Codes which are minimal generators of languages of biinfinite words (Q2729633)

The author proposes at the end of this paper a conjecture: let \(C\) be a code and \({^\omega C^\omega}\) be the set of bi-infinite words on \(C\); then \(C\) is a minimal generator of \({^\omega C^\omega}\). This conjecture implies in particular that, if \(A\) is an alphabet and \(C\) a code such that \(C\) is a generator of \({^\omega A^\omega}\), then \(C\) is a maximal code. To support her conjecture she proves in the paper under review that it is true for two families of codes: the precircular codes and the very thin codes. The first family contains all circular codes, whereas the second family contain all rational codes.