Abstract
A language is factorial if it is closed under taking factors (i.e. contiguous subwords). Every factorial language can be described by an antidictionary, i.e. a minimal set of forbidden factors. We show that the problem of deciding whether a factorial language given by a finite antidictionary is well-quasi-ordered under the factor containment relation can be solved in polynomial time.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Atkinson, M.D., Murphy, M.M., Ruškuc, M.: Partially well-ordered closed sets of permutations. Order 19(2), 101–113 (2002)
Brignall, R., Ruškuc, N., Vatter, V.: Simple permutations: decidability and unavoidable substructures. Theoretical Computer Science 391(1-2), 150–163 (2008)
Cherlin, G.L., Latka, B.J.: Minimal antichains in well-founded quasi-orders with an application to tournaments. J. Comb. Theory, Ser. B 80(2), 258–276 (2000)
Crochemore, M., Mignosi, F., Restivo, A.: Automata and forbidden words. Inf. Process. Lett. 67(3), 111–117 (1998)
Ding, G.: Subgraphs and well-quasi-ordering. J. Graph Theory 16(5), 489–502 (1992)
Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theor. Comput. Sci. 256(1-2), 63–92 (2001)
Hine, N., Oxley, J.: When excluding one matroid prevents infinite antichains. Advances in Applied Mathematics 45(1), 74–76 (2010)
Korpelainen, N., Lozin, V.V.: Two forbidden induced subgraphs and well-quasi-ordering. Discrete Mathematics 311(6), 1813–1822 (2011)
Kruskal, J.B.: The theory of well-quasi-ordering: a frequently discovered concept. J. Comb. Theory, Ser. A 13(3), 297–305 (1972)
de Luca, A., Varricchio, S.: Well quasi-orders and regular languages. Acta Inf. 31(6), 539–557 (1994)
Robertson, N., Seymour, P.: Graph Minors. XX. Wagner’s conjecture. J. Comb. Theory, Ser. B 92(2), 325–357 (2004)
Spielman, D.A., Bóna, M.: An infinite antichain of permutations. The Electr. J. Comb. 7 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Atminas, A., Lozin, V., Moshkov, M. (2013). Deciding WQO for Factorial Languages. In: Dediu, AH., MartÃn-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2013. Lecture Notes in Computer Science, vol 7810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37064-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-37064-9_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37063-2
Online ISBN: 978-3-642-37064-9
eBook Packages: Computer ScienceComputer Science (R0)