CS 598mp: Fall 2005: Homework #2
Due on Fri 16 Sep
Hand over in class or to Colin Robertson at 3229 SC
Problem.
We showed in class that Presburger arithmetic, which is the first-order logic
over the structure (N, S, <, +,0,1,=) is decidable.
•Show Presburger arithmetic with the extra predicate Even is decidable
where Even is a monadic predicate such that Even(i) is true iff iis even.
•Similarly, show Presburger arithmetic with predicate PowerOfTwo is de-
cidable where PowerOfTwo is a monadic predicate such that PowerOfTwo(i)
is true iff iis a power of 2, i.e. i= 2jfor some j∈N.
•Is Presburger arithmetic with the predicate PowerofThree decidable, where
PowerOfThree(i) is true iff iis a power of 3?
Don’t give entire proofs; just give proofs of the extra constructions needed in
order to prove the results.