H-bounded and semi-discrete languages

M. Kunze, H.J. Shyr, G. Thierrin
1981 Information and Control  
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, some
more » ... es of the syntactic monoid Synt(L) of an h-bounded (semi-discrete) language are derived. If L is not disjunctive, then Synt(L) contains a zero element: Every subgroup of Synt(L) is a finite cyclic group. The idempotents of Synt(L)\{0, 1} form an antichain with respect to the usual partial order.
doi:10.1016/s0019-9958(81)90253-9 fatcat:56yhkvdt3fbeziz6o32tgf7rke