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Non-deterministic languages to express deterministic transformations

Authors:
Serge Abiteboul
I.N.R.I.A., BP. 105, 78153 Le Chesnay, France
,
Eric Simon
I.N.R.I.A., BP. 105, 78153 Le Chesnay, France
,
Victor Vianu
CSE Dept., U.C. San Diego
Authors Info & Claims
Published: 02 April 1990 Publication History

Abstract

The use of non-deterministic database languages is motivated using pragmatic and theoretical considerations. It is shown that non-determinism resolves some difficulties concerning the expressive power of deterministic languages: there are non-deterministic languages expressing low complexity classes of queries/updates, whereas no such deterministic languages exist. Various mechanisms yielding non-determinism are reviewed. The focus is on two closely related families of non-deterministic languages. The first consists of extensions of Datalog with negations in bodies and/or heads of rules, with non-deterministic fixpoint semantics. The second consists of non-deterministic extensions of first-order logic and fixpoint logics, using the witness operator. The ability of the various non-deterministic languages to express deterministic transformation is characterized. In particular, non-deterministic languages expressing exactly the queries/updates computable in polynomial time are exhibited, whereas it is conjectured that no analogous deterministic language exists. The connection between non-deterministic languages and determinism is also explored. Several problems of practical interest are examined, such as checking (statically or dynamically) if a given program is deterministic, detecting coincidence of deterministic and non-deterministic semantics, and verifying termination for non-deterministic programs.

References

[1]
Abiteboul, S., G. Grahne, Update Semantics for Incomplete Databases, VLDB (1985), 1-12.
[2]
Abiteboul, S., R. Hull, Data Functions, Datalog and Negation, SIGMOD (1988), 143-153.
[3]
Abiteboul, S., E. Simon, Fundamental Properties of Deterministic and Non-deterministic Extensions of Datalog, submitted to Theoretical Computer Science.
[4]
Abiteboul, S., V.Vianu, Fixpoint Extensions of First-Order Logic and Datalog-like Languages, Proc. Fourth Syrup. on Logic in Computer Science (1989), 71-79.
[5]
Abiteboul, S., V. Vianu, Datalog extensions for database updates and queries, I.N.R.I.A. Technical Report No.715 (1988). Submitted to J. of Computer and Systems Science.
[6]
Chandra, A.K., Programming Primitives for Database Languages, Proc. ACM Symposium on Principles of Programming Languages, Williamsburg (1981), 50-62.
[7]
Chandra, A.K., D. ttarel, Computable Queries for Relational Databases, Journal of Computer and System Sciences 21:2 (1980), 156-178.
[8]
Chandra, A., M. Vardi, The Implication Problem for Functional and Inclusion Dependencies is Undecidable, SIAM J. Computing 14,3 (1985), 671-677.
[9]
Fagin, R., Generalized First-Order Spectra and Polynomial-Time Recognizable Sets, Complezity o/ Computation, ed. tt.Karp, SIAM-AMS Proc. 7 (1974), 43-73.
[10]
Gurevich, Y., S. Shelah, Fixed-Point Extensions of First-Order Logic, 26th Symp. on Found. of Comp. Sci. (1985), 346-353.
[11]
Imielinski, T., W. Lipski, Incomplete Information in Relational Databases, JACM 31, 4 (1984), 761-791.
[12]
Immerman, N., Relational Queries Computable in Polynomial Time, Inf. and Control 68 (1986), 86-104.
[13]
Immerman, N., Languages Which Capture Complexity Classes, SIAM J. Computing 16, 4 (1987), 760-778.
[14]
de Kleer, J., An Assumption-based Truth Maintenance System, Artificial Intelligence 28 (1), Jan. 1986, 127-162.
[15]
Leisenring, A.C., Mathematical Logic and Hilbert's e-symbol. Gordon and Breach ed. (1969).
[16]
de Maindreville, C., E. Simon, Modelling Non-deterministic Queries and Updates in Deductive Databases, Proc. of Internat. Conf. on Very Large Databases, 1988, Los Angeles.
[17]
Naqvi, S., S.Tsur, A Logical Language .for Data and Knowledge Bases, Computer Science Press, New York (1989).
[18]
Sagiv, Y., Optimizing Datalog Programs, Proc. 6th ACM Symp. on Principles of Database Systems, (1987), 349-362.
[19]
Shmueli, O., Decidability and expressiveness aspects of logic queries, Proc. 6th ACM Symp. on Principles of Database Systems, 1987, 237-249.
[20]
Simon, E., C. de Maindreville, Deciding whether a production rule is relational computable, Proc. 2nd Internat. Conf. on Database Theory, 1988, Bruges, Belgium.
[21]
Ullman, J.D., Principles of Database and Knowledge Base Systems, Computer Science Press (1988).
[22]
Vardi, M., Relational Queries Computable in Polynomial Time, 14th ACM Symp. on Theory of Computing (1982), 137-146.

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cover image ACM Conferences
PODS '90: Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
April 1990
425 pages
ISBN:0897913523
DOI:10.1145/298514
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Permissions@acm.org

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Published: 02 April 1990

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  • (2018)When Can We Answer Queries Using Result-Bounded Data Interfaces?Proceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3196959.3196965(281-293)Online publication date: 27-May-2018
  • (2015)Partial grounded fixpointsProceedings of the 24th International Conference on Artificial Intelligence10.5555/2832581.2832638(2784-2790)Online publication date: 25-Jul-2015
  • (2013)Datalog and Recursive Query ProcessingFoundations and Trends in Databases10.1561/19000000175:2(105-195)Online publication date: 21-Nov-2013
  • (2012)Win-move is coordination-free (sometimes)Proceedings of the 15th International Conference on Database Theory10.1145/2274576.2274588(99-113)Online publication date: 26-Mar-2012
  • (2010)Fixed-point definability and polynomial time on chordal graphs and line graphsFields of logic and computation10.5555/1983702.1983721(328-353)Online publication date: 1-Jan-2010
  • (2010)Fixed-Point Definability and Polynomial Time on Chordal Graphs and Line GraphsFields of Logic and Computation10.1007/978-3-642-15025-8_17(328-353)Online publication date: 2010
  • (2008)Towards a logic for abstract metafinite state machinesProceedings of the 5th international conference on Foundations of information and knowledge systems10.5555/1786094.1786120(365-380)Online publication date: 11-Feb-2008
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  • (2005)Deterministic semantics for datalog ⌝: complexity and expressive powerDeductive and Object-Oriented Databases10.1007/3-540-63792-3_24(337-350)Online publication date: 17-Aug-2005
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References

References

[1]
Abiteboul, S., G. Grahne, Update Semantics for Incomplete Databases, VLDB (1985), 1-12.
[2]
Abiteboul, S., R. Hull, Data Functions, Datalog and Negation, SIGMOD (1988), 143-153.
[3]
Abiteboul, S., E. Simon, Fundamental Properties of Deterministic and Non-deterministic Extensions of Datalog, submitted to Theoretical Computer Science.
[4]
Abiteboul, S., V.Vianu, Fixpoint Extensions of First-Order Logic and Datalog-like Languages, Proc. Fourth Syrup. on Logic in Computer Science (1989), 71-79.
[5]
Abiteboul, S., V. Vianu, Datalog extensions for database updates and queries, I.N.R.I.A. Technical Report No.715 (1988). Submitted to J. of Computer and Systems Science.
[6]
Chandra, A.K., Programming Primitives for Database Languages, Proc. ACM Symposium on Principles of Programming Languages, Williamsburg (1981), 50-62.
[7]
Chandra, A.K., D. ttarel, Computable Queries for Relational Databases, Journal of Computer and System Sciences 21:2 (1980), 156-178.
[8]
Chandra, A., M. Vardi, The Implication Problem for Functional and Inclusion Dependencies is Undecidable, SIAM J. Computing 14,3 (1985), 671-677.
[9]
Fagin, R., Generalized First-Order Spectra and Polynomial-Time Recognizable Sets, Complezity o/ Computation, ed. tt.Karp, SIAM-AMS Proc. 7 (1974), 43-73.
[10]
Gurevich, Y., S. Shelah, Fixed-Point Extensions of First-Order Logic, 26th Symp. on Found. of Comp. Sci. (1985), 346-353.
[11]
Imielinski, T., W. Lipski, Incomplete Information in Relational Databases, JACM 31, 4 (1984), 761-791.
[12]
Immerman, N., Relational Queries Computable in Polynomial Time, Inf. and Control 68 (1986), 86-104.
[13]
Immerman, N., Languages Which Capture Complexity Classes, SIAM J. Computing 16, 4 (1987), 760-778.
[14]
de Kleer, J., An Assumption-based Truth Maintenance System, Artificial Intelligence 28 (1), Jan. 1986, 127-162.
[15]
Leisenring, A.C., Mathematical Logic and Hilbert's e-symbol. Gordon and Breach ed. (1969).
[16]
de Maindreville, C., E. Simon, Modelling Non-deterministic Queries and Updates in Deductive Databases, Proc. of Internat. Conf. on Very Large Databases, 1988, Los Angeles.
[17]
Naqvi, S., S.Tsur, A Logical Language .for Data and Knowledge Bases, Computer Science Press, New York (1989).
[18]
Sagiv, Y., Optimizing Datalog Programs, Proc. 6th ACM Symp. on Principles of Database Systems, (1987), 349-362.
[19]
Shmueli, O., Decidability and expressiveness aspects of logic queries, Proc. 6th ACM Symp. on Principles of Database Systems, 1987, 237-249.
[20]
Simon, E., C. de Maindreville, Deciding whether a production rule is relational computable, Proc. 2nd Internat. Conf. on Database Theory, 1988, Bruges, Belgium.
[21]
Ullman, J.D., Principles of Database and Knowledge Base Systems, Computer Science Press (1988).
[22]
Vardi, M., Relational Queries Computable in Polynomial Time, 14th ACM Symp. on Theory of Computing (1982), 137-146.