1. (⊓xp(x)⊓xq(x))  ⊓x(p(x)q(x))
Homework 4 (June 13)
Material covered: Slides
1. Let p(x) and q(x) be some unary predicates (elementary games). Write a legal run Γ of the game
(⊓xp(x)⊓xq(x))  ⊓x(p(x)q(x))
such that Γ contains three moves and it is won by the machine no matter what particular predicates p(x) and q(x) are. You
shall list all three moves of Γ together with their labels (colors). You can write ⊤ instead of green  and ⊥ instead of red .
2. Let p(x,y) be some binary predicate. Write a legal run Γ of the game x⊓yp(x,y)  ⊓x⊓yp(x,y) such that Γ contains
three moves and it is won by the machine no matter what particular predicate p(x,y) is.
3. Write, precisely, the run (sequence of actual moves together with their labels) that generated the evolution sequence shown
on Slide Use constant 7 instead of Tom, constant 8 instead of John, and constant 9 instead of Peggy.
4. You should be able to reproduce the definition of the blind quantifiers.
5. Consider the game xy((Even(x)⊔Odd(x))  (Even(y)⊔Odd(y))  Even(x+y)⊔Odd(x+y)). In the style of slide 8.7,
construct the evolution sequence generated by some run of length 3 won by Machine, and indicate all moves of that run.
6. Describe (informally) Machine’s winning strategies for those games of Slide 8.8 for which the answer is “Yes”.