Presburger Arithmetic and Its Use in Verification

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APPENDIX A. EXAMPLES OF MULTICORE PARALLELISM IN F# Array.append m1.Result m2 let rec msort ls = if Array.length ls
Appendix B Source code of experiments B.1 Utilities.fs module Utilities open System open System.Threading.Tasks open System.Collections.Concurrent type System.Threading.Tasks.Task with static member WaitAll(ts) = Task.WaitAll [| for t in ts −> t :> Task |] let (%|)ab=(b % a =0) let rec gcd(l1, l2) = if l2 =0then l1 else gcd(l2, l1 % l2) // Calculate gcd of a list of postive integer. // Rewrite to use tail recursion. let gcds ls = let rec recGcds ls res = match ls with |[]−> res | l::ls’ −> recGcds ls’ (gcd(res, abs(l))) match ls with |[]−> 1 |[l]−> abs(l) | l::ls’ −> recGcds ls’ l let gcda ls = Array.fold(fun acc l −> gcd(abs(l), acc)) 1 ls let lcm(l1, l2) = (l1 / gcd(l1, l2)) ∗ l2 71
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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 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 78 and 79: 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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