We study cellular automata on regular rooted trees. This includes the characterization of sofic tree shifts in terms of unrestricted Rabin automata and the decidability of the surjectivity problem for cellular automata between sofic tree shifts.

An ω-grammar is a formal grammar used to generateω-words (i.e. infinite length words), while an ω-automaton is an automaton used to recognize ω-words. This paper gives clean and uniform definitions for ω-grammars and ω-automata, provides a systematic study of the generative power of ω-grammars with respect to ω-automata, and presents a complete set of results for various types of ω-grammars and...

We study two-player games played on finite graphs equipped with costs on edges and introduce two winning conditions, cost-parity and cost-Streett, which require bounds on the cost between requests and their responses. Both conditions generalize the corresponding classical omega-regular conditions and the corresponding finitary conditions. For parity games with costs we show that the first playe...

The regular !-languages can be deened by deterministic !-automata with the Rabin acceptance condition, referring to a list of pairs (Ek; Fk) 1km of state sets of the automaton: A successful run should visit some Ek only nitely often but the corresponding Fk innnitely often. If only the non-existence, respectively existence of such visits is required, precisely the Staiger-Wagner deenable !-lang...

In this paper, we are concerned with the following fractional Schrödinger-Poisson system:    (−∆s)u + V (x)u + φu = m(x)|u|q−2|u|+ f(x,u), x ∈ Ω, (−∆t)φ = u2, x ∈ Ω, u = φ = 0, x ∈ ∂Ω, where s,t ∈ (0,1], 2t + 4s > 3, 1 < q < 2 and Ω is a bounded smooth domain of R3, and f(x,u) is linearly bounded in u at infinity. Under some assumptions on m, V and f we obtain the existence of non-trivial so...