp. on Found, of Comp. Science, (1976), 109–121.Google Scholar
  23. [T]
    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

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • David Harel
    • 1
  • Dexter Kozen
    • 2
  1. 1.The Weizmann InstituteRehovotIsrael
  2. 2.Aarhus UniversityAarhusDenmark

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