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We study the one-dimensional two-state totalistic probabilistic cellularautomata (TPCA) having an absorbing state with long-range interactions, whichcan be considered as a natural extension of the Domany-Kinzel model. Weestablish the conditions for existence of a site-bond representation andself-dual property. Moreover we present an expression of a set-to-setconnectedness between two sets, a matrix expression for a condition of theself-duality, and a convergence theorem for the TPCA.Comment: 11 pages, minor corrections, journal reference adde

Site–bond representation and self-duality for totalistic probabilistic cellular automata in one dimension