Fahad Alsharari and Mohd Salmi Md Noorani
An Alternative Proof for the Topological Entropy of the Motzkin Shift
90 - 93
2015
9
2
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/10000537
https://publications.waset.org/vol/98
World Academy of Science, Engineering and Technology
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 nonzero 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.
Open Science Index 98, 2015