pushdown automaton part in README

README.md

@@ -1,2 +1,71 @@
 # IN620
 
+## pushdown automaton
+Input word = i0, I, K  
++ i0 total length of input word
++ I = i1, J
+	* i1, size of automaton input word
+	* J automaton input, list of integers
++ K, list of transitions
+### transition (q, a, A, w, q')
++ q : state before
++ q' : state after
+	* 0 : start state
+	* 1 : accepting state
++ a : symbol in input
+	* 2 : ε
++ A : symbol on stack (pop operation)
+	* 2 : ε (no pop)
+	* 3 : stack start symbol
++ w : word to push on stack  
+	* w = u, V  
+	  u : length of V, 0 if nothing to push  
+	  V : list of integers to push (Vn, Vn-1... V0)  
+	  Leftmost element of the list will be at the top of the stack after the transition (Vn here).
+	  
+output:
++ 0 : accept
++ 1 : reject
+
+### examples :
+transition (q, a, A, w, q') = (0, 3, 4, 54, 1)
+```
+(0, 3, 4, 2, 5, 4, 1)
+```
+transition (q, a, A, w, q') = (0, ε, 1, ε, 1)
+```
+(0, 2, 1, 2, 0, 1)
+```
+  
+#### 0<sup>n</sup>1<sup>n</sup>
+0<sup>n</sup>1<sup>n</sup> automaton:
+```
+(0, 0, 3, 2, 1, 3, 0)	// stack empty, read 0, push 1, stay in state 0
+(0, 0, 1, 2, 1, 1, 0)	// stack with 1 on top, read 0, push 1, stay in state 0
+(0, 1, 1, 0, 2)		// stack with 1 on top, read 1, pop 1, go to state 2
+(2, 1, 1, 0, 2)		// stack with 1 on top, read 1, pop 1, stay in state 2
+(2, 2, 3, 1, 3, 1)	// stack empty in state 2, go to accepting state
+```  
+#### 0<sup>n</sup>1<sup>n</sup> inputs
+
+0<sup>n</sup>1<sup>n</sup>  
+input 000111 (output should be 0)
+```
+(37, 6, 0, 0, 0, 1, 1, 1, 0, 0, 3, 2, 1, 3, 0, 0, 0, 1, 2, 1, 1, 0, 0, 1, 1, 0, 2, 2, 1, 1, 0, 2, 2, 2, 3, 1, 3, 1)
+```
+
+0<sup>n</sup>1<sup>m</sup> n<m  
+input 001111 (output should be 1)
+```
+(37, 6, 0, 0, 1, 1, 1, 1, 0, 0, 3, 2, 1, 3, 0, 0, 0, 1, 2, 1, 1, 0, 0, 1, 1, 0, 2, 2, 1, 1, 0, 2, 2, 2, 3, 1, 3, 1)
+```
+0<sup>n</sup>1<sup>m</sup> n>m  
+input 000011 (output should be 1)
+```
+(37, 6, 0, 0, 0, 0, 1, 1, 0, 0, 3, 2, 1, 3, 0, 0, 0, 1, 2, 1, 1, 0, 0, 1, 1, 0, 2, 2, 1, 1, 0, 2, 2, 2, 3, 1, 3, 1)
+```
+!=0<sup>n</sup>1<sup>m</sup>  
+input 001011 (output should be 1)
+```
+(37, 6, 0, 0, 1, 0, 1, 1, 0, 0, 3, 2, 1, 3, 0, 0, 0, 1, 2, 1, 1, 0, 0, 1, 1, 0, 2, 2, 1, 1, 0, 2, 2, 2, 3, 1, 3, 1)
+```