@article{(Open Science Index):https://publications.waset.org/pdf/10000537, title = {An Alternative Proof for the Topological Entropy of the Motzkin Shift}, author = {Fahad Alsharari and Mohd Salmi Md Noorani}, country = {}, institution = {}, abstract = {A Motzkin shift is a mathematical model for constraints on genetic sequences. In terms of the theory of symbolic dynamics, the Motzkin shift is nonsofic, and therefore, we cannot use the Perron- Frobenius theory to calculate its topological entropy. The Motzkin shift M(M,N) which comes from language theory, is defined to be the shift system over an alphabet A that consists of N negative symbols, N positive symbols and M neutral symbols. For an x in the full shift, x will be in the Motzkin subshift M(M,N) if and only if every finite block appearing in x has a non-zero reduced form. Therefore, the constraint for x cannot be bounded in length. K. Inoue has shown that the entropy of the Motzkin shift M(M,N) is log(M + N + 1). In this paper, a new direct method of calculating the topological entropy of the Motzkin shift is given without any measure theoretical discussion. }, journal = {International Journal of Mathematical and Computational Sciences}, volume = {9}, number = {2}, year = {2015}, pages = {90 - 93}, ee = {https://publications.waset.org/pdf/10000537}, url = {https://publications.waset.org/vol/98}, bibsource = {https://publications.waset.org/}, issn = {eISSN: 1307-6892}, publisher = {World Academy of Science, Engineering and Technology}, index = {Open Science Index 98, 2015}, }