Presburger Arithmetic and Its Use in Verification

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APPENDIX A. EXAMPLES OF MULTICORE PARALLELISM IN F# (fun iloopState(local:float) −> let x =(float i +0.5)∗steps local +4.0/(1.0+x ∗ x) ), (fun local −> lock (monitor) (fun () −> sum := !sum + local))) |> ignore !sum ∗ steps // Overall best function let compute2() = let rangeSize = NUM_STEPS /(Environment.ProcessorCount ∗10) let partitions = Partitioner.Create(0, NUM_STEPS, if rangeSize >= 1 then rangeSize else 1) let sum = ref 0.0 let monitor = new Object() Parallel.ForEach( partitions, new ParallelOptions(), (fun () −> 0.0), (fun (min, max) loopState l −> let local = ref 0.0 for i in min .. max − 1 do let x =(float i +0.5)∗steps local := !local +4.0/(1.0+x ∗ x) l +!local), (fun local −> lock (monitor) (fun () −> sum := !sum + local))) |> ignore !sum ∗ steps let sqr x = x ∗ x module Linq = // LINQ let compute1() = (Enumerable .Range(0, NUM_STEPS) .Select(fun i −> 4.0/(1.0+sqr ((float i +0.5)∗steps))) .Sum()) ∗ steps // PLINQ let compute2() = (ParallelEnumerable .Range(0, NUM_STEPS) .Select(fun i −> 4.0/(1.0+sqr ((float i +0.5)∗steps))) .Sum()) ∗ steps 68
A.2. SOURCE CODE OF MERGESORT A.2 Source code of MergeSort module MergeSort open System open System.IO open System.Threading.Tasks open Microsoft.FSharp.Collections let split fs = let len = Array.length fs fs.[0..(len/2)−1], fs.[len/2..] let rec binarySearch (ls: _ [], v, i, j) = if i = j then j else let mid =(i+j)/2 if ls.[mid]
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Presburger Arithmetic and Its Use i
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Abstract Today, when every computer
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Preface The thesis is a part of the
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List of Abbreviations CPU DAG DC DN
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5.2 Simplification of Presburger fo
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CHAPTER 1. INTRODUCTION functional
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Chapter 2 Multicore parallelism on
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2.1. MULTICORE PARALLELISM: A BRIEF
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2.2. MULTICORE PARALLELISM ON .NET
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Page 27 and 28: 2.2. MULTICORE PARALLELISM ON .NET
Page 29 and 30: Chapter 3 Functional paradigm and m
Page 31 and 32: 3.1. PARALLEL FUNCTIONAL ALGORITHMS
Page 33 and 34: 3.2. SOME PITFALLS OF FUNCTIONAL PA
Page 35 and 36: 3.2. SOME PITFALLS OF FUNCTIONAL PA
Page 37 and 38: Chapter 4 Theory of Presburger Arit
Page 39 and 40: 4.2. DECISION PROCEDURES FOR PRESBU
Page 45 and 46: Chapter 5 Duration Calculus and Pre
Page 47 and 48: 5.1. DURATION CALCULUS AND SIDE-CON
Page 49 and 50: 5.2. SIMPLIFICATION OF PRESBURGER F
Page 51: 5.3. SUMMARY occur in equation do n
Page 54 and 55: CHAPTER 6. EXPERIMENTS ON PRESBURGE
Page 56 and 57: CHAPTER 6. EXPERIMENTS ON PRESBURGE
Page 59 and 60: Chapter 7 Parallel execution of dec
Page 61 and 62: 7.1. A PARALLEL VERSION OF COOPER
Page 63 and 64: 7.1. A PARALLEL VERSION OF COOPER
Page 65 and 66: 7.2. A PARALLEL VERSION OF THE OMEG
Page 71 and 72: Chapter 8 Conclusions In this work,
Page 73 and 74: References [1] Nikolaj Bjørner. Li
Page 75: [28] C. R. Reddy and D. W. Loveland
Page 80 and 81: APPENDIX A. EXAMPLES OF MULTICORE P
Page 82 and 83: APPENDIX B. SOURCE CODE OF EXPERIME
Page 100: TRITA-CSC-E 2011:108 ISRN-KTH/CSC/E
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Presburger Arithmetic and Its Use in Verification

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