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Download Cellular Automata and Discrete Complex Systems: 21st IFIP WG by Jarkko Kari PDF

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 includes four invited talks in full-paper size and 15 normal papers, that have been rigorously reviewed and chosen from a complete of 33 submissions. issues of curiosity contain, the subsequent facets and contours of such platforms: dynamical, topological, ergodic and algebraic features; algorithmic and complexity concerns; emergent houses; formal language processing facets; symbolic dynamics; versions of parallelism and allotted platforms; timing schemes; phenomenological descriptions; medical modeling; and useful applications.

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Read Online 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

Example text

More precisely, in the construction, depending on whether f halts, we obtain either a finite dihedral group Dn , or the infinite dihedral group D∞ = Z2 ∗ Z2 . One can easily perform a similar proof to for example show that the finiteness of a group generated by automorphisms of order 3 is undecidable. We prove a more general result of this form. Theorem 8. Let X be a positive entropy sofic, and let G be an arbitrary nonempty finite group. Then, given two finite subgroups F, F ≤ Aut(X) with F ∼ = G, =F ∼ it is undecidable whether F ∪ F is finite.

These questions are, at least a priori, outside our scope, as there is no known algebraic property satisfied by, for example, the mixing CA, but not the rest. However, the dynamical notion of equicontinuity turns out to be equivalent to eventual periodicity on all subshifts. For automorphisms f ∈ Aut(S Z ), this is the question of whether f k = idX for some k ≥ 1, that is, the torsion problem. Though the result is not stated in group-theoretic terms, in [KO08], this problem is shown undecidable on full shifts.

We write L(X) for the language of X, that is, the set of words occurring in X. It is always factor closed, and L(L−1 (L)) = F (L) and L−1 (L(X)) = X for an extendable language L and a subshift X. We write Ln (X) = L(X) ∩ S n . A sofic shift is a subshift that can be defined by a regular language of forbidden words, or alternatively as L−1 (L) for an extendable regular language L. An SFT is a subshift that can be defined by a finite set of forbidden words. The endomorphism monoid of a subshift consists of the continuous functions on X which commute with the translations: End(X) = {f : X → X | f continuous and ∀v ∈ Zk : σv ◦ f = f ◦ σv }.

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