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 | ||
|
sav08:evaluating_formulas_in_finite_structures [2008/03/19 00:36] vkuncak |
sav08:evaluating_formulas_in_finite_structures [2008/03/19 00:46] vkuncak |
||
|---|---|---|---|
| Line 6: | Line 6: | ||
| Then evaluation functions $e_F$ and $e_T$ give algorithms to determine the truth value of $F$. | Then evaluation functions $e_F$ and $e_T$ give algorithms to determine the truth value of $F$. | ||
| + | |||
| + | This is the model checking problem for first-order logic on finite structures: is a given interpretation model of $F$. | ||
| + | |||
| ===== Applications of Formula Evaluation ===== | ===== Applications of Formula Evaluation ===== | ||
| Line 25: | Line 28: | ||
| ===== Efficiency of Evaluating Formulas ===== | ===== Efficiency of Evaluating Formulas ===== | ||
| - | Given a language ${\cal L}$, formula a formula $F$ in ${\cal L}$ and an interpretation $I=(D,\alplha)$, determine $e_F(F)(I)$. | + | Given a language ${\cal L}$, formula a formula $F$ in ${\cal L}$ and an interpretation $I=(D,\alpha)$, determine $e_F(F)(I)$. |
| * fix formula: LOGSPACE (iterate over elements) | * fix formula: LOGSPACE (iterate over elements) | ||
| - | * fix language: PSPACE (reduce to [[QBF and Quantifier Elimination|QBF]]) | + | * fix language with symbols of bounded arity: PSPACE (reduce to [[QBF and Quantifier Elimination|QBF]]) |
| ===== References ===== | ===== References ===== | ||
| - | * Neil Immerman: Descriptive Complexity | + | * [[http://citeseer.ist.psu.edu/burch90symbolic.html|Symbolic Model Checking: 10^20 States and Beyond]] |
| + | * Neil Immerman: Descriptive Complexity, Springer | ||
| + | |||