%0 Journal Article
	%A Fahad Alsharari and  Mohd Salmi Md Noorani
	%D 2015
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 98, 2015
	%T An Alternative Proof for the Topological Entropy of the Motzkin Shift
	%U https://publications.waset.org/pdf/10000537
	%V 98
	%X 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.

	%P 90 - 93