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sav08:small_solutions_for_quantifier-free_presburger_arithmetic [2010/05/03 11:06] vkuncak |
sav08:small_solutions_for_quantifier-free_presburger_arithmetic [2012/05/21 09:57] vkuncak |
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We also do not need divisibility constraints: $K|t$ is satisfiable iff ++| $t= K q$ is satisfiable, for $q$ fresh ++ | We also do not need divisibility constraints: $K|t$ is satisfiable iff ++| $t= K q$ is satisfiable, for $q$ fresh ++ | ||
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===== Integer Linear Ineqautions ===== | ===== Integer Linear Ineqautions ===== | ||
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Each QFPA formula can be reduced to a disjunction of linear integer inequations. | Each QFPA formula can be reduced to a disjunction of linear integer inequations. | ||
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===== Theorem on Solution Bounds ===== | ===== Theorem on Solution Bounds ===== | ||
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* $m$ is number of constraints | * $m$ is number of constraints | ||
* $n$ is number of variables | * $n$ is number of variables | ||
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===== Extending Theorem to QFPA ===== | ===== Extending Theorem to QFPA ===== | ||
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===== Reduction to SAT ===== | ===== Reduction to SAT ===== | ||
- | We observed before that if we have bounded integers we can encode formula into SAT. | + | Observe that if we have bounded integers we can encode the formula into SAT. |
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===== Implementation ===== | ===== Implementation ===== |