On the injectivity of the global function of a cellular automaton in the hyperbolic plane (extended abstract)
نویسنده
چکیده
In this paper, we look at the following question. We consider cellular automata in the hyperbolic plane, see [5, 16, 7, 9] and we consider the global function defined on all possible configurations. Is the injectivity of this function undecidable? The problem was answered positively in the case of the Euclidean plane by Jarkko Kari, in 1994, see [3]. In the present paper, we show that the answer is also positive for the hyperbolic plane: the problem is undecidable.
منابع مشابه
Is the injectivity of the global function of a cellular automaton in the hyperbolic plane undecidable?
In this paper, we look at the following question. We consider cellular automata in the hyperbolic plane, see [5,16,9,12] and we consider the global function defined on all possible configurations. Is the injectivity of this function undecidable? The problem was answered positively in the case of the Euclidean plane by Jarkko Kari, in 1994, see [3]. In the present paper, we give a partial answer...
متن کاملar X iv : 0 80 6 . 16 02 v 1 [ cs . C G ] 1 0 Ju n 20 08 The injectivity of the global function of a cellular automaton in the hyperbolic plane is undecidable
In this paper, we look at the following question. We consider cellular automata in the hyperbolic plane, see [5,18,9,13] and we consider the global function defined on all possible configurations. Is the injectivity of this function undecidable? The problem was answered positively in the case of the Euclidean plane by Jarkko Kari, in 1994, see [3]. In the present paper, we show that the answer ...
متن کاملGlobal attractor for a nonlocal hyperbolic problem on ${mathcal{R}}^{N}$
We consider the quasilinear Kirchhoff's problem$$ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+f(u)=0 ,;; x in {mathcal{R}}^{N}, ;; t geq 0,$$with the initial conditions $ u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ; f(u)=|u|^{a}u$ and $(phi (x))^{-1} in L^{N/2}({mathcal{R}}^{N})cap L^{infty}({mathcal{R}}^{N} )$ is a positive function. The purpose of our work is to ...
متن کاملA Cellular Automaton Based Algorithm for Mobile Sensor Gathering
In this paper we proposed a Cellular Automaton based local algorithm to solve the autonomously sensor gathering problem in Mobile Wireless Sensor Networks (MWSN). In this problem initially the connected mobile sensors deployed in the network and goal is gather all sensors into one location. The sensors decide to move only based on their local information. Cellular Automaton (CA) as dynamical sy...
متن کاملOne-Dimensional Cellular Automata: Injectivity From Unambiguity
New algorithms for deciding the injectivit y of the global update funct ion associat ed with a cellular automaton C A of dimension one are presented. This is done by interpreting each ordered pair dete rmined by the local update function as th e edge of a labeled directed graph GR which has the prope rty that each bi-infinite sequence of states of the cellular automaton is th e sequence of inpu...
متن کامل