Abstract
The existence of a language expressing precisely the PTIME queries on arbitrary structures remains the central open problem in the theory of database query languages. As it turns out, two variants of this question have been formulated. Surprisingly, despite the importance of the problem, the relationship between these variants has not been systematically explored. A first contribution of the present paper is to revisit the basic definitions and clarify the connection between these two variants. We then investigate two relaxations to the original problem that appear as tempting alternatives in the absence of a language for the PTIME queries. The first consists in trying to express the PTIME queries using a richer language that can also express queries beyond PTIME, but for which there exists a query processor evaluating all PTIME queries in PTIME. The second approach, studied by many researchers, is to focus on PTIME properties on restricted sets of graphs. Our results are mostly negative, and point out limitations to both approaches. Finally, we turn to a natural class of languages that we call finitely generated, whose syntax is obtained by applying a fixed set of constructors to a given set of building blocks. We identify a broad class of such languages that cannot express all the PTIME queries.
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References
Abiteboul, S., Hull, R., Vianu, V.: Foundations of databases. Addison-Wesley, Reading (1995)
Blass, A., Gurevich, Y., Shelah, S.: Choiceless polynomial time. Annals of Pure and Applied Logic 100, 141–187 (1999)
Chandra, A., Harel, D.: Structure and complexity of relational queries. J. Comput. Syst. Sci. 25(1), 99–128 (1982)
Dawar, A., Hella, L.: The expressive power of finitely many generalized quantifiers. Inf. Comput. 123(2), 172–184 (1995)
Ebbinghaus, H.-D., Flum, J.: Finite Model Theory, 2nd edn. Springer, Heidelberg (1999)
Fagin, R.: Generalized first-order spectra and polynomial-time recognizable sets. In: Karp, R. (ed.) Complexity of Computation, pp. 43–73. SIAM-AMS Proceedings (1974)
Grohe, M.: The structure of fixed-point logics. PhD thesis, Albert-Ludwigs Universität Freiburg (1994)
Grohe, M.: Fixed-point logics on planar graphs. In: Proc. Symp. on Logic in Computer Science (1998)
Gurevich, Y.: Logic and the challenge of computer science. In: Borger, E. (ed.) Trends in Theoretical Computer Science, pp. 1–57. Computer Science Press, Rockville (1988)
Hopcroft, J., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison Wesley, Reading (1979)
Immerman, N.: Relational queries computable in polynomial time. Information and Control 68, 86–104 (1986)
Vardi, M.Y.: The complexity of relational query languages. In: Proc. ACM SIGACT Symp. on the Theory of Computing, pp. 137–146 (1982)
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© 2004 Springer-Verlag Berlin Heidelberg
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Nash, A., Remmel, J., Vianu, V. (2004). PTIME Queries Revisited. In: Eiter, T., Libkin, L. (eds) Database Theory - ICDT 2005. ICDT 2005. Lecture Notes in Computer Science, vol 3363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30570-5_19
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DOI: https://doi.org/10.1007/978-3-540-30570-5_19
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