author = "Mendon{\c{c}}a, J. Ricardo G. and Sim{\~o}es, Rolf Ezequiel de 
          affiliation = "{Universidade de S{\~a}o Paulo (USP)} and {Instituto Nacional de 
                         Pesquisas Espaciais (INPE)}",
                title = "Density classification performance and ergodicity of the 
                         Gacs-Kurdyumov-Levin cellular automaton model IV",
              journal = "Physical Review E",
                 year = "2018",
               volume = "98",
               number = "1",
                pages = "e012135",
                month = "July",
             abstract = "Almost four decades ago, Gacs, Kurdyumov, and Levin introduced 
                         three different cellular automata to investigate whether 
                         one-dimensional nonequilibrium interacting particle systems are 
                         capable of displaying phase transitions, and, as a byproduct, they 
                         introduced the density classification problem (the ability to 
                         classify arrays of symbols according to their initial density) in 
                         the cellular automata literature. Their model II became a 
                         well-known model in theoretical computer science and statistical 
                         mechanics. The other two models, however, did not receive much 
                         attention. Here we characterize the density classification 
                         performance of Gacs, Kurdyumov, and Levin's model IV, a four-state 
                         cellular automaton with three absorbing states-only two of which 
                         are attractive-by numerical simulations. We show that model IV 
                         compares well with its sibling model II in the density 
                         classification task: the additional states slow down the 
                         convergence to the majority state but confer a slight advantage in 
                         classification performance. We also show that, unexpectedly, 
                         initial states diluted in one of the nonclassifiable states are 
                         more easily classified. The performance of model IV under the 
                         influence of noise was also investigated, and we found signs of an 
                         ergodic-nonergodic phase transition at some small finite positive 
                         level of noise, although the evidence is not entirely conclusive. 
                         We set an upper bound on the critical point for the transition, if 
                  doi = "10.1103/PhysRevE.98.012135",
                  url = "http://dx.doi.org/10.1103/PhysRevE.98.012135",
                 issn = "1539-3755",
             language = "en",
           targetfile = "mendonca_density.pdf",
        urlaccessdate = "24 nov. 2020"