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We exhaustively explore the reprogrammability capabilities and the intrinsicuniversality of the Cartesian product $P \times C$ of the space $P$ of allpossible computer programs of increasing size and the space $C$ of all possiblecompilers of increasing length such that $p \in P$ emulates $p^\prime \in P$with $T|p^\prime|=|p|$ under a coarse-graining transformation $T$. Our approachyields a novel perspective on the complexity, controllability, causality and(re)programmability discrete dynamical systems. We find evidence that thedensity of (qualitatively different) computer programs that can be reprogrammedgrows asymptotically as a function of program and compiler size. To illustratethese findings we show a series of behavioural boundary crossing results,including emulations (for all initial conditions) of Wolfram class 2 ElementaryCellular Automata (ECA) by Class 1 ECA, emulations of Classes 1, 2 and 3 ECA byClass 2 and 3 ECA, and of Classes 1, 2 and 3 by Class 3 ECA, along with resultsof even greater emulability for general CA (neighbourhood $r=3/2$), includingClass 1 CA emulating Classes 2 and 3, and Classes 3 and 4 emulating all otherclasses (1, 2, 3 and 4). The emulations occur with only a linear overhead andcan be considered computationally efficient. We also found that there is nohacking strategy to compress the search space based on compiler profiling interms of e.g. similarity or complexity, suggesting that no strategy other thanexhaustive search is viable. We also introduce emulation networks, derive atopologically-based measure of complexity based upon out- and in-degreeconnectivity, and establish bridges to fundamental ideas of complexity,universality, causality and dynamical systems.

Cross-boundary Behavioural Reprogrammability Reveals Evidence of Pervasive Universality