day32 - j B = A X j 1 B but such a k may not exist – in...

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Click to edit Master subtitle style 10/4/11 Undecidability of Finite Convergence for Operators Relation to Real-Time (Constant Time) Execution

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10/4/11 Dec 2, © UCF (Charles E. 22 Simple Operators Concatenation b B } Insertion A & B = { xyz | y 6 A, xz 6 B, x, y, z ‘ l*} Clearly, since x can be ², A 5 B ³ A & B
10/4/11 Dec 2, © UCF (Charles E. 33 K-insertion A ± [ k ] B = { x1y1x2y2 … xkykxk+1 | y1y2 … yk v A, x1x2 … xkxk+1 & B, Clearly, A g B & A & [ k ] B , for all k>0

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10/4/11 Dec 2, © UCF (Charles E. 44 Iterated Insertion A (1) &[ n ] B = A y [ n ] B A (k+1) L [ n ] B = A L [ n ] (A (k) v n ] B)
10/4/11 Dec 2, © UCF (Charles E. 55 Shuffle Shuffle (product and bounded product) j ] B A ²[ k j ] B = A X[ k ] B One is tempted to define shuffle product as A c B = A t[ k ] B where k = “ y [ A ] [

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Unformatted text preview: j ] B = A X [ j +1] B ] but such a k may not exist – in fact, we wil 10/4/11 Dec 2, © UCF (Charles E. 66 More Shuffles • Iterated shuffle – A &0 B = A – A & k +1 B = (A ¤ [ k ] B) & B • Shuffle closure – A & * B = 7 k L 0 (A f k ] B) 10/4/11 Dec 2, © UCF (Charles E. 77 Crossover • Unconstrained crossover is defined by A & u B = { wz, yx | wx& A and yz&B} • Constrained crossover is defined by A &c B = { wz, yx | wx&A and yzW B, |w| = |y|, |x| = |z| } 10/4/11 Dec 2, © UCF (Charles E. 88 Who Cares? • People with no real life (me?) • Insertion and a related deletion operation are used in biomolecular computing and dynamical systems • Shuffle is used in analyzing concurrency as the arbitrary interleaving of parallel events • Crossover is used in genetic algorithms...
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This note was uploaded on 10/03/2011 for the course COT 5310 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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day32 - j B = A X j 1 B but such a k may not exist – in...

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