Abstract
Given a set I of words, the set L\(_{\rm \vdash}^{\epsilon}~_{\rm I}\) of all words obtained by the shuffle of (copies of) words of I is naturally provided with a partial order: for u, v in L\(_{\rm \vdash}^{\epsilon}~_{\rm I}\), u \(\vdash^{\rm *}_{I}\) v if and only if v is the shuffle of u and another word of L\(_{\rm \vdash}^{\epsilon}~_{\rm I}\). In [3], the authors have stated the problem of the characterization of the finite sets I such that \(\vdash_{I}^{\rm *}\) is a well quasi-order on L\(_{\rm \vdash}^{\epsilon}~_{\rm I}\). In this paper we give the answer in the case when I consists of a single word w.
This work was partially supported by MIUR project “Linguaggi formali e automi: teoria e applicazioni”.
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
D’Alessandro, F., Varricchio, S.: On Well Quasi-orders On Languages. In: Ésik, Z., Fülöp, Z. (eds.) DLT 2003. LNCS, vol. 2710, pp. 230–241. Springer, Heidelberg (2003)
D’Alessandro, F., Varricchio, S.: Well quasi-orders and context-free grammars. Theoretical Computer Science 327(3), 255–268 (2004)
D’Alessandro, F., Varricchio, S.: Well quasi-orders, unavoidable sets, and derivation systems. RAIRO Theoretical Informatics and Applications (to appear)
de Luca, A., Varricchio, S.: Well quasi-orders and regular languages. Acta Informatica 31, 539–557 (1994)
de Luca, A., Varricchio, S.: Finiteness and regularity in semigroups and formal languages. EATCS Monographs on Theoretical Computer Science. Springer, Berlin (1999)
Ehrenfeucht, A., Haussler, D., Rozenberg, G.: On regularity of context-free languages. Theoretical Computer Science 27, 311–332 (1983)
Harju, T., Ilie, L.: On quasi orders of words and the confluence property. Theoretical Computer Science 200, 205–224 (1998)
Haussler, D.: Another generalization of Higman’s well quasi-order result on Σ*. Discrete Mathematics 57, 237–243 (1985)
Higman, G.H.: Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 3, 326–336 (1952)
Ilie, L., Salomaa, A.: On well quasi orders of free monoids. Theoretical Computer Science 204, 131–152 (1998)
Intrigila, B., Varricchio, S.: On the generalization of Higman and Kruskal’s theorems to regular languages and rational trees. Acta Informatica 36, 817–835 (2000)
Ito, M., Kari, L., Thierrin, G.: Shuffle and scattered deletion closure of languages. Theoretical Computer Science 245(1), 115–133 (2000)
Jantzen, M.: Extending regular expressions with iterated shuffle. Theoretical Computer Science 38, 223–247 (1985)
Kruskal, J.: The theory of well-quasi-ordering: a frequently discovered concept. J. Combin. Theory, Ser. A 13, 297–305 (1972)
Lothaire: Combinatorics on words. Series Encyclopedia of Mathematics and its Applications, vol. 17. Addison-Wesley, Reading, Mass. (1983)
Puel, L.: Using unavoidable sets of trees to generalize Kruskal’s theorem. J. Symbolic Comput. 8(4), 335–382 (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
D’Alessandro, F., Richomme, G., Varricchio, S. (2006). Well Quasi Orders and the Shuffle Closure of Finite Sets. In: Ibarra, O.H., Dang, Z. (eds) Developments in Language Theory. DLT 2006. Lecture Notes in Computer Science, vol 4036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11779148_24
Download citation
DOI: https://doi.org/10.1007/11779148_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35428-4
Online ISBN: 978-3-540-35430-7
eBook Packages: Computer ScienceComputer Science (R0)