Computing with New Resources: Essays Dedicated to Jozef by Cristian S. Calude PDF

By Cristian S. Calude

ISBN-10: 3319133497

ISBN-13: 9783319133492

ISBN-10: 3319133500

ISBN-13: 9783319133508

Professor Jozef Gruska is a widely known desktop scientist for his many and large effects. He was once the daddy of theoretical laptop technological know-how study in Czechoslovakia and one of the first Slovak programmers within the early Nineteen Sixties. Jozef Gruska brought the descriptional complexity of grammars, automata, and languages, and is among the pioneers of parallel (systolic) automata. His different major study pursuits comprise parallel structures and automata, in addition to quantum details processing, transmission, and cryptography. he's co-founder of 4 typical sequence of meetings in informatics and in quantum info processing and the Founding Chair (1989-96) of the IFIP professional team on Foundations of computing device Science.

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If |α| is odd, let ui = α x v , with α ∈ Q∗o , x ∈ Qo , v ∈ { }∗ . Then ui+1 = f (α x v ) = f (α )f (x, )f (v ) = f (α ) (f (x, )) f (v ), and hence θ(ui+1 ) = f (α ) f (x, ) f (v ) = f (ui ) = ui+1 . – Case ui = αx v, with α ∈ Q∗o , x ∈ Qo , v ∈ { }∗ . It holds that ui = θ(ui ) = αxv. Systolic Automata and P Systems 25 If |α| is odd, let ui = α yx v, with α ∈ Q∗o , y ∈ Qo . Then ui+1 = f (α yx v) = f (α )f (y, x )f (v) = f (α ) (f (y, x)) f (v)); hence θ(ui+1 ) = f (α ) f (y, x) f (v) = f (ui ) = ui+1 .

Unsuccessful computations are those computations which never halt, thus yielding no result. Example 2. Figure 3 depicts a P system with two membranes, labelled 1 and 2. The rules r1 and r2 are associated with membrane 1, while membrane 2 has no rules associated with it. An application of rule r1 = a → a bin2 c2in2 causes a copy of object b and two copies of object c to be sent into the inner membrane 2. The object a is still present after the application, since it appears in the right-hand part of the rule.

MIT Press, Cambridge, MA, USA (1996) 3. : One Alternation Can Be More Powerful Than Randomization in Small and Fast Two-Way Finite Automata. , Wolter, F. ) FCT 2013. LNCS, vol. 8070, pp. 40–47. Springer, Heidelberg (2013). 1007/978-3-642-40164-0 7 4. : On the state complexity of ultrametric finite automata. In: SOFSEM 2013: Theory and Practice of Computer Science, vol. 2, pp. 1–9 (2013) 5. : Two-way automata and length-preserving homomorphisms. Mathematical Systems Theory 29(3), 191–226 (1996). 1007/BF01201276 6.

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Computing with New Resources: Essays Dedicated to Jozef Gruska on the Occasion of His 80th Birthday by Cristian S. Calude

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