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By Jean Krivine, Jean-Bernard Stefani

This e-book constitutes the refereed complaints of the seventh foreign convention on Reversible Computation, RC 2015, held in Grenoble, France in July 2015. the nineteen papers offered including 1 invited speak have been conscientiously reviewed and chosen from 30 submissions. The convention on Reversible Computation fairly contains the next subject matters: reversible machines, reversible languages, layout and verification of quantum circuits, layout of reversible circuits and circuit synthesis.

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Extra resources for Reversible Computation: 7th International Conference, RC 2015, Grenoble, France, July 16-17, 2015, Proceedings

Example text

1) , ) = (rX , 0, , 1) After having reached the $ in state qr , M uses the states qY , qZ , and ql to add a new symbol to the string of the form Y ∗ Z and to return to the beginning of the counter. Subsequently, the counter is increased again: 16. δ(qY , , Y ) = (qY , 0, Y, 1) 17. δ(qY , , Z) = (qZ , 0, Y, 1) The third phase is preceded by a sweep from the left end of the counter to its right end in state rX , whereby the digits (only 0 may appear) are overwritten by X again (this will be the distinguishable block required by Definition 2).

Danos et al. Note that the set G˜ contains the empty graph ∅, which makes A a unitary algebra with unit [∅]. 4 Jump-Closure of Marked Graph Observables We now have all the ingredients in place to derive moment semantics for (DPObased) marked graph rewriting. The set G˜ forms a countable state space over which we generate CTMCs from finite sets of marked rules and associated rate maps. The space A spanned by marked graph observables provides us with a ˜ candidate sub-algebra of RG . It remains to show that A is jump-closed with respect to the CTMCs generated by marked rules.

In order to clarify this notion we continue with an example of a 1RTM that time-constructs a fast-growing function. n Example 3. There is an increasing function of order Θ(22 ) which is 1RTM-timeconstructible. We construct a 1RTM M = S, Γ, Σ, , , δ, p0 , F as follows. , $, X, Y, Z}, Σ = {a} and F = ∅. $ to its working tape: 1. δ(p0 , , ) = (p0 , 1, , 0) 2. δ(p0 , a, ) = (p1 , 1, , 1) 3. δ(p1 , a, ) = (p1 , 1, X, 1) 4. , 1) 5. }, where ! denotes the leading 1. The counter is realized in the X-block of the working tape, starting on the right of the block with the most significant bit on the left.

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