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Since every hypercode is finite, one may ask for the significance of the property that a language L admits a uniform upper bound on the size of hypercodes included in L. Such a language L is called h-bounded. We prove that a rational language L is h-bounded iff it is thin iff it is semi-diserete, i.e., L contains at most k words of any given length for some fixed k C N. Moreover, a representation of these languages by regular expressions is established. Concerning the general case, somedoi:10.1016/s0019-9958(81)90253-9 fatcat:56yhkvdt3fbeziz6o32tgf7rke