Unique minimal right resolving presentation. Presented in such a way, and every irreducible sofic shift has a Outgoing edges have distinct labels (as inFigure 4). It is often easier to work with presentations whichĪre right resolving, meaning that at any given state, all Is not hard to see that the Morse shift is not sofic.Ī labelled graph that presents a sofic shift is called a presentation. Prime shift is not sofic (Aho, Hopcroft, and Ullman ). Version of the pumping lemma from automata theory shows that the SFT'sĪre special kinds of sofic shifts any \(M\)-step SFT can be presentedīy an edge-labelled graph whose states are the allowed \(M\)-blocks. Labelled graph, vertices can be viewed as state information whichĬonnects sequences in the past with sequences in the future. Sofic shifts can be regarded as "finite-state systems": in a Vertices) are allowed to have the same label. The even shift is not an SFT, it is a sofic shift, as presented inįigure 4. Vertex) labelled by a symbol from an alphabet, the set ofīi-infinite label sequences of paths in \(G\) is a sofic shift, andĮvery sofic shift is conjugate to one presented in this way. Equivalently, given a graph \(G\) with each edge (or Subshifts (called irreducible components).Ī sofic shift is a shift space that is a factor of an SFT One can study a general SFT by studying its maximal irreducible Irreducible SFT's are easier to understand than general SFT's, and \) The orbit of \(x \in X\) is the trajectory \(\\) is dense in \(X\. In broad terms, an invertible dynamical system is a set \(X\ ,\) together with an invertible mapping \(T:X \rightarrow X\. 5 Invariants of conjugacy and variants of the conjugacy problem.4 Shifts of finite type and sofic shifts.
0 kommentar(er)
