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sav08:introductory_remarks_on_smt_provers [2008/04/17 11:08] vkuncak |
sav08:introductory_remarks_on_smt_provers [2009/05/06 00:24] vkuncak |
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| Two layers: | Two layers: | ||
| * fast solving of quantifier-free formulas (see [[http://citeseer.ist.psu.edu/671087.html|DPLL(T) paper]]) | * fast solving of quantifier-free formulas (see [[http://citeseer.ist.psu.edu/671087.html|DPLL(T) paper]]) | ||
| - | * SAT solver to 'enumerate' conjunctions of disjunctive normal form | + | * SAT solver to 'enumerate' conjunctions of disjunctive normal form ([[sav09:Lecture 08a]]) |
| * **specialized algorithms for quantifier-free formulas** - this is what we will talk about today | * **specialized algorithms for quantifier-free formulas** - this is what we will talk about today | ||
| * heuristic quantifier instantiation (instantiation rule) | * heuristic quantifier instantiation (instantiation rule) | ||
| Line 29: | Line 29: | ||
| Consider the following formula, where $f$ denotes functions from integers to integers and $a,b$ are integers. | Consider the following formula, where $f$ denotes functions from integers to integers and $a,b$ are integers. | ||
| \[\begin{array}{l} | \[\begin{array}{l} | ||
| - | (\forall x. x \le y \rightarrow f(x) \le f(y))\ \land \\[0.5ex] | + | (\forall x.\forall y.\ x \le y \rightarrow f(x) \le f(y))\ \land \\ |
| - | (\forall x. f(x)=f(y) \rightarrow x=y)\ \land\\[0.5ex] | + | (\forall x.\forall y. f(x)=f(y) \rightarrow x=y)\ \land\\ |
| - | 2 f(a) \le 2f(b)+1\ \land\\[0.5ex] | + | 2 f(a) \le 2f(b)+1\ \land\\ |
| b < a | b < a | ||
| \end{array} | \end{array} | ||
| \] | \] | ||