Cybernetics and Systems Analysis, Vol. 50, No. 6, November, 2014 CONSTRUCTIVE-SYNTHESIZING STRUCTURES AND THEIR GRAMMATICAL INTERPRETATIONS. II. REFINING TRANSFORMATIONS 1 V. I. Shynkarenko a† and V. M. Ilman a UDC 510.23+510.25+510.54+512.567 Abstract. Methods of refining transformations such as specialization, interpretation, concretization, and implementation of a generalized constructive-production structure are proposed. It is shown how to use these methods to construct grammatical constructive-production structures, which are analogs of well-known grammars, their modifications, and grammar-like systems. Different types of formal grammars are analyzed and synthesized. Keywords: constructivism, formal grammar, constructive-production structure, specialization, interpretation, concretization. INTRODUCTION The first part of this article generalizes possibilities of different modifications of formal grammars and propose an apparatus of constructive-production (constructive-synthesizing) structures [1]. This part presents different approaches and methods of execution of refining transformations of a generalized constructive-synthesizing structure (GCSS). We will consider grammatical constructive-production structures (GrCSSs) whose analogues are classical grammars, their modifications, and grammar-like means, which are widely used in applied programming. This approach makes it possible to detect and study regularities in constructions different in nature with different interpretations of relations and to develop new methods for solving problems of recognition of patterns-constructions. The proposed generalizations provide new possibilities of “hybridization” of well-known means and reveal a number of existing problems. In particular, it is the problem of the ambiguity of interpretation, i.e., associating operations of a signature with several algorithms. On the one hand, any ambiguity is undesirable, but, on the other hand, new design possibilities arise. For each type of grammars considered in [2–11], generalized grammatical structures with constructive axiomatics are proposed. Introducing instructional constraints and supplements into the axiomatics of generalized structures and specifying concrete substitution productions, one can obtain constructive grammatical structures for classes of grammars. At the same time, a definite analogy between constructive-production structures and grammars is retained. Here, such an analogy adopts the ideology of inference used in definite formal languages. SPECIALIZATION OF GRAMMATICAL CONSTRUCTIVE-PRODUCTION STRUCTURES GCSSs can be specialized for different object domains such as biology, mechanics, music, etc. Let us consider two most important and widespread specializations in applied programming, namely, multi-symbol and graphic ones. 829 1060-0396/14/5006-0829 © 2014 Springer Science+Business Media New York 1 Part I of this article was published in No. 5 (2014). a V. Lazaryan Dnipropetrovsk National Railway Transport University, Dnipropetrovsk, Ukraine, † Shink@diit.edu.ua and Shinkarenko_vi@ua.fm. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 15–28, November–December, 2014. Original article submitted December 3, 2013. DOI 10.1007/s10559-014-9674-9