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sav08:quantifier_instantiation [2008/04/28 10:25] thomas.geek |
sav08:quantifier_instantiation [2012/05/21 10:00] vkuncak |
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| Quantifier instantiation: | Quantifier instantiation: | ||
| - | * most of the time handle quantifiers | ||
| * given a conjunct $\forall x.F(x)$ and a term $t$ occurring in other conjuncts, generate $F(t)$ and continue | * given a conjunct $\forall x.F(x)$ and a term $t$ occurring in other conjuncts, generate $F(t)$ and continue | ||
| * in general this is incomplete | * in general this is incomplete | ||
| - | * this cannot be complete because quantified combination of linear arithmetic with uninterpreted functions symbols is highly undecidable | + | * it cannot be complete because quantified combination of linear arithmetic with uninterpreted functions symbols is highly undecidable |
| Triggers: instantiate $\forall x. P(x) \rightarrow Q(x)$ only if you find $P(t)$ | Triggers: instantiate $\forall x. P(x) \rightarrow Q(x)$ only if you find $P(t)$ | ||
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| * also incorporated in recent versions | * also incorporated in recent versions | ||
| - | Traditionally resolution-based provers have more sophisticated quantifier handling (but no decision procedures). This is changing and both approaches integrate techniques from others. | + | Traditionally resolution-based provers have more sophisticated quantifier handling (but have no decision procedures). This is changing and both approaches integrate techniques from others. |
| * [[http://www.cs.nyu.edu/~barrett/pubs/GBT07.ps|Solving Quantified Verification Conditions using Satisfiability Modulo Theories]] | * [[http://www.cs.nyu.edu/~barrett/pubs/GBT07.ps|Solving Quantified Verification Conditions using Satisfiability Modulo Theories]] | ||
| * [[http://research.microsoft.com/projects/z3/cade07.pdf|Efficient E-matching for SMT solvers]] by Leonardo de Moura and Nikolaj Bjørner | * [[http://research.microsoft.com/projects/z3/cade07.pdf|Efficient E-matching for SMT solvers]] by Leonardo de Moura and Nikolaj Bjørner | ||
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| Recent approaches combine DPLL(T) solvers and resolution-based solvers | Recent approaches combine DPLL(T) solvers and resolution-based solvers | ||
| * [[http://www.mpi-inf.mpg.de/~uwe/paper/TSPASS-bibl.html|SPASS+T]] by Virgile Prevosto and Uwe Waldmann | * [[http://www.mpi-inf.mpg.de/~uwe/paper/TSPASS-bibl.html|SPASS+T]] by Virgile Prevosto and Uwe Waldmann | ||
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