Contribution to deterministic top-down analysis of context-free languages

In the present paper a generalization of ZX(A:)-grammars is given, the notion of the switching function for such grammars is introduced and the model of the Parsing Machine using the switch­ ing function is given. We introduce the necessary notions and notation, mainly according to D. E. Knuth: An alphabet X is a finite nonempty set of symbols, and X* denotes the set of all strings on the alphabet X. The length of a string u is denoted by \u\. A context free grammar is a 4-tuple (T N, P, S) where T, N are disjoint alphabets called terminal and nonterminal alphabets respectively; P is a finite nonempty set of productions. A production is a pair denoted by A—* u, where AeN,u e(N u T)*; S e N is an initial symbol. be a context-free grammar. For u, ue(TuiV)* let us write u => v if there exist strings x, y,we (Tu N)*, such that u = xAy, v = xwy and A-» we P. If x e T* we write u => v, if y e T* we write u => v. The reflexive transitive completion of relation => is denoted by =>* and the transi­ tive completion of => is denoted by => +. Similarly =>*, => + , =>*, => +. The set L(G) = {u e T* : S => + M} is called a context^ree language generated by G. If w^e (Tu JV)* we write L(w) = {« e T* : w =>* M}.