The article introduces the concept of word equation on context-free (CF) language and the finite representation (unifier) of the set of solutions for this type of equation. The article offers an algorithms for constructing the minimal unifier of word equation on CF language, where the last is described by the unambiguous acyclic CF grammar. The single and multiple variable instances cases are investigated as well as ambiguous and cyclical CF grammars cases of the designed mathematical apparatus. The incorrectness of J.A.Robinson's unification algorithm and resolution procedure in general case is proved. Linear and non-linear systems of word equations on CF languages are proposed and investigated. Some possible applications of the proposed concept to data and knowledge mathematical modelling as well as to genetics and social engineering are considered.
Sheremet Igor Anatolyevich, born in 1956, Doctor of Engineering Science (1993), Professor (1998), Professor at N.E. Bauman Moscow State Technical University. Member of Russian Academy of Natural Sciences and European Academy of Natural Sciences. L.Euler Medal Awards by European Academy of Natural Sciences for the fundamental results in data and knowledge bases mathematical modelling, systems analysis and information theory. P.L.Kapitsa (Nobel Prize winner) Medal Awards by International Association of the Authors of Scientific Discoveries for the monograph "Intelligent Software Medias for Computerized InformationProcessing Systems".