Presburger Arithmetic and Its Use in Verification

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APPENDIX B. SOURCE CODE OF EXPERIMENTS // Calculate lcm of a list of positive integer. // Rewrite to use tail recursion. let lcms ls = let rec recLcms ls res = match ls with |[]−> res | l::ls’ −> recLcms ls’ (lcm(res, abs(l))) recLcms ls 1 let lcma ls = Array.fold(fun acc l −> lcm(abs(l), acc)) 1 ls 72
B.2. TERM.FS B.2 Term.fs module Term open Microsoft.FSharp.Collections open Utilities type Term = struct val constant: int val coeffs: int [] // Order of fields matters val vars: string [] new(c, vs, cs) ={constant = c; vars = vs; coeffs = cs} override t.ToString() = "(" + string t.constant + ",␣[" + Array.fold2 (fun acc vc−> acc + "(" + string v + "," + string c + ")" + ",␣" ) "" t.vars t. coeffs + "])" end let newTerm (c, xs, cs) =Term(c, xs, cs) let term(c, x) =Term(0, [|x|], [|c|]) let var x = term(1, x) let constTerm i = Term(i, [||],[||]) let Zero = constTerm 0 let One = constTerm 1 let MinusOne = constTerm −1 let rec merge(n1, n2, l1, l2, t1: Term, t2: Term, acc1: ResizeArray, acc2: ResizeArray) = if n1 =0then for i = l2−n2 to l2−1 do acc1.Add(t2.vars.[i]) acc2.Add(t2.coeffs.[i]) elif n2 =0then for i = l1−n1 to l1−1 do acc1.Add(t1.vars.[i]) acc2.Add(t1.coeffs.[i]) else let v1 = t1.vars.[l1−n1] let c1 = t1.coeffs.[l1−n1] let v2 = t2.vars.[l2−n2] let c2 = t2.coeffs.[l2−n2] if v1 = v2 then if c1 + c2 0 then acc1.Add(v1) acc2.Add(c1+c2) merge(n1−1, n2−1, l1, l2, t1, t2, acc1, acc2) elif v1 < v2 then if c1 0 then acc1.Add(v1) 73
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Presburger Arithmetic and Its Use i
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Abstract Today, when every computer
Page 5 and 6:
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:
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 80 and 81: APPENDIX A. EXAMPLES OF MULTICORE P
Page 84 and 85: 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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