Finite Automaton Minimizer

An script which reads a valid FA as JSON from standard input and print the minimized FA to the output.

Algorithm

I implemented the algorithm that is provided in 2.6 section of "Introduction to Languages and the Theory of Computation 4th edition"

Motivation

This script has written for an asignment of my "Introduction to Theory of Computation" course by Dr. Rasoul Ramezanian at Ferdowsi University of Mashahd

Structure of the Input and Output JSON file

{
  "<node_name>": {
    "adjacency": {
      "<edge_name>": "<node_name>",
      "<edge_name>": "<node_name>"
    },
    "acceptance": true
  },
  "<node_name>": {
    "adjacency": {
      "<edge_name>": "<node_name>",
      "<edge_name>": "<node_name>"
    },
    "acceptance": false
  }
}

Examples

Important Note: This examples are the beautified version of them. script only reads inputs and prints output in one-line! So inputs should be stringify and then pass to script. An example can be found in the source code and you can use it via IO Run Extenstion in VSCode.

Example 1

Input

{
  "q0": {
    "acceptance": true,
    "adjacency": {
      "a": "q1",
      "b": "q1"
    }
  },
  "q1": {
    "acceptance": true,
    "adjacency": {
      "a": "q0",
      "b": "q0"
    }
  }
}

Output

{
  "q0q1": {
    "acceptance": true,
    "adjacency": {
      "a": "q0q1",
      "b": "q0q1"
    }
  }
}

Example 2

This example can be found in Page 76 of "Introduction to Languages and the Theory of Computation 4th edition" by John C. Martin

Input

{
  "q0": {
    "acceptance": false,
    "adjacency": {
      "a": "q1",
      "b": "q9"
    }
  },
  "q1": {
    "acceptance": false,
    "adjacency": {
      "a": "q8",
      "b": "q2"
    }
  },
  "q2": {
    "acceptance": false,
    "adjacency": {
      "a": "q3",
      "b": "q2"
    }
  },
  "q3": {
    "acceptance": true,
    "adjacency": {
      "a": "q2",
      "b": "q4"
    }
  },
  "q4": {
    "acceptance": true,
    "adjacency": {
      "a": "q5",
      "b": "q8"
    }
  },
  "q5": {
    "acceptance": false,
    "adjacency": {
      "a": "q4",
      "b": "q5"
    }
  },
  "q6": {
    "acceptance": false,
    "adjacency": {
      "a": "q7",
      "b": "q5"
    }
  },
  "q7": {
    "acceptance": false,
    "adjacency": {
      "a": "q6",
      "b": "q5"
    }
  },
  "q8": {
    "acceptance": true,
    "adjacency": {
      "a": "q1",
      "b": "q3"
    }
  },
  "q9": {
    "acceptance": true,
    "adjacency": {
      "a": "q7",
      "b": "q8"
    }
  }
}

Output

{
  "q0": {
    "acceptance": false,
    "adjacency": {
      "a": "q1q2q5",
      "b": "q9"
    }
  },
  "q1q2q5": {
    "acceptance": false,
    "adjacency": {
      "a": "q3q4q8",
      "b": "q1q2q5"
    }
  },
  "q3q4q8": {
    "acceptance": true,
    "adjacency": {
      "a": "q1q2q5",
      "b": "q3q4q8"
    }
  },
  "q6q7": {
    "acceptance": false,
    "adjacency": {
      "a": "q6q7",
      "b": "q1q2q5"
    }
  },
  "q9": {
    "acceptance": true,
    "adjacency": {
      "a": "q6q7",
      "b": "q3q4q8"
    }
  }
}

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Code released under the MIT License.