The goodness of {S, a}-EOL forms is decidable

Decidability problems constitute one of the central topics in formal language theory. In the theory of grammatical similarity, in particular the theory of EOL forms, a lot of decidability questions arise. Some of them are proved to be decidable, e.g., m-completeness for some subclass of EOL forms (see [2] and [3]), simulations of one EOL form by another EOL form (see [6], [7] and [S]), vompleteness of EOL forms (see [17]). Other problems turn out to be undecidable, e.g., the x-form equivalence problem where x is the full uniform interpretation mechanism (see [ll]) or the nonterminal fixed mechanism (see [16]). By now many problems are open or only partially solved, e.g., the completeness problem (see [5]) and the form equivalence problem (see [lo]) for EOL forms (under the ordinary interpretation mechanism as defined in [lo]). In this paper we attack the following problem: for an EOL form F is it decidable whether or not F is good. Goodness of EOL forms is first defined in [ 121 and further studied in [13]. In [12] also examples of good and bad EOL forms are given. A lot of conditions on EOL forms which imply badness are given in the literature (see [l], [4], [13], [IS] and [18]). We will concentrate on {S,a}-EOL forms, i.e., EOL forms with one nonterminal and one terminal. The paper is organized as follows. In Section 1 we recall some basics of the theory of EOL systems and forms and give some basic conditions which must hold in a good EOL form. In the following sections we study several subclasses of {S, a}-EOL forms separately, i.e., terminal propagating forms in Section 2, terminal erasing