...s. 1 Introduction A number of recent papers have investigated the language of all primitive words over an alphabet of at least two letters, and considered its placement to the Chomsky-hierarchy (see $=-=[1]-=--[7]$ ). In [1] the authors conjectured that this language is not context-free. This conjecture is still open. To help the research on this problem, in this report we consider certain ‘small’ and ‘max...

...ubcases, based on the productions involving $S$ : (a) Start generating with one of the productions $\{Sarrow XY, Sarrow YX, Sarrow XZ, Sarrow ZX\}$ . In this case the $n(Y)\pm 1=n(Z)$ equation holds. =-=(6)-=- Now start with the production $Sarrow$ yZ. We receive a skeleton which is letter-isomorphic to the case 9 of the 3 nonterminals which was proved in [4]. (The $X” x$ $XX$ production is unnecessary.) 6...

...ATH Department of Computer Science Institute of Mathematics and Informatics University of Debrecen Debrecen, Egyetem ter 1, $\mathrm{H}$-4032, Hungary $\mathrm{e}$-mail: geza@math.klte.hu Abstract In =-=[4]-=- P&l Domosi, Dirk Hauschildt, Geza Horvath and Manfred Kudlek gave all context-free grammars in Chomsky normal form with not more than three nonterminals generating only primitive words. In this paper...