We consider the regularity-preserving operations of intersection and marked catenation and construct an infinite sequence Ci, i = 1, 2,..., of compositions formed from the two operations. We construct also an infinite sequence of polynomials Si, i = 1, 2,..., with positive integer coefficients. As a main result we prove that it is undecidable whether or not Si is a state complexity function of Ci. All languages needed are over a fixed alphabet with at most 50 letters. We also consider some implications and generalizations, as well as present some open problems. © 2011 Springer-Verlag.
CITATION STYLE
Salomaa, A., Salomaa, K., & Yu, S. (2011). Undecidability of the state complexity of composed regular operations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6638 LNCS, pp. 489–498). Springer Verlag. https://doi.org/10.1007/978-3-642-21254-3_39
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