Coding with variable block maps (Q861282)

Let \(A\) be a finite alphabet and let \(A^+\), \(A^{\mathbb N}\) and \(A^{\mathbb Z}\) denote the set of finite, one-sided or two-sided infinite words over \(A\), respectively. By a pointed word is understood a finite word \(w\in A^+\) with a specified position, called the origin of \(w\), and a finite set \({\mathcal V}\) of pointed words, satisfying a certain condition is called a variable block map on \(A\). If \(B\) is another finite alphabet and \(X\subseteq B^+\cup B^{\mathbb N}\cup B^{\mathbb Z}\), the authors study the pair \([X,(L,O)]\), where \(L\) and \(O\) are functions from \(B\) to \(\mathbb N\) satisfying \(0\leq O(b)< L(b)\) for \(b\in B\). They introduce the notion of identifiability of the pair \([X,(L,O)]\) and establish the relation between this property and existence of a coding \(\Theta: {\mathcal V}\to B\), where \({\mathcal V}\) is a variable block map over an alphabet \(A\) and \(\Theta\) is a bijection.