By Helmut Jürgensen, Juhani Karhumäki, Alexander Okhotin
This publication constitutes the refereed lawsuits of the sixteenth overseas convention on Descriptional Complexity of Formal platforms, DCFS 2014, held in Turku, Finland, in August 2014. The 27 complete papers awarded have been conscientiously reviewed and chosen from 35 submissions. The convention handled the next issues: Automata, grammars, languages and different formal platforms; quite a few modes of operation and complexity measures; trade-offs among computational versions and modes of operation; succinctness of description of items, kingdom explosion-like phenomena; circuit complexity of Boolean features and comparable measures; resource-bounded or structure-bounded environments; frontiers among decidability and undecidability; universality and reversibility; structural complexity; formal platforms for functions (e.g., software program reliability, software program and trying out, modeling of typical languages); nature-motivated (bio-inspired) architectures and unconventional versions of computing; complexity features of combinatorics on phrases; Kolmogorov complexity.
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Additional info for Descriptional Complexity of Formal Systems: 16th International Workshop, DCFS 2014, Turku, Finland, August 5-8, 2014. Proceedings
Sequential Machines: Selected Papers. Addison-Wesley (1964) 7. : On ﬁnite monoids having only trivial subgroups. ru Abstract. Let ψ denote the square root of the golden ratio, √ ψ = ( 5 − 1)/2. A golden triangle is any right triangle with legs of lengths a, b where a/b = ψ. We consider tilings of the plane by two golden triangles: that with legs 1, ψ and that with legs ψ, ψ 2 . Under some natural constrains all such tilings are aperiodic. 1 Golden Triangles The altitude of every right triangle cuts it into two similar triangles.
Ammann tilings: a classiﬁcation and an application. 2896 (2012) 4. 5167 5. : Matching rules and substitution tilings. Ann. of Math. 147(1), 181–223 (1998) 6. : A puzzling journey to the reptiles and related animals. Privately published (1987) 7. : Dividing a polygon into two similar polygons. Discrete Math. 311(4), 220–231 (2011) 8. : The mysterious Mr. Ammann. Math. Intelligencer 26, 10–21 (2004) Aperiodic Tilings by Right Triangles A 37 Proof of the Lemma 1 Assume that ε is small enough (in the end we will see how small it should be).
Assume that n > 2. Then Stn is a disjoint union of two standard tilings Tn−1 and Tn−2 . Let I stand for the common segment of indexes of A, B. Coarsen Tn−1 and Tn−2 and denote the resulting tilings by Tn−2 and Tn−3 , respectively. Let A , B be the triangles from Tn−2 , Tn−1 including A, B. B also share the segment I and hence form a pattern of a smaller index than n. This observation allows to ﬁnd all standard patterns consisting of two adjacent triangles in the order of increasing its indexes.