Differences
This shows you the differences between two versions of the page.
|
sav08:homework09 [2008/04/25 15:06] vkuncak |
sav08:homework09 [2015/04/21 17:30] |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| - | ====== Homework 09 - Due Wednesday, April 30 ====== | ||
| - | |||
| - | ===== Problem 1 ===== | ||
| - | |||
| - | Describe current progress on your project. | ||
| - | |||
| - | ===== Problem 2 ===== | ||
| - | |||
| - | Prove that the quantifier-free theory of term algebras is convex (See [[Calculus of Computation Textbook]], Section 10.3.1). That is, show that, if $C$ is a conjunction of literals of form $t=t'$ and $t\neq t'$ where $t,t'$ are terms in some language (containing variables), and if formula | ||
| - | \[ | ||
| - | C \rightarrow \bigvee_{i=1} t_i=t'_i | ||
| - | \] | ||
| - | is valid (holds for all values of variables) in the Herbrand interpretation (where elements are ground terms and $\alpha(f)(t_1,\ldots,t_n)=f(t_1,\ldots,t_n)$), then for some $i$ | ||
| - | \[ | ||
| - | C \rightarrow t_i=t'_i | ||
| - | \] | ||
| - | holds for all values of variables in the Herbrand interpretation. | ||
| - | |||
| - | If you use in your solution any theorem about term algebras that we did not prove in the class, you need to prove the theorem as well. | ||