Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, December 15, 2016, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Ahad N. Zehmakan

Biased Majority Cellular Automata

Consider a graph $G=(V,E)$ and a random initial vertex-coloring such that each vertex is blue independently with probability $p_b$, and red with probability $1-p_b$. In each step, all vertices change their current color synchronously to the most frequent color in their neighborhood and in the case of a tie, a vertex becomes blue (a bias toward blue); this model is called biased majority model. We are interested in the behavior of this deterministic process, especially in a two-dimensional torus (cellular automata with biased majority rule). We discuss that biased majority cellular automata exhibit a threshold behavior with two phase transitions. More precisely, it is proved there are two thresholds $0 < p_1 < p_2 < 1$ such that $p_b \ll p_1$, $p_1 \ll p_b \ll p_2$, and $p_2 \ll p_b$ result in final complete occupancy by red, stable coexistence of both colors, and final complete occupancy by blue, respectively. We also present the tight bound of $O(n^2)$ on the consensus time of the process, the time after which the process reaches a periodic sequence of states.


Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks


Automatic MiSe System Software Version 1.4803M   |   admin login