Puzzle Update Koen Lindstrm Claessen a ; (b ; c) 5 zip (x ; y) 5 ; - - PowerPoint PPT Presentation

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Sep 28, 2023 390 likes •513 views

Puzzle Update Koen Lindstrm Claessen a ; (b ; c) 5 zip (x ; y) 5 ; z = ax ; (by ; cx) 4 ; by ; cz (p ; q) k = p ; (q ; p) k-1 ; q (a ; b) 6 zip (x ; y ; z) 4 = ((a ; b) 3 zip (x ; y ; z) 2 ) 2 p 3 zip q 2 = (p 3 zip (q ; q)) ((p ; p 2 )

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Puzzle Update

Koen Lindström Claessen

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a ; (b ; c)5 zip (x ; y)5 ; z ax ; (by ; cx)4 ; by ; cz (p ; q)k = p ; (q ; p)k-1 ; q =

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(a ; b)6 zip (x ; y ; z)4 ((a ; b)3 zip (x ; y ; z)2)2 =

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p3 zip q2 (p3 zip (q ; q)) ((p ; p2) zip q2) = ((p2 ; p) zip q2)

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p ; q zip r (p zip take k r) ; (q zip drop k r) =

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take k (rn) ra ; take b r take b r ; (drop b r ; take b r)a =

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(expanded string)

QuickCheck properties

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a ; b6 ; c2 zip (x ; y ; z)3 ax; by; bz; bx; by; bz; bx; cy; cz = ax ; (by ; bz ; bx)2 ; cy ; cz

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Ideas

Use Brzozowski-style derivatives -> state

machines

Generalizing the compressing method to

expressions

Show that it is NP-hard
Show that you can factor numbers with it

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