On the Descriptional Complexity of Operations on Semilinear Sets

Simon Beier
(Institut für Informatik, Universität Giessen)
Markus Holzer
(Institut für Informatik, Universität Giessen)
Martin Kutrib
(Institut für Informatik, Universität Giessen)

We investigate the descriptional complexity of operations on semilinear sets. Roughly speaking, a semilinear set is the finite union of linear sets, which are built by constant and period vectors. The interesting parameters of a semilinear set are: (i) the maximal value that appears in the vectors of periods and constants and (ii) the number of such sets of periods and constants necessary to describe the semilinear set under consideration. More precisely, we prove upper bounds on the union, intersection, complementation, and inverse homomorphism. In particular, our result on the complementation upper bound answers an open problem from [G. J. LAVADO, G. PIGHIZZINI, S. SEKI: Operational State Complexity of Parikh Equivalence, 2014].

In Erzsébet Csuhaj-Varjú, Pál Dömösi and György Vaszil: Proceedings 15th International Conference on Automata and Formal Languages (AFL 2017), Debrecen, Hungary, September 4-6, 2017, Electronic Proceedings in Theoretical Computer Science 252, pp. 41–55.
Published: 21st August 2017.

ArXived at: http://dx.doi.org/10.4204/EPTCS.252.8 bibtex PDF
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