[13645] | 1 | #region License Information |
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| 2 | /* HeuristicLab |
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| 3 | * Copyright (C) 2002-2015 Heuristic and Evolutionary Algorithms Laboratory (HEAL) |
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| 4 | * |
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| 5 | * This file is part of HeuristicLab. |
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| 6 | * |
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| 7 | * HeuristicLab is free software: you can redistribute it and/or modify |
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| 8 | * it under the terms of the GNU General Public License as published by |
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| 9 | * the Free Software Foundation, either version 3 of the License, or |
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| 10 | * (at your option) any later version. |
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| 11 | * |
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| 12 | * HeuristicLab is distributed in the hope that it will be useful, |
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| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
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| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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| 15 | * GNU General Public License for more details. |
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| 16 | * |
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| 17 | * You should have received a copy of the GNU General Public License |
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| 18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>. |
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| 19 | */ |
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| 20 | #endregion |
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| 21 | |
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[15060] | 22 | using System; |
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| 23 | using System.Collections.Generic; |
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[13645] | 24 | using System.Diagnostics.Contracts; |
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[15060] | 25 | using System.Linq; |
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[13645] | 26 | |
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| 27 | namespace HeuristicLab.Algorithms.DataAnalysis.MctsSymbolicRegression { |
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| 28 | |
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[15060] | 29 | // This class restricts the set of allowed transitions of the automaton to prevent exploration of duplicate expressions. |
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| 30 | // It would be possible to implement this class in such a way that the search never visits a duplicate expression. However, |
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| 31 | // it seems very intricate to detect this robustly and in all cases while generating an expression because |
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| 32 | // some for of lookahead is necessary. |
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| 33 | // Instead the constraint handler only catches the obvious duplicates directly, but does not guarantee that the search always produces a valid expression. |
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| 34 | // The ratio of the number of unsuccessful searches, that need backtracking should be tracked in the MCTS alg (MctsSymbolicRegressionStatic) |
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| 35 | |
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| 36 | // All changes to this class should be tested through unit tests. It is important that the ConstraintHandler is not too restrictive. |
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| 37 | |
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| 38 | // the constraints are derived from a canonical form for expressions. |
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| 39 | // overall we can enforce a limited number of variable references |
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| 40 | // |
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| 41 | // an expression is a sum of terms t_1 ... t_n where terms are ordered according to a relation t_i (<=)_term t_j for each pair t_i, t_j and i <= j |
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| 42 | // a term is a product of factors where factors are ordered according to relation f_i (<=)_factor f_j for each pair f_i,f_j and i <= j |
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| 43 | |
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| 44 | // we want to enforce lower-order terms before higher-order terms in expressions (based on number of variable references) |
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| 45 | // factors can have different types (variable, exp, log, inverse) |
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| 46 | |
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| 47 | // (<=)_term [IsSmallerOrEqualTerm(t_i, t_j)] |
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| 48 | // 1. NumberOfVarRefs(t_i) < NumberOfVarRefs(t_j) --> true enforce terms with non-decreasing number of var refs |
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| 49 | // 2. NumberOfVarRefs(t_i) > NumberOfVarRefs(t_j) --> false |
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| 50 | // 3. NumFactors(t_i) > NumFactors(t_j) --> true enforce terms with non-increasing number of factors |
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| 51 | // 4. NumFactors(t_i) < NumFactors(t_j) --> false |
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| 52 | // 5. for all k factors: Factor(k, t_i) (<=)_factor Factor(k, t_j) --> true // factors must be non-decreasing |
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| 53 | // 6. all factors are (=)_factor --> true |
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| 54 | // 7. else false |
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| 55 | |
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| 56 | // (<=)_factor [IsSmallerOrEqualFactor(f_i, f_j)] |
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| 57 | // 1. FactorType(t_i) < FactorType(t_j) --> true enforce terms with non-decreasing factor type (var < exp < log < inv) |
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| 58 | // 2. FactorType(t_i) > FactorType(t_j) --> false |
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| 59 | // 3. Compare the two factors specifically |
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| 60 | // - variables: varIdx_i <= varIdx_j (only one var reference) |
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| 61 | // - exp: number of variable references and then varIdx_i <= varIdx_j for each position |
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| 62 | // - log: number of variable references and ... |
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| 63 | // - inv: number of variable references and ... |
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| 64 | // |
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| 65 | |
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| 66 | // for log and inverse factors we allow all polynomials as argument |
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| 67 | // a polynomial is a sum of terms t_1 ... t_n where terms are ordered according to a relation t_i (<=)_poly t_j for each pair t_i, t_j and i <= j |
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| 68 | |
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| 69 | // (<=)_poly [IsSmallerOrEqualPoly(t_i, t_j)] |
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| 70 | // 1. NumberOfVarRefs(t_i) < NumberOfVarRefs(t_j) --> true // enforce non-decreasing number of var refs |
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| 71 | // 2. NumberOfVarRefs(t_i) > NumberOfVarRefs(t_j) --> false // enforce non-decreasing number of var refs |
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| 72 | // 3. for all k variables: VarIdx(k,t_i) > VarIdx(k, t_j) --> false // enforce non-decreasing variable idx |
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| 73 | |
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| 74 | |
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| 75 | // we store the following to make comparsions: |
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| 76 | // - prevTerm (complete & containing all factors) |
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| 77 | // - curTerm (incomplete & containing all completed factors) |
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| 78 | // - curFactor (incomplete) |
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[13645] | 79 | internal class ConstraintHandler { |
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| 80 | private int nVars; |
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| 81 | private readonly int maxVariables; |
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[15060] | 82 | private bool invalidExpression; |
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[13645] | 83 | |
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[15060] | 84 | public bool IsInvalidExpression { |
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| 85 | get { return invalidExpression; } |
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| 86 | } |
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[13645] | 87 | |
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| 88 | |
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[15060] | 89 | private TermInformation prevTerm; |
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| 90 | private TermInformation curTerm; |
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| 91 | private FactorInformation curFactor; |
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| 92 | |
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| 93 | |
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| 94 | private class TermInformation { |
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| 95 | public int numVarReferences { get { return factors.Sum(f => f.numVarReferences); } } |
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| 96 | public List<FactorInformation> factors = new List<FactorInformation>(); |
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| 97 | } |
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| 98 | |
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| 99 | private class FactorInformation { |
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| 100 | public int numVarReferences = 0; |
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| 101 | public int factorType; // use the state number to represent types |
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| 102 | |
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| 103 | // for variable factors |
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| 104 | public int variableState = -1; |
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| 105 | |
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| 106 | // for exp factors |
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| 107 | public List<int> expVariableStates = new List<int>(); |
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| 108 | |
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| 109 | // for log and inv factors |
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| 110 | public List<List<int>> polyVariableStates = new List<List<int>>(); |
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| 111 | } |
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| 112 | |
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| 113 | |
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[13645] | 114 | public ConstraintHandler(int maxVars) { |
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| 115 | this.maxVariables = maxVars; |
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| 116 | } |
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| 117 | |
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[15060] | 118 | // the order relations for terms and factors |
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[13645] | 119 | |
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[15060] | 120 | private static int CompareTerms(TermInformation a, TermInformation b) { |
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| 121 | if (a.numVarReferences < b.numVarReferences) return -1; |
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| 122 | if (a.numVarReferences > b.numVarReferences) return 1; |
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[13645] | 123 | |
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[15060] | 124 | if (a.factors.Count > b.factors.Count) return -1; // terms with more factors should be ordered first |
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| 125 | if (a.factors.Count < b.factors.Count) return +1; |
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[13645] | 126 | |
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[15060] | 127 | var aFactors = a.factors.GetEnumerator(); |
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| 128 | var bFactors = b.factors.GetEnumerator(); |
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| 129 | while (aFactors.MoveNext() & bFactors.MoveNext()) { |
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| 130 | var c = CompareFactors(aFactors.Current, bFactors.Current); |
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| 131 | if (c < 0) return -1; |
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| 132 | if (c > 0) return 1; |
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| 133 | } |
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| 134 | // all factors are the same => terms are the same |
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| 135 | return 0; |
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| 136 | } |
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[13645] | 137 | |
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[15060] | 138 | private static int CompareFactors(FactorInformation a, FactorInformation b) { |
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| 139 | if (a.factorType < b.factorType) return -1; |
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| 140 | if (a.factorType > b.factorType) return +1; |
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| 141 | // same factor types |
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| 142 | if (a.factorType == Automaton.StateVariableFactorStart) { |
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| 143 | return a.variableState.CompareTo(b.variableState); |
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| 144 | } else if (a.factorType == Automaton.StateExpFactorStart) { |
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| 145 | return CompareStateLists(a.expVariableStates, b.expVariableStates); |
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| 146 | } else { |
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| 147 | if (a.numVarReferences < b.numVarReferences) return -1; |
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| 148 | if (a.numVarReferences > b.numVarReferences) return +1; |
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| 149 | if (a.polyVariableStates.Count > b.polyVariableStates.Count) return -1; // more terms in the poly should be ordered first |
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| 150 | if (a.polyVariableStates.Count < b.polyVariableStates.Count) return +1; |
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| 151 | // log and inv |
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| 152 | var aTerms = a.polyVariableStates.GetEnumerator(); |
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| 153 | var bTerms = b.polyVariableStates.GetEnumerator(); |
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| 154 | while (aTerms.MoveNext() & bTerms.MoveNext()) { |
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| 155 | var c = CompareStateLists(aTerms.Current, bTerms.Current); |
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| 156 | if (c != 0) return c; |
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[13645] | 157 | } |
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[15060] | 158 | return 0; // all terms in the polynomial are the same |
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[13645] | 159 | } |
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[15060] | 160 | } |
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| 161 | |
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| 162 | private static int CompareStateLists(List<int> a, List<int> b) { |
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| 163 | if (a.Count < b.Count) return -1; |
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| 164 | if (a.Count > b.Count) return +1; |
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| 165 | for (int i = 0; i < a.Count; i++) { |
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| 166 | if (a[i] < b[i]) return -1; |
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| 167 | if (a[i] > b[i]) return +1; |
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[13645] | 168 | } |
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[15060] | 169 | return 0; // all states are the same |
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| 170 | } |
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[13645] | 171 | |
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| 172 | |
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[15060] | 173 | private bool IsNewTermAllowed() { |
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| 174 | // next term must have at least as many variable references as the previous term |
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| 175 | return prevTerm == null || nVars + prevTerm.numVarReferences <= maxVariables; |
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[13645] | 176 | } |
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| 177 | |
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[15060] | 178 | private bool IsNewFactorAllowed() { |
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| 179 | // next factor must have a larger or equal type compared to the previous factor. |
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| 180 | // if the types are the same it must have at least as many variable references. |
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| 181 | // so if the prevFactor is any other than invFactor (last possible type) then we only need to be able to add one variable |
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| 182 | // otherwise we need to be able to add at least as many variables as the previous factor |
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| 183 | return !curTerm.factors.Any() || |
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| 184 | (nVars + curTerm.factors.Last().numVarReferences <= maxVariables); |
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| 185 | } |
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[13645] | 186 | |
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[15060] | 187 | private bool IsAllowedAsNextFactorType(int followState) { |
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| 188 | // IsNewTermAllowed already ensures that we can add a term with enough variable references |
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[13645] | 189 | |
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[15060] | 190 | // enforce constraints within terms (compare to prev factor) |
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| 191 | if (curTerm.factors.Any()) { |
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| 192 | // enforce non-decreasing factor types |
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| 193 | if (curTerm.factors.Last().factorType > followState) return false; |
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| 194 | // when the factor type is the same, starting a new factor is only allowed if we can add at least the number of variables of the prev factor |
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| 195 | if (curTerm.factors.Last().factorType == followState && nVars + curTerm.factors.Last().numVarReferences > maxVariables) return false; |
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| 196 | } |
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[13645] | 197 | |
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[15060] | 198 | // enforce constraints on terms (compare to prev term) |
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| 199 | // meaning that we must ensure non-decreasing terms |
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| 200 | if (prevTerm != null) { |
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| 201 | // a factor type is only allowed if we can then produce a term that is larger or equal to the prev term |
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| 202 | // (1) if we the number of variable references still remaining is larger than the number of variable references in the prev term |
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| 203 | // then it is always possible to build a larger term |
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| 204 | // (2) otherwise we try to build the largest possible term starting from current factors in the term. |
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| 205 | // |
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| 206 | |
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| 207 | var numVarRefsRemaining = maxVariables - nVars; |
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| 208 | Contract.Assert(!curTerm.factors.Any() || curTerm.factors.Last().numVarReferences <= numVarRefsRemaining); |
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| 209 | |
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| 210 | if (prevTerm.numVarReferences < numVarRefsRemaining) return true; |
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| 211 | |
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| 212 | // variable factors must be handled differently because they can only contain one variable reference |
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| 213 | if (followState == Automaton.StateVariableFactorStart) { |
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| 214 | // append the variable factor and the maximum possible state from the previous factor to create a larger factor |
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| 215 | var varF = CreateLargestPossibleFactor(Automaton.StateVariableFactorStart, 1); |
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| 216 | var maxF = CreateLargestPossibleFactor(prevTerm.factors.Max(f => f.factorType), numVarRefsRemaining - 1); |
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| 217 | var origFactorCount = curTerm.factors.Count; |
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| 218 | // add this factor to the current term |
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| 219 | curTerm.factors.Add(varF); |
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| 220 | curTerm.factors.Add(maxF); |
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| 221 | var c = CompareTerms(prevTerm, curTerm); |
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| 222 | // restore term |
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| 223 | curTerm.factors.RemoveRange(origFactorCount, 2); |
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| 224 | // if the prev term is still larger then this followstate is not allowed |
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| 225 | if (c > 0) { |
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| 226 | return false; |
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| 227 | } |
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| 228 | } else { |
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| 229 | var newF = CreateLargestPossibleFactor(followState, numVarRefsRemaining); |
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| 230 | |
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| 231 | var origFactorCount = curTerm.factors.Count; |
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| 232 | // add this factor to the current term |
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| 233 | curTerm.factors.Add(newF); |
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| 234 | var c = CompareTerms(prevTerm, curTerm); |
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| 235 | // restore term |
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| 236 | curTerm.factors.RemoveAt(origFactorCount); |
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| 237 | // if the prev term is still larger then this followstate is not allowed |
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| 238 | if (c > 0) { |
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| 239 | return false; |
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| 240 | } |
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| 241 | } |
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| 242 | } |
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| 243 | return true; |
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[13645] | 244 | } |
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| 245 | |
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[15060] | 246 | // largest possible factor of the given kind |
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| 247 | private FactorInformation CreateLargestPossibleFactor(int factorType, int numVarRefs) { |
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| 248 | var newF = new FactorInformation(); |
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| 249 | newF.factorType = factorType; |
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| 250 | if (factorType == Automaton.StateVariableFactorStart) { |
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| 251 | newF.variableState = int.MaxValue; |
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| 252 | newF.numVarReferences = 1; |
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| 253 | } else if (factorType == Automaton.StateExpFactorStart) { |
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| 254 | for (int i = 0; i < numVarRefs; i++) |
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| 255 | newF.expVariableStates.Add(int.MaxValue); |
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| 256 | newF.numVarReferences = numVarRefs; |
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| 257 | } else if (factorType == Automaton.StateInvFactorStart || factorType == Automaton.StateLogFactorStart) { |
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| 258 | for (int i = 0; i < numVarRefs; i++) { |
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| 259 | newF.polyVariableStates.Add(new List<int>()); |
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| 260 | newF.polyVariableStates[i].Add(int.MaxValue); |
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| 261 | } |
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| 262 | newF.numVarReferences = numVarRefs; |
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| 263 | } |
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| 264 | return newF; |
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| 265 | } |
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[13645] | 266 | |
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[15060] | 267 | private bool IsAllowedAsNextVariableFactor(int variableState) { |
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| 268 | Contract.Assert(variableState >= Automaton.FirstDynamicState); |
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| 269 | return !curTerm.factors.Any() || curTerm.factors.Last().variableState <= variableState; |
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| 270 | } |
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[13645] | 271 | |
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[15060] | 272 | private bool IsAllowedAsNextInExp(int variableState) { |
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| 273 | Contract.Assert(variableState >= Automaton.FirstDynamicState); |
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| 274 | if (curFactor.expVariableStates.Any() && curFactor.expVariableStates.Last() > variableState) return false; |
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| 275 | if (curTerm.factors.Any()) { |
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| 276 | // try and compare with prev factor |
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| 277 | curFactor.numVarReferences++; |
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| 278 | curFactor.expVariableStates.Add(variableState); |
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| 279 | var c = CompareFactors(curTerm.factors.Last(), curFactor); |
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| 280 | curFactor.numVarReferences--; |
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| 281 | curFactor.expVariableStates.RemoveAt(curFactor.expVariableStates.Count - 1); |
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| 282 | return c <= 0; |
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| 283 | } |
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| 284 | return true; |
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| 285 | } |
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[13645] | 286 | |
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[15060] | 287 | private bool IsNewTermAllowedInPoly() { |
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| 288 | return nVars + curFactor.polyVariableStates.Last().Count() <= maxVariables; |
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| 289 | } |
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[13645] | 290 | |
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[15060] | 291 | private bool IsAllowedAsNextInPoly(int variableState) { |
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| 292 | Contract.Assert(variableState >= Automaton.FirstDynamicState); |
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| 293 | return !curFactor.polyVariableStates.Any() || |
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| 294 | !curFactor.polyVariableStates.Last().Any() || |
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| 295 | curFactor.polyVariableStates.Last().Last() <= variableState; |
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[13645] | 296 | } |
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[15060] | 297 | private bool IsTermCompleteInPoly() { |
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| 298 | var nTerms = curFactor.polyVariableStates.Count; |
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| 299 | return nTerms == 1 || |
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| 300 | curFactor.polyVariableStates[nTerms - 2].Count <= curFactor.polyVariableStates[nTerms - 1].Count; |
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[13645] | 301 | |
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[15060] | 302 | } |
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| 303 | private bool IsCompleteExp() { |
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| 304 | return !curTerm.factors.Any() || CompareFactors(curTerm.factors.Last(), curFactor) <= 0; |
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| 305 | } |
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[13645] | 306 | |
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[15060] | 307 | public bool IsAllowedFollowState(int currentState, int followState) { |
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| 308 | // an invalid action was taken earlier on => nothing can be done anymore |
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| 309 | if (invalidExpression) return false; |
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| 310 | // states that have no alternative are always allowed |
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| 311 | // some ending states are only allowed if enough variables have been used in the term |
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| 312 | if ( |
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| 313 | currentState == Automaton.StateTermStart || // no alternative |
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| 314 | currentState == Automaton.StateExpFactorStart || |
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| 315 | currentState == Automaton.StateLogFactorStart || |
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| 316 | currentState == Automaton.StateInvFactorStart || |
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| 317 | followState == Automaton.StateVariableFactorEnd || // no alternative |
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| 318 | followState == Automaton.StateExpFEnd || // no alternative |
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| 319 | followState == Automaton.StateLogTFEnd || // no alternative |
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| 320 | followState == Automaton.StateInvTFEnd || // no alternative |
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| 321 | followState == Automaton.StateFactorEnd || // always allowed because no alternative |
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| 322 | followState == Automaton.StateExprEnd // we could also constrain the minimum number of terms here |
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| 323 | ) return true; |
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[13645] | 324 | |
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| 325 | |
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[15060] | 326 | // starting a new term is only allowed if we can add a term with at least the number of variables of the prev term |
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| 327 | if (followState == Automaton.StateTermStart && !IsNewTermAllowed()) return false; |
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| 328 | if (followState == Automaton.StateFactorStart && !IsNewFactorAllowed()) return false; |
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| 329 | if (currentState == Automaton.StateFactorStart && !IsAllowedAsNextFactorType(followState)) return false; |
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| 330 | if (followState == Automaton.StateTermEnd && prevTerm != null && CompareTerms(prevTerm, curTerm) > 0) return false; |
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| 331 | |
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| 332 | // all of these states add at least one variable |
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| 333 | if ( |
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| 334 | followState == Automaton.StateVariableFactorStart || |
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| 335 | followState == Automaton.StateExpFactorStart || followState == Automaton.StateExpFStart || |
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| 336 | followState == Automaton.StateLogFactorStart || followState == Automaton.StateLogTStart || |
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| 337 | followState == Automaton.StateLogTFStart || |
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| 338 | followState == Automaton.StateInvFactorStart || followState == Automaton.StateInvTStart || |
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| 339 | followState == Automaton.StateInvTFStart) { |
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| 340 | if (nVars + 1 > maxVariables) return false; |
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[13645] | 341 | } |
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| 342 | |
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[15060] | 343 | if (currentState == Automaton.StateVariableFactorStart && !IsAllowedAsNextVariableFactor(followState)) return false; |
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| 344 | else if (currentState == Automaton.StateExpFStart && !IsAllowedAsNextInExp(followState)) return false; |
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| 345 | else if (followState == Automaton.StateLogTStart && !IsNewTermAllowedInPoly()) return false; |
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| 346 | else if (currentState == Automaton.StateLogTFStart && !IsAllowedAsNextInPoly(followState)) return false; |
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| 347 | else if (followState == Automaton.StateInvTStart && !IsNewTermAllowedInPoly()) return false; |
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| 348 | else if (currentState == Automaton.StateInvTFStart && !IsAllowedAsNextInPoly(followState)) return false; |
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| 349 | // finishing an exponential factor is only allowed when the number of variable references is large enough |
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| 350 | else if (followState == Automaton.StateExpFactorEnd && !IsCompleteExp()) return false; |
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| 351 | // finishing a polynomial (in log or inv) is only allowed when the number of variable references is large enough |
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| 352 | else if (followState == Automaton.StateInvTEnd && !IsTermCompleteInPoly()) return false; |
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| 353 | else if (followState == Automaton.StateLogTEnd && !IsTermCompleteInPoly()) return false; |
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| 354 | |
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| 355 | else if (nVars > maxVariables) return false; |
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| 356 | else return true; |
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[13645] | 357 | } |
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| 358 | |
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| 359 | |
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[15060] | 360 | public void Reset() { |
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| 361 | nVars = 0; |
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| 362 | prevTerm = null; |
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| 363 | curTerm = null; |
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| 364 | curFactor = null; |
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| 365 | invalidExpression = false; |
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| 366 | } |
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[13645] | 367 | |
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[15060] | 368 | public void StartTerm() { |
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| 369 | curTerm = new TermInformation(); |
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| 370 | } |
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[13645] | 371 | |
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[15060] | 372 | public void StartFactor(int state) { |
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| 373 | curFactor = new FactorInformation(); |
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| 374 | curFactor.factorType = state; |
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| 375 | } |
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[13645] | 376 | |
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| 377 | |
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[15060] | 378 | public void AddVarToCurrentFactor(int state) { |
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| 379 | Contract.Assert(Automaton.FirstDynamicState <= state); |
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| 380 | Contract.Assert(curTerm != null); |
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| 381 | Contract.Assert(curFactor != null); |
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| 382 | |
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[13645] | 383 | nVars++; |
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[15060] | 384 | curFactor.numVarReferences++; |
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| 385 | |
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| 386 | if (curFactor.factorType == Automaton.StateVariableFactorStart) { |
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| 387 | Contract.Assert(curFactor.variableState < 0); // not set before |
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| 388 | curFactor.variableState = state; |
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| 389 | } else if (curFactor.factorType == Automaton.StateExpFactorStart) { |
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| 390 | curFactor.expVariableStates.Add(state); |
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| 391 | } else if (curFactor.factorType == Automaton.StateLogFactorStart || |
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| 392 | curFactor.factorType == Automaton.StateInvFactorStart) { |
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| 393 | curFactor.polyVariableStates.Last().Add(state); |
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| 394 | } else throw new InvalidProgramException(); |
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[13645] | 395 | } |
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| 396 | |
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[15060] | 397 | public void StartNewTermInPoly() { |
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| 398 | curFactor.polyVariableStates.Add(new List<int>()); |
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| 399 | } |
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| 400 | |
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[13645] | 401 | public void EndFactor() { |
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[15060] | 402 | // enforce non-decreasing factors |
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| 403 | if (curTerm.factors.Any() && CompareFactors(curTerm.factors.Last(), curFactor) > 0) |
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| 404 | invalidExpression = true; |
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| 405 | curTerm.factors.Add(curFactor); |
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| 406 | curFactor = null; |
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[13645] | 407 | } |
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| 408 | |
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| 409 | public void EndTerm() { |
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[15060] | 410 | // enforce non-decreasing terms (TODO: equal terms should not be allowed) |
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| 411 | if (prevTerm != null && CompareTerms(prevTerm, curTerm) > 0) |
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| 412 | invalidExpression = true; |
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| 413 | prevTerm = curTerm; |
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| 414 | curTerm = null; |
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[13645] | 415 | } |
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| 416 | } |
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| 417 | } |
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