713 research outputs found

    A Max-Plus Model of Asynchronous Cellular Automata

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    This paper presents a new framework for asynchrony. This has its origins in our attempts to better harness the internal decision making process of cellular automata (CA). Thus, we show that a max-plus algebraic model of asynchrony arises naturally from the CA requirement that a cell receives the state of each neighbour before updating. The significant result is the existence of a bijective mapping between the asynchronous system and the synchronous system classically used to update cellular automata. Consequently, although the CA outputs look qualitatively different, when surveyed on "contours" of real time, the asynchronous CA replicates the synchronous CA. Moreover, this type of asynchrony is simple - it is characterised by the underlying network structure of the cells, and long-term behaviour is deterministic and periodic due to the linearity of max-plus algebra. The findings lead us to proffer max-plus algebra as: (i) a more accurate and efficient underlying timing mechanism for models of patterns seen in nature, and (ii) a foundation for promising extensions and applications.Comment: in Complex Systems (Complex Systems Publications Inc), Volume 23, Issue 4, 201

    Modelling legacy telecommunications switching systems for interaction analysis

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    The influence of the update dynamics on the evolution of cooperation

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    We investigate the influence of the update dynamics on the evolution of cooperation. Three of the most studied games in this area are used: Prisoner’s Dilemma, Snowdrift and the Stag Hunt. Previous studies with the Prisoner’s Dilemma game reported that less cooperators survive with the asynchronous version of the game than with the synchronous one. On the other side, studies with the Snowdrift game are not conclusive about this subject. Based on simulations with these three games, played on different types of networks and using different levels of noise in the choice of the next strategy to be adopted by the agents, we conclude that, in general, an asynchronous dynamics favors the evolution of cooperation. Results concerning the monotonicity of these models and their sensitivity to small changes in the synchrony rate are also reported. This work is a contribution to a better understanding of the conditions under which cooperation can emerge and how different parameters may influence this emergence

    Fault-Tolerant Consensus in Unknown and Anonymous Networks

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    This paper investigates under which conditions information can be reliably shared and consensus can be solved in unknown and anonymous message-passing networks that suffer from crash-failures. We provide algorithms to emulate registers and solve consensus under different synchrony assumptions. For this, we introduce a novel pseudo leader-election approach which allows a leader-based consensus implementation without breaking symmetry
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