Abstract
The notion of EOL forms was introduced by Maurer, Salomaa and Wood recently. The study of complete EOL form is of particular interest since it suggests to attempt a systematic classification of all possible short normal forms for EOL systems. In this paper we investigate under which conditions an EOL form with a single nonterminal S and a single terminal a with the length of the right side of each production one or two is complete. We can summarize the main results in this paper as follows. 1. (1) We present a complete analysis of the case when both productions a→ S and S→ S occur. 2. (2) We show that each complete form must contain at least one of a→ S, S→ S. 3. (3) We are not able to give a complete analysis if exactly one of a→ S, S→ S occurs but we show that in both cases complete forms with only four productions exist.
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