5.

Here are the transitions of a determininstic pushdown automaton. The start state is q₀, and f is the accepting state.

State-Symbol	a	b
q0-Z0	(q1,AAZ0)	(q2,BZ0)	(f,)
q1-A	(q1,AAA)	(q1,)	-
q1-Z0	-	-	(q0,Z0)
q2-B	(q3,)	(q2,BB)	-
q2-Z0	-	-	(q0,Z0)
q3-B	-	-	(q2,)
q3-Z0	-	-	(q1,AZ0)

Describe informally what this PDA does. Then, identify below the one input string that the PDA accepts.

a)

bbaabab

b)

abbbab

c)

abbbbaa

d)

bababbaa