solutions - UCLA Department of Mathematics
... bird that eats fish, and this bird is not a Pelican. Now, for all creatures c, if P (c) then F (c) is true. So, the contrapositive must also be true: for all creatures c, if ∼ F (c) then ∼ P (c). That is, we know that (iv) is true. To summarize so far, we know that (i) and (iv) are true, but we can ...
... bird that eats fish, and this bird is not a Pelican. Now, for all creatures c, if P (c) then F (c) is true. So, the contrapositive must also be true: for all creatures c, if ∼ F (c) then ∼ P (c). That is, we know that (iv) is true. To summarize so far, we know that (i) and (iv) are true, but we can ...
High Level Verification of Control Intensive Systems
... sive systems, a blowup of the abstract model is likely when using existing predicate abstraction methods. Furthermore, building the abstract model using equations (6) and (7) is time consuming. Both these problems can be avoided by using our technique of combining the localization reduction with pre ...
... sive systems, a blowup of the abstract model is likely when using existing predicate abstraction methods. Furthermore, building the abstract model using equations (6) and (7) is time consuming. Both these problems can be avoided by using our technique of combining the localization reduction with pre ...
A Proof Theory for Generic Judgments
... Γ0 , ∀xB −→ C is proved using the introduction of ∀ on the left from the premise Γ0 , B[t/x] −→ C, where t is some term. To reduce the rank of the cut formula ∀x.B between the sequents Γ −→ ∀x.B and Γ0 , ∀xB −→ C, the eigenvariable c in the sequent calculus proof Π(c) must be substituted by t to yie ...
... Γ0 , ∀xB −→ C is proved using the introduction of ∀ on the left from the premise Γ0 , B[t/x] −→ C, where t is some term. To reduce the rank of the cut formula ∀x.B between the sequents Γ −→ ∀x.B and Γ0 , ∀xB −→ C, the eigenvariable c in the sequent calculus proof Π(c) must be substituted by t to yie ...
Constraint Satisfaction Problems with Infinite Templates
... vertices x and y if there is the constraint ‘x < y’ in the instance. It is easy to see that an instance homomorphically maps to (Q, <) if and only if there is no directed cycle in the graph. Again, this can be tested in linear time, e.g., by depth-first search. Example 3. The so-called betweenness ...
... vertices x and y if there is the constraint ‘x < y’ in the instance. It is easy to see that an instance homomorphically maps to (Q, <) if and only if there is no directed cycle in the graph. Again, this can be tested in linear time, e.g., by depth-first search. Example 3. The so-called betweenness ...
