2017/08/22 by Simon Beier, Markus Holzer, Martin Kutrib · 1 citation
Computer Science · #cs.FL
paper · pdf · doi:10.4204/eptcs.252.8
published as EPTCS 252, 2017, pp. 41-55 · In Proceedings AFL 2017, arXiv:1708.06226
arxiv created 2017/08/22 · arxiv updated 2017/08/23
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].