Sentence examples for infinite words from inspiring English sources

The homomorphism (kappa ) is defined to act on infinite words analogously.

Each of the infinite words articulated in the All-Merciful Breath discloses Being in a limited form.

The automata-based methods transform temporal formulae into automata on infinite words (for linear time logics) or infinite trees (for branching time logics) and represent models for the logics as respective input objects (infinite words or trees) for their associated automata.

We denote by ({mathscr {A}}^{mathbb {N}}) the set of all infinite words over the alphabet ({mathscr {A}}) and equip it with the discrete product topology.

The elements of Λ can be written as infinite words (alpha=alpha_{1}alpha_{2}alpha_{3}cdots) and the elements of (Lambda _{n}) as finite words (alpha=alpha_{1}alpha_{2}cdotsalpha_{n}).

On the other hand, if such a path exists for a pair of infinite words (x_1x_2cdots, y_1y_2cdots ), then the maps (psi _{x_1x_2cdots x_n, y_1y_2cdots y_n}) are non-empty for every n.

We use the same notations when v is an infinite word.

Given a finite or infinite word v, we consider the set M v) of minimal forbidden factors of v.

Let (alpha ge 1) be given and let x denote an infinite word over a finite alphabet.

An infinite word x over a finite alphabet ({mathscr {A}}) is called recurrent if every factor has infinitely many different occurrences in x.

It is known that there exists a unique infinite word (eta in { a, x, y, z }^{mathbb {N}}) such that (kappa (eta ) = eta ), see for instance [20].