We then define a lattice over the set l a b a b z

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Unformatted text preview: < +∞ for any integer n. We then define a lattice over the set L = {[a, b] | a, b ∈ Z∗ ∧ a ≤ b} ∪ {⊤}. a. Explain what the element ⊤ represents and why we need it for this analysis. Define the partial order and the meet operator for elements in this lattice (including ⊤). b. Using this lattice to compute ranges of variables will fail in general. Explain why. c. To solve the problems from part (b), we define a lattice L′ = {[a, b] | a, b ∈ {−∞, -k, -2, −1, 0, 1, 2,...,k, +∞} ∧ a ≤ b } ∪ {⊤} (with the same partial order as befo...
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