In [A. Frid, S. Puzynina, L.Q. Zamboni, On palindromic factorization of words, Adv. in Appl. Math. 50 (2013), 737-748], it was conjectured that any infinite word whose palindromic lengths of factors are bounded is ultimately periodic. We introduce variants of this conjecture and prove this conjecture in particular cases. Especially we introduce left and right greedy palindromic lengths. These l...

We introduce the notion of ultimately bipartite impartial games. These are games that are ultimately periodic in the simplest possible manner. We examine ultimately bipartite subtraction games and demonstrate a curious feature: for ‘large’ games it is clear who has the winning position and how the game should be strategically played, but during play, as the game eventually becomes small, it is ...

The polychronous (synchronous, multiclocked) language Signal is used for the design and analysis of reactive systems. For the purpose of modeling eventdriven systems, we consider an extension of the polychronousmodel of computation of Signal with periodic equations denoted by ultimately periodic infinite words. These equations express periodic constraints on the signals of programs, that can be...