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sav07_lecture_3 [2007/03/30 21:55] vkuncak |
sav07_lecture_3 [2007/04/18 09:39] (current) kremena.diatchka |
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assume true = skip (does nothing) | assume true = skip (does nothing) | ||
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==== Composing formulas using relation composition ==== | ==== Composing formulas using relation composition ==== | ||
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In sequential composition we follow the rule for composition of relations. We want to get again formula with free variables x_0,y_0,x,y. So we need to do renaming. Let x_1,y_1,error_1 be fresh variables. | In sequential composition we follow the rule for composition of relations. We want to get again formula with free variables x_0,y_0,x,y. So we need to do renaming. Let x_1,y_1,error_1 be fresh variables. | ||
- | CR(c1 ; c2) = exists x_1,y_1,error_1. CR(c1)[x:=x_1,y:=y_1,error:=error_1] & CR(c2)[x:=x_1,y:=y_1,error:=error_1] | + | CR(c1 ; c2) = exists x_1,y_1,error_1. CR(c1)[x:=x_1,y:=y_1,error:=error_1] & CR(c2)[x_0:=x_1,y_0:=y_1,error_0:=error_1] |
The base case is | The base case is | ||
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Proof: small model theorem. | Proof: small model theorem. | ||
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* [[http://www.cs.nyu.edu/acsys/cvc3/download.html|CVC3]] (successor of CVC Lite) | * [[http://www.cs.nyu.edu/acsys/cvc3/download.html|CVC3]] (successor of CVC Lite) | ||
* [[http://combination.cs.uiowa.edu/smtlib/|SMT-LIB]] Standard for formulas, competition | * [[http://combination.cs.uiowa.edu/smtlib/|SMT-LIB]] Standard for formulas, competition | ||
+ | * [[http://doi.acm.org/10.1145/135226.135233|Omega test]] for conjunctions of integer inequalities | ||
==== Full Presburger arithmetic ==== | ==== Full Presburger arithmetic ==== |