By Jarkko Kari
This quantity constitutes the completely refereed lawsuits of the twenty first foreign Workshop on mobile Automata and Discrete complicated structures, AUTOMATA 2015, held in Turku, Finland, in June 2015. This quantity comprises four invited talks in full-paper size and 15 ordinary papers, which have been conscientiously reviewed and chosen from a complete of 33 submissions. themes of curiosity comprise, the subsequent points and lines of such platforms: dynamical, topological, ergodic and algebraic elements; algorithmic and complexity concerns; emergent homes; formal language processing facets; symbolic dynamics; types of parallelism and disbursed structures; timing schemes; phenomenological descriptions; medical modeling; and functional applications.
Read or Download Cellular Automata and Discrete Complex Systems: 21st IFIP WG 1.5 International Workshop, AUTOMATA 2015, Turku, Finland, June 8-10, 2015. Proceedings PDF
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Extra info for Cellular Automata and Discrete Complex Systems: 21st IFIP WG 1.5 International Workshop, AUTOMATA 2015, Turku, Finland, June 8-10, 2015. Proceedings
It is well-known that cellular automata are precisely the functions End(X). The local rule of a cellular automaton gives a computational presentation of the function, and thus a way to give a ﬁnite list of elements of the endomorphism monoid to an algorithm. This allows us to ask algorithmic questions about the monoid End(X), on any subshift X, even a highly uncomputable one. Note that from the local rules of f, g : X → X, we can easily form a local rule for the composition of two cellular automata by composing the local rules in an obvious way, again no matter what the subshift is.
In Section 6, we show that similar constructions, and much more, can be carried out on the larger classes of synchronized and coded systems – in particular on coded systems we obtain a large set of groups as automorphism groups [FF96]. We also show examples of subshifts on which the automorphism group is essentially smaller, and some ways to control this. In Section 5 we discuss some interesting recent results in the case where either the word complexity grows slowly or recurrence times are short.
The following construction of synchronized systems is shown in [FF96]: Theorem 19 ([FF96]). Given any subshift X with periodic points dense, there is a synchronized system Y such that Aut(Y ) contains a copy of Aut(X). A coded system is a subshift X of the form X = L−1 (W ∗ ), where W is any countable set of words over a ﬁnite alphabet. In other words, points of X are the limit points of inﬁnite concatenations of words in W . Every synchronized system is coded, but the converse does not hold. There is much freedom in the construction of automorphism groups of coded systems, as shown by the following strong result.