Abstract
This paper demonstrates the generation of a linear time query processing algorithm based on the constructive proof of Higman’s lemma described by Murthy-Russell (IEEE LICS 1990). A linear time evaluation of a fixed disjunctive monadic query in an indefinite database on a linearly ordered domain, first posed by Van der Meyden (ACM PODS 1992), is used as an example. Van der Meyden showed the existence of a linear time algorithm, but an actual construction has, until now, not been published elsewhere.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Chomicki. Temporal query languages: a survey. In D.M. Gabbay and H.J. Ohlbach, editors, Temporal Logic: (ICTL’94), pages 506–534, 1994. Lecture Notes in Artificial Intelligence, Vol. 827, Springer-Verlag.
T. Coquand and D. Fridlender. A proof of Higman’s lemma by structural induction, November 1993. available at http://www.md.chalmers.se/~coquand/intuitionism.html.
R.M. Fellows and M.A. Langston. Nonconstructive tools for proving polynomialtime decidability. Journal of the ACM, 35(3):727–739, 1988.
D. Fridlender. Higman’s lemma in type theory. In E. Gimnez and C. P.-Mohring, editors, Types for Proofs andPr ograms, TYPES’96, pages 112–133, 1996. Lecture Notes in Computer Science, Vol. 1512, Springer-Verlag.
A. Geser. A proof of Higman’s lemma by open induction. Technical Report MIP-9606, Passau University, April 1996.
A. Gupta. A constructive proof that tree are well-quasi-ordered under minors. In A. Nerode and M. Taitslin, editors, Logical foundations of computer science-Tver’92, pages 174–185, 1992. Lecture Notes in Computer Science, Vol. 620, Springer-Verlag.
G. Higman. Ordering by divisibility in abstract algebras. Proc. London Mathematical Society, 2:326–336, 1952.
M. Koubarakis. The complexity of query evaluation in indefinite temporal constraint databases. Theoretical Computer Science, 171:25–60, 1997.
C.R. Murthy and J.R. Russell. A constructive proof of Higman’s lemma. In Proc. 5th IEEE sympo. on Logic in Computer Science, pages 257–267, 1990.
C.ST.J.A. Nash-Williams. On well-quasi-ordering finite trees. Proc. Cambridge Phil. Soc., 59:833–835, 1963.
N. Dershowitz and Z. Manna. Proving termination with multiset orderings. Communications of the ACM, 22(8):465–476, 1979.
L. Perković and B. Reed. An improved algorithm for finding tree decompositions of small width. In et.al. Widmayer, editor, WG’99, pages 148–154, 1999. Lecture Notes in Computer Science, Vol. 1665, Springer-Verlag.
F. Richman and G. Stolzenberg. Well quasi-ordered sets. Advances in Mathematics, 97:145–153, 1993.
N. Robertson and P.D. Seymour. Graph minors XX. Wagner’s conjecture, 1988. Manuscript.
N. Robertson and P.D. Seymour. Graph minors XIII. the disjoint path problem. Journal of Combinatorial Theory Series B, 63:65–110, 1995.
S.G. Simpson. Ordinal numbers and the Hilbert basis theorem. Journal of Symbolic Logic, 53(3):961–974, 1988.
W. Thomas. Automata on infinite objects. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B, chapter 4, pages 133–192. Elsevier Science Publishers, 1990.
R. van der Meyden. The complexity of querying indefinite data about linearly ordered domains. Journal of Computer andSystem Science, 54(1):113–135, 1997. Previously presented at 11th ACM sympo. on Principles of Database Systems, pp.331-345, 1992.
W. Veldman. An intuitionistic proof of Kruskal’s theorem. Technical Report 17, Department of Mathematics, University of Nijmegen, April 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ogawa, M. (2001). Generation of a Linear Time Query Processing Algorithm Based on Well-Quasi-Orders. In: Kobayashi, N., Pierce, B.C. (eds) Theoretical Aspects of Computer Software. TACS 2001. Lecture Notes in Computer Science, vol 2215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45500-0_14
Download citation
DOI: https://doi.org/10.1007/3-540-45500-0_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42736-0
Online ISBN: 978-3-540-45500-4
eBook Packages: Springer Book Archive