Encoding Trees by Linear Recurrence Sequences

Abstract

A unified encoding of ordered binary trees with integer-valued labels at their vertices is proposed using linear forms of neighboring members of linear recursive sequences of the form Pn + 2 = an + 2 Pn + 1 + P, where P1 = P2 = 1; a3 and a4 … are natural numbers. Encoding and decoding procedures are simply implemented and use the recursive technique of direct pre-order depth-first tree traversal. A brief review of possible applications of the proposed encoding in problems of tree processing and cryptographic symmetric encryption is presented.