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Unformatted text preview: COT 5310 Fall 2007 Midterm#1 Name: KEY 12 1 . Choosing from among (REC) recursive , (RE) re nonrecursive, (coRE) core nonrecursive , (NR) nonre/noncore , categorize each of the sets in a) through d). Justify your answer by showing some minimal quantification of some known recursive predicate. a.) { f  whenever x>y and f(x) and f(y) then f(x)>f(y) } coRE Justification: x y t [(STP(x,f,t) & STP(y,f,t) & (x>y)) (VALUE(x,f,t)>VALUE(y,f,t))] b.) { f  size of range(f) is at most 1 } coRE Justification: x y t [(STP(x, f, t) & STP(y, f, t)) (VALUE(x, f, t) = VALUE(y, f, t))] I allowed K x t [STP(x, f, t) (VALUE(x, f, t) = K)], which is NR c.) { <f,x>  f(x) converges in at most x 2 steps } REC Justification: STP(x, f, x 2 ) d.) { f  domain(f) contains the value 0 } RE Justification: t STP(0, f, t) 12 2 . Let set A be recursive, and both B and C be re nonrecursive. Choosing from among (REC) recursive , (RE) re nonrecursive , (NR) nonre , categorize the set D in each of a) through d) by listing all possible categories. No justification is required. You may find it useful to know that, if possible categories....
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