Almost specification ‎and ‎renewality‎ in spacing shifts

Let (ΣP,σP) be the space of a spacing shifts where P⊂N0=N∪{0} and ΣP={s∈{0,1}N0:ýsi=sj=1 if |i−j|∈P∪{0}} and σP the shift mapý. ýWe will show that ΣP is mixing if and only if it has almost specification property with at least two periodic pointsý. ýMoreoverý, ýwe show that if h(σP)=0ý, ýthen ΣP is almost specified and if h(σP)>0 and ΣP is almost specifiedý, ýthen it is weak mixingý. ýAlsoý, ýsome sufficient conditions for a coded ΣP being renewal or uniquely decipherable is givený. ýAt last we will show that here are only two conjugacies from a transitive ΣP to a subshift of {0,1}N0.