Consider the alphabet $\mathcal{A} = \{0,1\}$ and consider a finite set of words $W = \{\omega\_1, \ldots , \omega\_n\}$ over $\mathcal{A}$. Then the renewal system $\Sigma\_{W}$ generated by $W$ is formed by bi-infinite concatenations of words of $W$. My first question is, does every renewal system is intrinsically ergodic? 


Secondly, is there a one sided version of the definition of renewal subshift?


On the other hand, Adler asked the following question: Is every transitive subshift of finite type topologically conjugated to a renewal system? To the best of my knowledge the conjecture stills open. Is the conjecture open when the alphabet is $\{0,1\}$? 


My third question is: Are there any examples of renewal systems $\Sigma\_W \subset \mathcal{A}^{\mathbb{Z}}$ that are subshifts of finite type and viceversa? 



Renewal systems: Intrinsic ergodicity and a question related to the Adler's conjecture
There are some examples related to your third question in "Renewal Systems, Sharp-Eyed Snakes, and Shifts of Finite Type" by Johnson and Madden, Amer. Math. Monthly 109 (2002), 258-272. A long time ago Goldberger, Smorodinsky, and I showed that for every possible entropy of a shift of finite type (or, what amounts to the same thing, for the logarithm of every Perron number), there is a renewal system with that entropy. However, as far as I know, Adler's question is still open.


