Skip to main content
SpringerLink
Log in

Decidability of confluence and termination of monadic term rewriting systems

  • Conference paper
  • First Online:
Book cover Rewriting Techniques and Applications (RTA 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 488))

Included in the following conference series:

Abstract

Term rewriting systems where the right-hand sides of rewrite rules have height at most one are said to be monadic. These systems are a generalization of the well known monadic Thue systems. We show that termination is decidable for right-linear monadic systems but undecidable if the rules are only assumed to be left-linear. Using the Peterson-Stickel algorithm we show that confluence is decidable for right-linear monadic term rewriting systems. It is known that ground confluence is undecidable for both left-linear and right-linear monadic systems. We consider partial results for deciding ground confluence of linear monadic systems.

This research has been supported by the Academy of Finland.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Bachmair and N. Dershowitz, Completion for rewriting modulo a congruence, Theoret. Comput. Sci. 67 (1989) 173–201.

    Google Scholar 

  2. R.V. Book, Confluent and other types of Thue systems, J.Assoc.Comput.Mach. 29 (1982) 171–182.

    Google Scholar 

  3. R.V. Book, Thue systems as rewriting systems, J. Symbolic Computation 3 (1987) 39–68.

    Google Scholar 

  4. R.V. Book, M. Jantzen and C. Wrathall, Monadic Thue systems, Theoret. Comput. Sci. 19 (1982) 231–251.

    Google Scholar 

  5. M. Dauchet, Simulation of Turing machines by a left-linear rewrite-rule, Proc. of 3rd RTA, Lect. Notes Comput. Sci. 355 (1989) 109–120.

    Google Scholar 

  6. M.Dauchet, S.Tison, T.Heuillard and P.Lescanne, Decidability of the confluence of ground term rewriting systems, Proc. of the 2nd LICS, 1987, 353–359.

    Google Scholar 

  7. N. Dershowitz, Termination of rewriting, J. Symbolic Computation 3 (1987) 69–116.

    Google Scholar 

  8. N. Dershowitz, Completion and its applications, in: H.Aït-Kaci and M.Nivat, eds., Resolution of equations in algebraic structures, Vol. 2, Academic Press (1989) 31–85.

    Google Scholar 

  9. N. Dershowitz and J.-P. Jouannaud, Rewrite systems, in: J. van Leeuwen, ed., Handbook of Theoretical Computer Science, Vol. B, Elsevier (1990) 243–320.

    Google Scholar 

  10. F. Fages and G. Huet, Complete sets of unifiers and matchers in equational theories, Theoret. Comput. Sci. 43 (1986) 189–200.

    Google Scholar 

  11. J.H. Gallier and R.V. Book, Reductions in tree replacement systems, Theoret. Comput. Sci. 37 (1985) 123–150.

    Google Scholar 

  12. F.Gécseg and M.Steinby, Tree automata, Akadémiai Kiadó, 1984.

    Google Scholar 

  13. R. Göbel, Ground confluence, Proc. of the 2nd RTA, Lect. Notes Comput. Sci. 256 (1987) 156–167.

    Google Scholar 

  14. T.Harju and J.Karhumäki, Decidability of the multiplicity equivalence of multitape finite automata, Proceedings of the 22nd STOC (1990) 477–481.

    Google Scholar 

  15. A.Herold, Combination of unification algorithms in equational theories, Ph.D. thesis, University of Kaiserslautern, 1987.

    Google Scholar 

  16. G. Huet, Confluent reductions: Abstract properties and applications to term rewriting systems, J. Assoc. Comput. Mach. 27 (1980) 797–821.

    Google Scholar 

  17. G. Huet and D.S. Lankford, On the uniform halting problem for term rewriting systems, Rapport Laboria 283, INRIA, Le Chesnay, France, 1978.

    Google Scholar 

  18. G.Huet and D.C.Oppen, Equations and rewrite rules, in: R.V.Book, ed., Formal language theory, Perspectives and open problems, Academic Press (1980) 349–393.

    Google Scholar 

  19. M.Jantzen, Confluent string rewriting, EATCS Monographs on Theoretical Computer Science 14, Springer-Verlag, 1988.

    Google Scholar 

  20. J.-P. Jouannaud and H. Kirchner, Completion of a set of rules modulo a set of equations, SIAM J. Comput. 15 (1986) 1155–1194.

    Google Scholar 

  21. D. Kapur, P. Narendran and F. Otto, On ground confluence of term rewriting systems, Information and computation 86 (1990) 14–31.

    Google Scholar 

  22. J.W. Klop, Term rewriting systems: From Church-Rosser to Knuth-Bendix and beyond, Proc. of 17th ICALP, Lect. Notes Comput. Sci. 443 (1990) 350–369.

    Google Scholar 

  23. D.Knuth and P.Bendix, Simple word problems in universal algebras, in: J.Leech, ed., Computational problems in abstract algebra, Pergamon Press (1970) 263–297.

    Google Scholar 

  24. G.A. Kucherov, A new quasi-reducibility testing algorithm and its application to proofs by induction, Proc. of Algebraic and Logic Programming '88, Lect. Notes Comput. Sci. 343 (1988) 204–213.

    Google Scholar 

  25. M.H.A. Newman, On theories with a combinatorial definition of “equivalence”, Ann. Math. 43 (1942) 223–243.

    Google Scholar 

  26. M. Oyamaguchi, The Church-Rosser property for ground term-rewriting systems is decidable, Theoret. Comput. Sci. 49 (1987) 43–79.

    Google Scholar 

  27. G. Peterson and M. Stickel, Complete sets of reductions for some equational theories, J. Assoc. Comput. Mach. 28 (1981) 233–264.

    Google Scholar 

  28. K. Salomaa, Deterministic tree pushdown automata and monadic tree rewriting systems, J. Comput. System Sci. 37 (1988) 367–394.

    Google Scholar 

  29. M. Schmidt-Schauss, Solution to problem P140 and P141, Bull. of EATCS 34 (1988) 274–275.

    Google Scholar 

  30. M. Schmidt-Schauss, Unification in permutative equational theories is undecidable, J. Symbolic Computation 8 (1989) 415–421.

    Google Scholar 

  31. J. Siekmann, Matching under commutativity, Proc. of EUROSAM'79, Lect. Notes Comput. Sci. 72 (1979) 531–545.

    Google Scholar 

  32. L. Slagle, Automated theorem proving for theories with simplifiers, commutativity and associativity, J. Assoc. Comput. Mach. 21 (1974) 622–642.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Turku, SF-20500, Turku, Finland

    Kai Salomaa

Authors
  1. Kai Salomaa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Ronald V. Book

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Salomaa, K. (1991). Decidability of confluence and termination of monadic term rewriting systems. In: Book, R.V. (eds) Rewriting Techniques and Applications. RTA 1991. Lecture Notes in Computer Science, vol 488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53904-2_103

Download citation

  • DOI: https://doi.org/10.1007/3-540-53904-2_103

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53904-9

  • Online ISBN: 978-3-540-46383-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation