Self-replication, Evolvability and Asynchronicity in Stochastic Worlds

We consider temporal aspects of self-replication and evolvability – in particular, the massively asynchronous parallel and distributed nature of living systems. Formal views of self-reproduction and time are surveyed, and a general asynchronization construction for automata networks is presented. Evolution and evolvability are distinguished, and the evolvability characteristics of natural and artificial examples are overviewed. Minimal implemented evolvable systems achieving (1) asynchronous self-replication and evolution, as well as (2) protocultural transmission and evolution, are presented and analyzed for evolvability. Developmental genetic regulatory networks (DGRNs) are suggested as a novel paradigm for massive asynchronous computation and evolvability. An appendix classifies modes of life (with different degrees of aliveness) for natural and artificial living systems and possible transitions between them. 1 Models of Time: Logical vs. Physical Time We consider time in discrete dynamical systems. St. Augustine considered time as something intuitively graspable yet ineffable. Varshavsky distinguished two kinds of time: Time as a logical variable in a system defined by events vs. time as an independent physical variable [96], and studied self-timing and asynchrony theory for computing devices as the problem of reconciling the two types of time via design of system timing for the appropriate functioning asynchronous devices interacting with external environments. For a single observer or location, we can consider three main views of the (logical) time: O. B. Lupanov et al. (Eds.): SAGA 2005, LNCS 3777, pp. 126–169, 2005. c © Springer-Verlag Berlin Heidelberg 2005 [This version includes minor corrections to the published text.] 1.1 Partial Orders as Models of Time Aristotle considered events in time via ordering related to casuality (and motion), and time as defined by differences between states before and after (thus change is required for the passage of time). 1.2 Time as a Random Variable Another view is to regard logical events, such as a discrete event clock-tick, as embedded in physical time but where a random variable takes values event or no event according to some distribution at successive discrete moments of physical time. (Instead of just one type of event more generally different particular events might be generated.) Here the passage of logical time, if used to increment a measuring counter, is monotonically but not deterministically related to the passage of physical time. 1.3 Algebras of Time: Semigroups as Models of Time Following J. L. Rhodes (who refers to Aristotle), we can describe time algebraically. If α, β, and γ are each sequences of events in time, and the composite sequence β then γ is preceded by α, this is exactly in the same as when β follows α and after both γ occurs. That is, the associative law