This chapter discusses various problems relating to the general synthesis problem in the meta-language situation. These include the existence, uniqueness, and construction of an automaton conforming to conditions expressed in the meta-language. The situation is similar to that obtaining, for example, in the theory of functional equations, when analogous questions arise for formulas of a certain
... [Show full abstract] meta-language, such as, differential equations. The investigation proceeds in regard to several meta-languages (sources, finite trees, regular formulas, ω-regular formulas) and, finally, a special meta-language (the language I) based on monadic second-order predicate logic. The aim of the argument presented in the chapter is to show that this meta-language is considerably more expressive than others. The algorithms described in the proofs that the class of finite-state languages (ω-languages, operators) is closed under various types of operations are constituent parts of the synthesis procedure. These algorithms are merely assembled and combined into a single synthesis algorithm in the chapter.