By Helmut Jürgensen, Juhani Karhumäki, Alexander Okhotin
This ebook constitutes the refereed complaints 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 rigorously reviewed and chosen from 35 submissions. The convention handled the next subject matters: Automata, grammars, languages and different formal structures; a number of modes of operation and complexity measures; trade-offs among computational versions and modes of operation; succinctness of description of items, country explosion-like phenomena; circuit complexity of Boolean services and comparable measures; resource-bounded or structure-bounded environments; frontiers among decidability and undecidability; universality and reversibility; structural complexity; formal structures for functions (e.g., software program reliability, software program and checking out, modeling of common languages); nature-motivated (bio-inspired) architectures and unconventional types of computing; complexity features of combinatorics on phrases; Kolmogorov complexity.
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Extra info for Descriptional Complexity of Formal Systems: 16th International Workshop, DCFS 2014, Turku, Finland, August 5-8, 2014. Proceedings
The syntactic monoid of a regular language (for instance, given by a nondeterministic automaton) is eﬀectively computable. Hence, from the equivalence of conditions “1” and “2” in Theorem 1 it follows that star-freeness is a decidable property of regular languages. The equivalence of “1” and “3” can be written as SF(A∗ ) = AP(A∗ ). g. . Acknowlegdements. The author would like to thank Volker Diekert and Benjamin Steinberg for many interesting discussions on the proof method for Proposition 1.
S 44 F. Ablayev and M. Ablayev For K = |X| and integer s ≥ 1 we deﬁne a (K; s) classical-quantum function to be a map of the elements w ∈ X to quantum states |ψ(w) ∈ (H2 )⊗s ψ : X → (H2 )⊗s . (1) We will also use the notation ψ : w → |ψ(w) for ψ. 2 Quantum Hashing What we need to deﬁne for quantum hashing and what is implicitly assumed in various papers (see for example  for more information) is a collision resistance property. However, there is still no such notion as quantum collision. The reason why we need to deﬁne it is the observation that in quantum hashing there might be no collisions in the classical sense: since quantum hashes are quantum states they can store an arbitrary amount of data and can be diﬀerent for different messages.
1 The work was in part supported by the RFBR grant 14-01-93107. This hexagon is attributed to Robert Ammann in . Independently the hexagon was discovered by Scherer  who called it the Golden Bee. H. J¨ urgensen et al. ): DCFS 2014, LNCS 8614, pp. 29–41, 2014. c Springer International Publishing Switzerland 2014 30 N. Vereshchagin Let us go back to the right triangle, whose altitude cuts it into two similar triangles. Assume that its hypotenuse and legs are proportional to 1, ψ and ψ 2 , respectively, so that Pythagorean theorem hold: ψ2 1 ψ Call any such triangle a golden triangle.