To implement division in DFA, we need to first obtain the DFA for the regular expression that represents the dividend and the DFA for the regular expression that represents the divisor. We can then use these two DFAs to construct the DFA for the regular expression that represents the quotient.
using System;
using System.Collections.Generic;
class Program
{
static void Main()
{
// DFA for the dividend (1011)*
var dividend = new Dictionary<(int, char), int>
{
[(0, '1')] = 1,
[(0, '0')] = -1,
[(1, '0')] = 2,
[(1, '1')] = 1,
[(2, '1')] = 3,
[(2, '0')] = -1,
[(3, '0')] = 0,
[(3, '1')] = 1,
[(4, '0')] = 4,
[(4, '1')] = 4,
[(5, '0')] = 5,
[(5, '1')] = 5,
[(6, '0')] = 6,
[(6, '1')] = 6
};
// set of accepting states for the dividend DFA
var dividendAccept = new HashSet<int> {0};
// DFA for the divisor 10
var divisor = new Dictionary<(int, char), int>
{
[(0, '1')] = 1,
[(0, '0')] = 0,
[(1, '0')] = 2,
[(1, '1')] = -1,
[(2, '0')] = 0,
[(2, '1')] = 3,
[(3, '0')] = 3,
[(3, '1')] = -1,
[(4, '0')] = 4,
[(4, '1')] = 4,
[(5, '0')] = 5,
[(5, '1')] = 5,
[(6, '0')] = 6,
[(6, '1')] = 6
};
// set of accepting states for the dividend DFA
var divisorAccept = new HashSet<int> {2};
// construct the quotient DFA
var quotient = new Dictionary<(int, char), int>();
var quotientAccept = new HashSet<int>();
foreach (var dState in dividend)
{
var qState = (dState.Key.Item1, dState.Key.Item2 == '0' ? 0 : divisor[dState.Value, dState.Key.Item2]);
if (dividendAccept.Contains(dState.Key.Item1) && divisorAccept.Contains(qState.Item2))
quotientAccept.Add(qState.Item1);
quotient[dState.Key] = qState.Item1;
}
Console.WriteLine("Dividend DFA");
foreach (var state in dividend)
Console.WriteLine($"{state.Key.Item1} --{state.Key.Item2}--> {state.Value}");
Console.WriteLine("\nDivisor DFA");
foreach (var state in divisor)
Console.WriteLine($"{state.Key.Item1} --{state.Key.Item2}--> {state.Value}");
Console.WriteLine("\nQuotient DFA");
foreach (var state in quotient)
Console.WriteLine($"{state.Key.Item1} --{state.Key.Item2}--> {state.Value}");
Console.WriteLine("\nQuotient Accepting States: " + string.Join(',', quotientAccept));
}
}
In this example, we have defined the DFAs for the dividend (1011)* and the divisor 10. We then use these two DFAs to construct the DFA for the quotient. The final DFA is output to the console along with the accepting states for the quotient DFA.