https://github.com/gyakobo/recognizing-context-free-languages-with-a-pda
The following project should define a PDA that in its turn would recognize a specific context-free language.
https://github.com/gyakobo/recognizing-context-free-languages-with-a-pda
context-free-language proofs pushdown-automaton python3 theoretical-computer-science
Last synced: 9 days ago
JSON representation
The following project should define a PDA that in its turn would recognize a specific context-free language.
- Host: GitHub
- URL: https://github.com/gyakobo/recognizing-context-free-languages-with-a-pda
- Owner: Gyakobo
- License: mit
- Created: 2024-05-13T05:53:23.000Z (about 2 years ago)
- Default Branch: main
- Last Pushed: 2024-06-02T12:46:45.000Z (about 2 years ago)
- Last Synced: 2025-03-04T23:12:59.628Z (over 1 year ago)
- Topics: context-free-language, proofs, pushdown-automaton, python3, theoretical-computer-science
- Language: Python
- Homepage:
- Size: 107 KB
- Stars: 3
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# Language Recognition with a PDA(Pushdown Automaton)
Author: [Andrew Gyakobo](https://github.com/Gyakobo)
## Introduction
The following project should define a PDA that in its turn would recognize a specific context-free language.
## Let's have a look at Language A
* A, in simple terms, is a language that defines all necessary arithmetic floating point numbers and valid operations on said decimal or whole numbers.
* A select string of language A is of the form:
$ab^kaEab^ka, k>=0$
* Here is an example string: $abba(1.2*(1.-2.+3.1))abba$
>[!Note]
>Language A is not a regular language, however, it's a context-free language
### Context Free Grammar for A
Language A can be defined by a 4-tuple context-free grammar $G = (V, \Sigma, R, S)$, where:
* V = {S, T, C, H, Y, N} (set of variables, or non-terminals)
* $\Sigma$ = {., 0, 1, 2, ..., 9, +, -, *, /, (, ), a, b} (Mind you $\Sigma$ is the alphabet of all available letters, digits, and characters)
* S (start variable)
Speaking about R, the rules are as follows:
* $S \rightarrow aTa$
* $T \rightarrow bTb|aCa$
* $C \rightarrow C+C|C-C|C*C|C/C|(C)|H$
* $H \rightarrow Y.Y|Y.|.Y$
* $Y \rightarrow NY|N$
* $N \rightarrow 0|1|2|3|4|5|6|7|8|9$
## Let's now handle a sample example
$S \Rightarrow aTa \Rightarrow abTba \Rightarrow abbTbba \Rightarrow abba(C)abba \Rightarrow abba(C * C)abba$
$\Rightarrow abba(C* (C))abba \Rightarrow abba(C * (C-C+C))abba$
$\Rightarrow abba(H * (C-C+C))abba \Rightarrow abba(Y.Y * (C-C+C))abba \Rightarrow abba(N.N * (C-C+C))abba$
$\Rightarrow abba(1.2*(C-C+C))abba \Rightarrow abba(1.2*(H-C+C))abba \Rightarrow abba(1.2 * (Y.-C+C))abba$
$\Rightarrow abba(1.2*(N.-C+C))abba \Rightarrow abba(1.2*(1.-C+C))abba \Rightarrow abba(1.2 * (1. - H + C))abba$
$\Rightarrow abba(1.2 * (1. - Y. + C))abba \Rightarrow abba(1.2 * (1. - N. + C))abba \Rightarrow abba(1.2 * (1. - 2. + C))$
$\Rightarrow abba(1.2 * (1. - 2. + H))abba \Rightarrow abba(1.2 * (1. - 2. + Y.Y))abba \Rightarrow abba(1.2 * (1. - 2. + 3.1))abba$
### Pushdown Automaton 'M'
Here's a simple graphic demonstration of the PDA:
#### Examples
Let's run the Pushdown Automaton M on the following string:
>[!Note]
>The PDA also utilizes a stack data structure in order to keep track of the a's and b's in the said string. Basically it's using two main commands to do so: push and pop. Each of these commands either insert a value on the top of the stack or remove the said value also from the top of the stack.
```
w = abbba43.51386abbba
```
```
Enter string 1 of 15: abbba43.51386abbba
Starting on State Q1
$: Q1
Read '$'
Popped 'ε' from stack
Pushed '$' to stack
Moving to state Q2
a: Q2
Read 'a'
Popped 'ε' from stack
Pushed 'a' to stack
Moving to state Q3
b: Q3
Read 'b'
Popped 'ε' from stack
Pushed 'b' to stack
Moving to state Q3
b: Q3
Read 'b'
Popped 'ε' from stack
Pushed 'b' to stack
Moving to state Q3
b: Q3
Read 'b'
Popped 'ε' from stack
Pushed 'b' to stack
Moving to state Q3
a: Q3
Read 'a'
Popped 'ε' from stack
Pushed 'a' to stack
Moving to state Q4
4: Q4
Read '4'
Popped 'ε' from stack
Pushed 'ε' to stack
Moving to state Q5
3: Q5
Read '3'
Popped 'ε' from stack
Pushed 'ε' to stack
Moving to state Q5
.: Q5
Read '.'
Popped 'ε' from stack
Pushed 'ε' to stack
Moving to state Q7
5: Q7
Read '5'
Popped 'ε' from stack
Pushed 'ε' to stack
Moving to state Q7
1: Q7
Read '1'
Popped 'ε' from stack
Pushed 'ε' to stack
Moving to state Q7
3: Q7
Read '3'
Popped 'ε' from stack
Pushed 'ε' to stack
Moving to state Q7
8: Q7
Read '8'
Popped 'ε' from stack
Pushed 'ε' to stack
Moving to state Q7
6: Q7
Read '6'
Popped 'ε' from stack
Pushed 'ε' to stack
Moving to state Q7
a: Q7
Read 'a'
Popped 'a' from stack
Pushed 'ε' to stack
Moving to state Q9
b: Q9
Read 'b'
Popped 'b' from stack
Pushed 'ε' to stack
Moving to state Q9
b: Q9
Read 'b'
Popped 'b' from stack
Pushed 'ε' to stack
Moving to state Q9
b: Q9
Read 'b'
Popped 'b' from stack
Pushed 'ε' to stack
Moving to state Q9
a: Q9
Read 'a'
Popped 'a' from stack
Pushed 'ε' to stack
Moving to state Q10
ε: Q10
Read 'ε'
Popped '$' from stack
Pushed 'ε' to stack
String is accepted!
```
## License
MIT