ALMOST SPECIFICATION AND RENEWALITY IN SPACING SHIFTS.

Let (ΣP ; σP) be the space of a spacing shifts where P ⊂ N0 = N ∐0{0} and ΣP = {s ∈ {0,1}N0 : si = sj = 1 if |i - j| ∈ P ∐ {0}} and σP the shift map. We will show that ΣP is mixing if and only if it has almost specification property with at least two periodic points. Moreover, we show that if h(σP) = 0, then ΣP is almost specified and if h(σP) > 0 and ΣP is almost specified, then it is weak mixing. Also, some sufficient conditions for a coded ΣP being renewal or uniquely decipherable is given. At last we will show that here are only two conjugacies from a transitive ΣP to a subshift of {0; 1}N0. [ABSTRACT FROM AUTHOR]