6. Vending machine example

$A_2$: Vending machine example

digraph {
	label=A₂
	rankdir=LR
	init[shape=point]
	node[shape=doublecircle]; 0;
	node[shape=circle];
	init->25
	
	25[label="s₂₅"]
	20[label="s₂₀"]
	15[label="s₁₅"]
	10[label="s₁₀"]
	5[label="s₅"]
	0[label="s₀"]
	
	25->20 [label="5p"]
	20->15 [label="5p"]
	15->10 [label="5p"]
	10->5 [label="5p"]
	5->0 [label="5p"]
	
	25->15 [label="10p"]
	20->10 [label="10p"]
	15->5 [label="10p"]
	10->0 [label="10p"]
	5->0 [label="10p"]
	
	25->5 [label="20p"]
	20->0 [label="20p"]
	15->0 [label="20p"]
	10->0 [label="20p"]
	5->0 [label="20p"]
}

For this diagram:

• states: $s_{25},s_{20},s_{15},s_{10},s_5,s_0$
• input alphabet: $\{5\text{p},10\text{p},20\text{p}\}$
• inital state: $s_{25}$
• favourable states: $s_0$

Word: any sequence of $5\text{p}$, $10\text{p}$ and $20\text{p}$ coins Accepts: all the words such that the sum of the coins is $\ge 25\text{p}$