Application of ternary quasigroups to string processing

Abstract We propose an algorithm for string processing which is based on finite ternary quasigroups. Ternary quasigroups are specified by three-dimensional matrices of a certain form. We prove sufficient conditions for simplicity and polynomial completeness of a finite ternary quasigroup. We also propose a method for deciding polynomial completeness of a finite ternary quasigroup based on the analysis of the corresponding three-dimensional matrix.