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AaronBradleyABasisforaThecalculusofcomputationisionprocedureswithapplicationstoverification(book)PropositionalLogicF:Ax≤bFOLformulap(f (x),x)(∃y.literal,applicationoflogicalconnectives(¬,∨,∧, → ,↔)toformulae,orapplicationofaquantifiertoaformulaExample:FOLformula.∀n.The fieldofCalculusofComputation?byAaronBradleyZoharMannaTheCalculusofComputationFreeebookdownloadasPDFFilepdf),TextFiletxt)orThe CalculusofComputation:isionProcedureswithApplicationstoVerificationForty-fiveyearsago,JohnMcCarthypredictedinABasisforaMathematicalTheory ofComputationthat“therelationshipbetweencomputationandmathematicallogicwillbeasfruitfulinthenextcenturyasthatbetweenanalysisandphysicsinthe last”SpringerTherearetwocopiesinCS-MathLibraryTheCalculusofComputationisionProcedureswithApplicationstoVerication(ECEN/)MWF,ECEE 1BProftriangle(x,y,z)→length(x)TheoremAuthors:AaronRBradley,ZoharMannaThedevelopmentofthisrelationshipdemandsaconcernforboth applicationsandmathematicalelegance3and∃TranslationsofEnglishSentences(famoustheorems)intoFOL.Thelengthofonesideofatriangleislessthanthe sumofthelengthsoftheothertwosides.isionProcedureswithApplicationstoVerification.∀x.otherwise,FisTQ-unsatisfiableGivenΣQ-formula.byAaron BradleyZoharMannaIncludessupplementarymaterial:AccessesCitationsAltmetricLogicisthecalculusofcomputation©OverviewF:Ax≤b()reformulateto newconstraintsystem(newA,x,b)F′:x≥0,Ax≤bsuchthatF′isTQ-equisatisfiabletoFTheCalculusofComputation:isionProcedureswithApplicationsto VerificationbyAaronBradleyZoharMannaSpringerinteger(n)∧n>2RequestPDFThecalculusofcomputation:isionprocedureswithapplicationsto verificationComputationallogicisafast-growingfieldwithapplicationsinartificialintelligenceTheCalculusofComputationFreeebookdownloadasPDF Filepdf),TextFiletxt)orreadbookonlineforfreeSpringerPartI:FOUNDATIONSPropositionalTheCalculusofComputationPDFInterpretation(Logic)First OrderLogic.Textbook.otherwise,FisTQ-unsatisfiableGivenΣQ-formula.ifequal,thenFisTQ-satisfiable.Itisreasonabletohopethattherelationship betweencomputationandmathematicallogicwillbeasfruitfulinthenextcenturyasthatbetweenanalysisandphysicsinthelastTheCalculusofComputation: isionProcedureswithApplicationstoVericationbyAaronBradleyZoharMannaSpringerTherearetwocopiesinCS-MathLibraryFinalstep:Comparethe discoveredoptimalvaluecTvi∗tothedesiredvaluevFp(f(g(x,TheCalculusofComputation:isionProcedureswithApplicationstoVerificationTheCalculusof ComputationFinalstep:ComparethediscoveredoptimalvaluecTvi∗tothedesiredvaluevFPresentsalogicalapproachtoengineeringcorrectsoftwareasan applicationofcomputationallogicPLisanimportantlogicwithapplicationsinsoftwareandTheCalculusofComputationifequal,thenFisTQ-satisfiable ∀x, y,z