Computing by Temporal Order: Asynchronous Cellular Automata

Our concern is the behaviour of the elementary cellular automata with state set 0,1 over the cell set Z/nZ (one-dimensional finite wrap-around case), under all possible update rules (asynchronicity). Over the torus Z/nZ (n<= 11),we will see that the ECA with Wolfram rule 57 maps any v in F_2^n to any w in F_2^n, varying the update rule. We furthermore show that all even (element of the alternating group) bijective functions on the set F_2^n = 0,...,2^n-1, can be computed by ECA57, by iterating it a sufficient number of times with varying update rules, at least for n <= 10. We characterize the non-bijective functions computable by asynchronous rules.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

Hard, firm, soft … Etherealware:Computing by Temporal Order of Clocking

We define Etherealware as the concept of implementing the functionality of an algorithm by means of the clocking scheme of a cellular automaton (CA). We show, which functions can be implemented in this way, and by which CAs

EcoDesign for Production Plants

AbstractDue to rising energy prices and stricter regulations of carbon dioxide emissions, it is not sufficient to optimize energy consumption only during the utilization of products; production has to become more energy efficient, too. In order to reduce the energy demand, energy concerning aspects must be considered early in the development process of the production plants. In these phases, attributes that are responsible for the later energy consumption are predetermined. But the energy demand is often not in focus of the development process. For that reason a methodology for the development of energy efficient production plants is currently being developed by the authors

Linear Complexity Profiles: Hausdorff Dimensions for Almost Perfect Profiles and Measures for General Profiles

AbstractStream ciphers usually employ some sort of pseudorandomly generated bit strings to be added to the plaintext. The cryptographic properties of such a sequenceacan be stated in terms of the so-called linear complexity profile (l.c.p.),La(t),t∈ N. If the l.c.p. isLa(t) =t/2 +O(1), it is called (almost)perfect. This paper examines first those subsets Ad(q)of Fq∞where for fixedd∈ N the l.c.p. satisfies |2 ·La(t) −t| ≤dfor allt∈ N. It turns out that (after suitably mapping Ad(q)on [0, 1] ⊂ R) the Hausdorff dimension is1+logqϕd(q)2where ϕd(q)is the largest real root ofxd= (q− 1) · ∑i=0d−1xi. The second part deals with nondecreasing boundsd: N → N. Sinced(t) → ∞ ast→ ∞ always leads to a Hausdorff dimension 1, here we consider the measure of the set Ad(q)