https://github.com/dankolesnikov/dfatoturingmachine

Turing Machine that simulates behavior of any Deterministic Finite Automata
https://github.com/dankolesnikov/dfatoturingmachine

deterministic-finite-automata dfa theoretical-computer-science theory-of-computation turing-machine

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Turing Machine that simulates behavior of any Deterministic Finite Automata

• Host: GitHub
• URL: https://github.com/dankolesnikov/dfatoturingmachine
• Owner: dankolesnikov
• Created: 2017-11-07T05:46:49.000Z (over 8 years ago)
• Default Branch: master
• Last Pushed: 2017-12-13T06:20:36.000Z (over 8 years ago)
• Last Synced: 2025-07-22T12:52:07.366Z (11 months ago)
• Topics: deterministic-finite-automata, dfa, theoretical-computer-science, theory-of-computation, turing-machine
• Homepage:
• Size: 11.8 MB
• Stars: 3
• Watchers: 2
• Forks: 5
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

          
# Turing Machine

> Turing Machine that takes an encoded DFA and prints out A to accept or R to reject the string input 

![](readme_pics/header.png)

# Description

This Standard Turing Machine simulates behavior of any Deterministic Finite Automata that is properly encoded. The machine will return A or R for accepting or rejecting a string. Run the FinalRelease.jff in the the transducer mode of JFLAP program. Please be aware of potential bugs in this machine. 

## Deterministic Finite Automata (DFA) Fundamentals

DFA can be mathematically defined as M = (Q,Σ,δ,q0,F), where:

* Q - List of states 

* Σ - Alphabet

* δ - Transition function

* q0 - Initial state

* F - List of final(accepting) states 

### Example: 

L = {bnam} where n ≥ 0 and m = 0 or 1

![](readme_pics/example_dfa.png)

Machine M constructed above can be mathematically broken down to:

* Q = {q2,q5,q9}

* Σ = {a,b}

* q0 = q2

* F = {q2,q5}

Transition function δ of the constructed DFA above will be:

* δ(q2, b) = q2

* δ(q2, a) = q5

* δ(q5, b) = q9

* δ(q5, a) = q9

* δ(q9, b) = q9

* δ(q9, a) = q9

Let input string w = aab

## Encoding a DFA 

We will encode all element of M and w in unary numbers.

Q = {q2, q5, q9}


The first element of Q is encoded as 1, the second one as 11 and so forth.

So, the encoded version of Q would be: Q = {1, 11, 111}

q0


We always put the initial state as the first element of Q. So, q0 (e.g. q2 in the example) is always encoded as 1.

Σ = {a, b}


The first element of Σ is encoded as 1, the second one as 11 and so forth. So, the encoded version of Σ would be: Σ = {1, 11}

F = {q2, q5}


The set of final states follows the same codes of Q. So, the encoded version of F would be F = {1, 11}.

δ(q0, x) = qj


The elements of sub-rules are encoded by the same codes of Q and Σ and are formatted as the following figure shows. We use '0' (zero) as the separator between the elements.

![](readme_pics/separators_dfa.png)

Note that q5 and b have the same code (i.e. 11), but their locations in the string give them different meaning.


All sub-rules of the example have been encoded in the following table. 

![](readme_pics/table_dfa.png)

Input string w = bba

The symbols of the input string are encoded by the codes of Σ and are separated by '0' (zero). So, the encoded version of w would be: w = 1101101


Let's put all together and construct the TM's input string that contains the DFA's description and its input string.

![](readme_pics/encoded_dfa.png)

#### Final Result

After applying all of the rules of encoding our DFA will look like this:

```sh

1101101D101101D101011D110110111D11010111D1110110111D111010111F1011

```

### Technical Notes

1. The order of the elements of Q does not matter. The only restriction would be the first element that must be the q0 of the DFA.

2. The order of the elements of Σ does not matter.

3. We don't need to put Q and Σ in the TM's input string because we just need to use their codes in δ, w, and F.

4. We assume that the input string of the TM is 100% correct. It means, M and w are encoded and formatted correctly. Therefore, your  TM is not supposed to have any error checking or error reporting.

5. Test your Turing machine as a transducer option of JFLAP.

6. There are bugs in this machine.

## Usage

Use JFLAP 7 provided in the repository. Run inputs in transducer mode.

## Meta

Danil Kolesnikov – danil.kolesnikov@sjsu.edu

Distributed under the MIT license.