A note on the descriptional complexity of semi-conditional grammars

The descriptional complexity of semi-conditional grammars (SCG) has been presented. Semi-conditional grammars (SCG) are context-free grammars with a permitting and a forbidding condition associated to each production. The class of recursively enumerable languages is characterized by SCGs of degree with six conditional productions and seven non terminals. It is proved that the class of recursively enumerable languages is characterized by simple SCGs of degree with eight conditional productions and nine non terminals. Simple semi-conditional grammars of degree with erasing productions characterize the class of recursively enumerable languages and the classes of languages generated by simple semi-conditional grammars of degree and with erasing productions are included in the class of recursive languages.