The article discusses: 1. Representation of ternary symbolic matrix, as States of the Markov chains and ergodic methods to study the asymptotic geometry of the shortest k-path. 2. The representation of symbolic matrix in the form of recursive object and the construction of genetic space for the shortest k-paths based on Cayley trees. 3. The influence of symbolic computation on the architecture of future computers.
Keywords: n-cube, a finite alphabet, the shortest k-path symbolic ternary matrix, Markov chain, asymptotic structure, recursion, the Cayley tree, genetic space.