In this article, we give a negative answer to a question of Hof, Knill and Simon (1995) concerning purely morphic sequences obtained from primitive morphism containing an infinite number of palindromes. Their conjecture states that such palindromic sequences arise from substitutions that are in class P. The conjecture was proven for the binary alphabet by B. Tan in 2007. We give here a countere...

In this paper, we extend the concept of factorization on finite words to ω-rational languages and show how to compute them. We define a normal form for Büchi automata and introduce a universal automaton for Büchi automata in normal form. We prove that, for every ω-rational language, this Büchi automaton, based on factorization, is canonical and that it is the smallest automaton that contains th...

We investigate the recursive structure of differentiable sequences over the alphabet {1, 2}. We derive a recursive formula for the (n + 1)-th symbol of a differentiable sequence, which yields to a new recursive formula for the Kolakoski sequence. Finally, we show that the sequence of absolute differences of consecutive symbols of a differentiable sequence u is a morphic image of the run-length ...

For a given function f : Σ∗ → Σ∗ over an alphabet Σ, a language X ⊆ Σ∗ is said to f -commute with a language Y ⊆ Σ∗ if the equality XY = f(Y )X holds. This paper investigates the maximal solution to such f -commutative language equations for both morphic and antimorphic involutions f , under the condition that the known quantity (either X or Y ) is a singleton. We prove that, in most cases, the...

It is shown that a subgroup of SL(2, H), denoted Spin(2, H) in this paper, which is defined by two conditions in addition to unit quaternionic determinant, is locally iso-morphic to the restricted Lorentz group, L ↑ +. On the basis of the Dirac theory using the spinor group Spin(2, H), in which the charge conjugation transformation becomes linear in the quaternionic Dirac spinor, it is shown th...