Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
|
sav07_lecture_5_skeleton [2007/03/28 10:50] vkuncak |
sav07_lecture_5_skeleton [2007/03/28 11:08] vkuncak |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| ====== Lecture 5 Skeleton ====== | ====== Lecture 5 Skeleton ====== | ||
| - | + | Two important techniques: | |
| - | + | * Nelson-Oppen combination method | |
| - | + | * Resolution | |
| ===== Basic idea of Nelson-Oppen combination ===== | ===== Basic idea of Nelson-Oppen combination ===== | ||
| Line 45: | Line 44: | ||
| * the same number of nodes | * the same number of nodes | ||
| * same properties on shared symbols (equality and sometimes more) | * same properties on shared symbols (equality and sometimes more) | ||
| + | |||
| + | Lazy approach to integrating solvers for conjunctions and SAT solvers | ||
| ==== General case ==== | ==== General case ==== | ||
| Line 78: | Line 79: | ||
| * f(5) | * f(5) | ||
| * ALL x. 0 <= x --> f(x) > 0 | * ALL x. 0 <= x --> f(x) > 0 | ||
| + | |||
| Line 101: | Line 103: | ||
| Two different techniques (recall we can take negation of formulas): | Two different techniques (recall we can take negation of formulas): | ||
| * Enumerating finite models (last time) gives us a way to show formula is satisfiable | * Enumerating finite models (last time) gives us a way to show formula is satisfiable | ||
| - | * Enumerating proofs gives us a way to show that formula is valid | + | * Enumerating proofs gives us a way to show that formula is valid: semi decision procedure (complete but non-terminating) |
| The gap in the middle: invalid formulas with only infinite models | The gap in the middle: invalid formulas with only infinite models | ||
| * an example with only infinite models: strict partial order with no upper bound | * an example with only infinite models: strict partial order with no upper bound | ||
| - | |||
| - | |||
| - | |||
| - | |||
| - | |||
| ===== Resolution theorem proving ===== | ===== Resolution theorem proving ===== | ||