regex.cs

//
// Copyright 2012 Hakan Kjellerstrand
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

using System;
using System.Collections.Generic;
using System.Linq;
using Google.OrTools.ConstraintSolver;

public class RegexGeneration
{

  /*
   * Global constraint regular
   *
   * This is a translation of MiniZinc's regular constraint (defined in
   * lib/zinc/globals.mzn), via the Comet code refered above.
   * All comments are from the MiniZinc code.
   * """
   * The sequence of values in array 'x' (which must all be in the range 1..S)
   * is accepted by the DFA of 'Q' states with input 1..S and transition
   * function 'd' (which maps (1..Q, 1..S) -> 0..Q)) and initial state 'q0'
   * (which must be in 1..Q) and accepting states 'F' (which all must be in
   * 1..Q).  We reserve state 0 to be an always failing state.
   * """
   *
   * x : IntVar array
   * Q : number of states
   * S : input_max
   * d : transition matrix
   * q0: initial state
   * F : accepting states
   *
   */
  static void MyRegular(Solver solver,
                        IntVar[] x,
                        int Q,
                        int S,
                        int[,] d,
                        int q0,
                        int[] F) {



    // d2 is the same as d, except we add one extra transition for
    // each possible input;  each extra transition is from state zero
    // to state zero.  This allows us to continue even if we hit a
    // non-accepted input.
    int[][] d2 = new int[Q+1][];
    for(int i = 0; i <= Q; i++) {
      int[] row = new int[S];
      for(int j = 0; j < S; j++) {
        if (i == 0) {
          row[j] = 0;
        } else {
          row[j] = d[i-1,j];
        }
      }
      d2[i] = row;
    }

    int[] d2_flatten = (from i in Enumerable.Range(0, Q+1)
                        from j in Enumerable.Range(0, S)
                        select d2[i][j]).ToArray();

    // If x has index set m..n, then a[m-1] holds the initial state
    // (q0), and a[i+1] holds the state we're in after processing
    // x[i].  If a[n] is in F, then we succeed (ie. accept the
    // string).
    int m = 0;
    int n = x.Length;

    IntVar[] a = solver.MakeIntVarArray(n+1-m, 0,Q+1, "a");
    // Check that the final state is in F
    solver.Add(a[a.Length-1].Member(F));
    // First state is q0
    solver.Add(a[m] == q0);

    for(int i = 0; i < n; i++) {
      solver.Add(x[i] >= 1);
      solver.Add(x[i] <= S);
      // Determine a[i+1]: a[i+1] == d2[a[i], x[i]]
      solver.Add(a[i+1] == d2_flatten.Element(((a[i]*S)+(x[i]-1))));
    }

  }



  /**
   *
   * Simple regular expression.
   *
   * My last name (Kjellerstrand) is quite often misspelled
   * in ways that this regular expression shows:
   *   k(je|ä)ll(er|ar)?(st|b)r?an?d
   *
   * This model generates all the words that can be construed
   * by this regular expression.
   *
   *
   * Also see http://www.hakank.org/or-tools/regex.py
   *
   */
  private static void Solve(int n, List<String> res)
  {
    Solver solver = new Solver("RegexGeneration");

    Console.WriteLine("\nn: {0}", n);

    // The DFS (for regular)
    int n_states = 11;
    int input_max = 12;
    int initial_state = 1; // 0 is for the failing state
    int[] accepting_states = {12};

    // The DFA
    int [,] transition_fn =  {
      // 1 2 3 4 5 6 7 8 9 0 1 2   //
      {0,2,3,0,0,0,0,0,0,0,0,0},   //  1 k
      {0,0,0,4,0,0,0,0,0,0,0,0},   //  2 je
      {0,0,0,4,0,0,0,0,0,0,0,0},   //  3 ä
      {0,0,0,0,5,6,7,8,0,0,0,0},   //  4 ll
      {0,0,0,0,0,0,7,8,0,0,0,0},   //  5 er
      {0,0,0,0,0,0,7,8,0,0,0,0},   //  6 ar
      {0,0,0,0,0,0,0,0,9,10,0,0},  //  7 st
      {0,0,0,0,0,0,0,0,9,10,0,0},  //  8 b
      {0,0,0,0,0,0,0,0,0,10,0,0},  //  9 r
      {0,0,0,0,0,0,0,0,0,0,11,12}, // 10 a
      {0,0,0,0,0,0,0,0,0,0,0,12},  // 11 n
                                   // 12 d
    };

    // Name of the states
    String[] s = {"k","je","ä","ll","er","ar","st","b","r","a","n","d"};


    //
    // Decision variables
    //
    IntVar[] x = solver.MakeIntVarArray(n, 1, input_max, "x");

    //
    // Constraints
    //
    MyRegular(solver, x, n_states, input_max, transition_fn,
              initial_state, accepting_states);


    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(x,
                                          Solver.CHOOSE_FIRST_UNBOUND,
                                          Solver.ASSIGN_MIN_VALUE);

    solver.NewSearch(db);

    while (solver.NextSolution()) {
      List<String> res2 = new List<String>();
      // State 1 (the start state) is not included in the
      // state array (x) so we add it first.
      res2.Add(s[0]);
      for(int i = 0; i < n; i++) {
        res2.Add(s[x[i].Value()-1]);
      }
      res.Add(String.Join("", res2.ToArray()));
    }

    Console.WriteLine("\nSolutions: {0}", solver.Solutions());
    Console.WriteLine("WallTime: {0}ms", solver.WallTime());
    Console.WriteLine("Failures: {0}", solver.Failures());
    Console.WriteLine("Branches: {0} ", solver.Branches());


    solver.EndSearch();

  }

  public static void Main(String[] args)
  {
    List<String> res = new List<String>();
    for(int n = 4; n <= 9; n++) {
      Solve(n, res);
    }
    Console.WriteLine("\nThe following {0} words where generated", res.Count);
    foreach(string r in res) {
      Console.WriteLine(r);
    }
  }
}