Monadic Logic Programs and Functional Complexity

Problems related to the complexity and to the decidability of several languages weaker than Prolog are studied in this paper. In particular, monadic logic programs, that is, programs containing only monadic functions and monadic predicates, are considered in detail. The functional complexity of a monadic logic program is the language of all words fi fk such that the literal p(fi(...(fk(a)). ..)) IS a logical consequence of the program. The relationship between several subclasses of monadic programs, their functional complexities and the corresponding automata is studied. It is proved that the class of monadic programs corresponds exactly to the class of regular languages. As a consequence, the “SUCCESS” problem is decidable for that class. It is also proved that the success set of a specific subclass of monadic programs (“simple” programs) corresponds exactly to regular languages with star-height not exceeding 1.