assignment4

assignment4 - f(1 0 f(1 1 f(1 2 and f(5 0 f(5 1 f(5 2 4 The...

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CSC544 Assignment #4 due Tuesday 4/5 in class version 1.0 Problems 1. Let g ( x, y, z ) be a primitive recursive function. Show that the following functions are primitive recursive, (a) f ( x, y ) = g ( x, y, x ) (b) f ( x, y, z, w ) = g ( x, y, x ) (c) f ( x ) = g (1 , 2 , x ) 2. Show that max ( x, y ) = x if x y y otherwise is primitive recursive. 3. Let g ( x ) = x 2 and h ( x, y, z ) = x + y + z and let f ( x, y ) be the func- tion defined from g and h by primitive recursion.
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Unformatted text preview: f (1 , 0) , f (1 , 1) , f (1 , 2), and f (5 , 0) , f (5 , 1) , f (5 , 2). 4. The functions below were deFned in Table 13.1. Explicitly give the func-tions g and h that make the deFnitions legal deFnitions as given in the deFnition for primitive recursive functions. (a) sg (b) sub (c) exp 1...
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