Pseudo-cyclic renewal systems

Abstract

A finite set W of words over an alphabet A is cyclic if, whenever u, v is an element of A* and uv, vu is an element of W*, we have u, v is an element of W*. If it is only assumed that the property holds for all u, v is an element of A* with a large length, then W is called pseudo-cyclic, that is, there is N is an element of N such that, whenever u, v is an element of A* with vertical bar u vertical bar, vertical bar v vertical bar >= N and uv, vu is an element of W*, we have u, v is an element of W*. We analyze the class of pseudo-cyclic sets and describe how it is related to the open question which asks whether every irreducible shift of finite type is conjugate to a renewal system. (C) 2011 Elsevier B.V. All rights reserved.