https://github.com/gyakobo/recognizing-an-email-adress-with-dfa
The following example is meant to demonstrate how a Deterministic Finite Automata(DFA) algorithm is supposed to guide identify whether a string is an email adress ending with .gov or .gr
https://github.com/gyakobo/recognizing-an-email-adress-with-dfa
dfa finite-state-machine njit proofs python3 theoretical-computer-science
Last synced: about 2 months ago
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The following example is meant to demonstrate how a Deterministic Finite Automata(DFA) algorithm is supposed to guide identify whether a string is an email adress ending with .gov or .gr
- Host: GitHub
- URL: https://github.com/gyakobo/recognizing-an-email-adress-with-dfa
- Owner: Gyakobo
- License: mit
- Created: 2024-02-13T18:40:08.000Z (about 1 year ago)
- Default Branch: main
- Last Pushed: 2024-07-02T08:03:08.000Z (10 months ago)
- Last Synced: 2024-11-15T02:29:56.721Z (5 months ago)
- Topics: dfa, finite-state-machine, njit, proofs, python3, theoretical-computer-science
- Language: Python
- Homepage:
- Size: 134 KB
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# DFA illustration
Author: [Andrew Gyakobo](https://github.com/Gyakobo)
## Intro
The following example is meant to demonstrate how a Deterministic Finite Automata(DFA) algorithm is supposed to guide identify whether a string is an email adress ending with **.gov** or **.gr**. The source file [dfa.py](https://github.com/Gyakobo/Recognizing_an_email_adress_with_DFA/blob/main/dfa.py) would serve as a demonstration of the aforementioned algorithm.
## In-depth analysis of 'L'
* Given the Lanaguage "L", it is defined over an alphabet $\Sigma$, also defined as $\Sigma = \psi \cup \pi \cup \phi$
* $\psi$ = { a, b, ..., z }
* $\pi$ = {.}
* $\phi$ = {@}
* Let's now fully define Language 'L', thus $L = S_{1}S_{2}^* \phi S_{1}S_{2}^*(S_{3} \cup S_{4})$, where:
* $S_{1} = \psi \psi^*$ (numbers of at least length 1)
* $S_{2} = \pi \psi \psi^*$ (strings of $S_{1}$ beginning with a dot)
* $S_{3}$ = {.gov} (valid enging for email adress)
* $S_{4}$ = {.gr} (valid enging for email adress)
* Delving more into discrete math, language 'L' is a regular language and as later on proved there exists a DFA which recognizes said regular language.
## Deterministic Finite Automaton(DFA) M for Language L
5-Tuple Definition for $M = (Q, \Sigma, \delta, Q_{1}, F)$
* Q = { $Q_{1}, Q_{2}, Q_{3}, Q_{4}, Q_{5}, Q_{6}, Q_{7}, Q_{8}, Q_{9}, Q_{10}$ }
* $\Sigma = \psi \cup \pi \cup \phi$
* $\delta: Q × \Sigma \rightarrow Q$
| Q | $\psi-\{o,r,g,v\}$ | $\pi$ | $\phi$| o | r | g | v |
|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|
| Q1 | Q2 | Q10 | Q10 | Q2 | Q2 | Q2 | Q2 |
| Q2 | Q2 | Q1 | Q3 | Q2 | Q2 | Q2 | Q2 |
| Q3 | Q4 | Q10 | Q10 | Q4 | Q4 | Q4 | Q4 |
| Q4 | Q4 | Q5 | Q10 | Q4 | Q4 | Q4 | Q4 |
| Q5 | Q4 | Q10 | Q10 | Q4 | Q4 | Q6 | Q4 |
| Q6 | Q4 | Q5 | Q10 | Q7 | Q8 | Q4 | Q4 |
| Q7 | Q4 | Q5 | Q10 | Q4 | Q4 | Q4 | Q9 |
| Q8 | Q4 | Q4 | Q10 | Q4 | Q4 | Q4 | Q4 |
| Q9 | Q4 | Q5 | Q10 | Q4 | Q4 | Q4 | Q4 |
| Q10 | Q10 | Q10 | Q10 | Q10 | Q10 | Q10 | Q10 |
* $Q_{1}$ - start state
* F = { $q_{8}, q_{9}$ } - set of accepting states
## Drawing the DFA 'M'
> [!Note]
>Please note that the state "Q10" is a trap state for non-specified edges
### Here is a sample example with the word "[email protected]"
```
Enter string 1 of 20: [email protected]
Starting on State Q1
t: Q2
u: Q2
v: Q2
@: Q3
w: Q3
x: Q4
y: Q4
z: Q4
.: Q5
g: Q6
r: Q8
Success
```
## License:
MIT