TY - JFULL AU - Fahad Alsharari and Mohd Salmi Md Noorani PY - 2015/3/ TI - An Alternative Proof for the Topological Entropy of the Motzkin Shift T2 - International Journal of Mathematical and Computational Sciences SP - 89 EP - 93 VL - 9 SN - 1307-6892 UR - https://publications.waset.org/pdf/10000537 PU - World Academy of Science, Engineering and Technology NX - Open Science Index 98, 2015 N2 - 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. ER -