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| - | ====== Lecture 15: Quantifier Elimination for Presburger Arithmetic and BAPA ====== | + | ====== Lecture 15: Quantifier Elimination for Presburger Arithmetic and Beyond ====== |
| ===== Introduction ===== | ===== Introduction ===== | ||
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| ===== Presburger Arithmetic ===== | ===== Presburger Arithmetic ===== | ||
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| - | [[Minimalistic Language of Presburger Arithmetic]] | ||
| [[Definition of Presburger Arithmetic]] | [[Definition of Presburger Arithmetic]] | ||
| [[QE for Presburger Arithmetic]] | [[QE for Presburger Arithmetic]] | ||
| - | |||
| - | [[Cooper's Method for Presburger Arithmetic]] | ||
| ===== Boolean Algebra with Presburger Arithmetic ===== | ===== Boolean Algebra with Presburger Arithmetic ===== | ||
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| + | [[Definition of Boolean Algebra with Presburger Arithmetic]] | ||
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| + | [[Deciding Boolean Algebra with Presburger Arithmetic]] | ||
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| + | Paper: [[http://lara.epfl.ch/~kuncak/papers/KuncakETAL06DecidingBooleanAlgebraPresburgerArithmetic.pdf|Deciding Boolean Algebra with Presburger Arithmetic]] | ||
| ===== Remarks ====== | ===== Remarks ====== | ||
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| [[List of Theories Admitting QE]] | [[List of Theories Admitting QE]] | ||
| - | Definable relations and the use of quantifier-free fragments. | + | [[Applications of Quantifier Elimination]] |
| - | + | ||
| - | Use of QE for relation composition. | + | |
| - | + | ||
| - | Bibliography. | + | |