doc: basic readme and documentation for FA classes

README.md

@@ -0,0 +1,57 @@
+# TS Automata
+
+[![NPM Package](https://img.shields.io/npm/v/ts-automata.svg?style=flat)](https://npmjs.org/package/ts-automata "View this project on npm")
+
+A TypeScript/JavaScript library for managing automata. 
+
+```shell
+npm i ts-automata
+```
+
+## Overview
+
+Currently supported are the Deterministic and Non-deterministic finite state automata. 
+Make use of the provided TSDoc and JSDoc for each method to see 
+
+## Usage
+
+Automatons can be created by initialising an `Alphabet` to feed to the Automaton,
+defining the states of the automaton and finally the transition function. 
+The code below is an example of creating and running input on a DFA.
+
+```typescript
+/* Create an alphabet for the Finite Automaton */
+const alphabet = new Set<Symbol>();
+alphabet.add(toChar("a"));
+alphabet.add(toChar("b"));
+
+/* Initialize the DFA */
+const dfa = new DFA(alphabet, "q0", false)
+
+/* Add states to the DFA */
+dfa.addState("q1", false);
+dfa.addState("q2", true)
+
+/* Define the transition function for each state */
+dfa.addEdge("q0", toChar('b'), "q0");
+dfa.addEdge("q0", toChar('a'), "q1");
+dfa.addEdge("q1", toChar('a'), "q2");
+dfa.addEdge("q1", toChar('b'), "q0");
+dfa.addEdge("q2", toChar('a'), "q2");
+dfa.addEdge("q2", toChar('b'), "q2");
+
+/* Check for validity */
+console.log(dfa.isValid()); 
+
+/* Run strings on the DFA */
+dfa.runString("ababababaa") // true
+dfa.runString("aa") // true
+dfa.runString("abb") // false
+```
+_Figure 1: The code for the deterministic finite automaton D._
+
+![There are three stares: q0, q1 and q2
+q0 is the starting state
+q2 is the only accepting state](https://i.imgur.com/pRuPlEv.jpeg "Image of the DFA described in the code abov")
+_Figure 2: Visual representation of D._
+

package.json

@@ -16,7 +16,7 @@
     "test": "jest",
     "build": "tsup"
   },
-  "keywords": ["automata", "typescript"],
+  "keywords": ["automata", "typescript", "math"],
   "author": "Kiril Panayotov",
   "license": "MIT",
   "devDependencies": {

src/automata/regular/DFA.ts

@@ -6,7 +6,7 @@ import {IllegalArgument, IllegalAutomatonState} from "../../exceptions/exception
 /**
  * Represents a deterministic finite automaton.
  *
- * @class DFA
+ * @extends FiniteAutomaton with DFAState.
  */
 export class DFA extends FiniteAutomaton<DFAState> {
 

src/automata/regular/NFA.ts

@@ -3,6 +3,11 @@ import {DFA, Symbol, toChar} from "../../index";
 import {NFAState} from "../../states/RegularStates";
 import {IllegalArgument} from "../../exceptions/exceptions";
 
+/**
+ * Class representation of a non-deterministic finite automaton.
+ *
+ * @extends FiniteAutomaton with NFAState.
+ */
 export class NFA extends FiniteAutomaton<NFAState> {
 
     /**