Conflict serializable and 2pl schedule

Question

Can someone write one example of a schedule which is conflict serializable but is not allowed by 2pl protocol. I have read that 2pl-> css, but css-> 2pl is not necessary?

Answer 1

T1	T2	T3
	W(A)
W(A)
		W(A)
	W(B)
W(B)
		W(B)

Comments

No above schedule is not allowed in 2PL.

You can,t lock data item B in transaction T1 because it is already locked by T2.So unlocking of A can,t be performed by T1 so T3 is n,t allowed to lock data item A.So not allowed in 2PL.

IN 2PL you should keep in mind that All the lock operations precedes all the unlock operations.

Every 2PL schedule is also conflict serializable schedule but converse is not true.i.e

Every conflict serializable schedule may or may not in 2PL.

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But when t2 will release lock on b, t1 can aquire as waiting is allowed

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How

Answer 2

I am not a hundred percent sure but,

W1A R2A R1A

This is conflict Serializable but not in 2pl. Please correct me.

Comments

That is correct, T1 releases its exclusive lock for T2 to acquire a shared lock to R2(A), and subsequently reacquires a shared lock to R1(A). Hence this is not a 2PL schedule.

However, it is conflict serializable since there is only one WR conflict, and if you sketch the conflict serializability graph, it is acyclic. It is conflict equivalent to a serial execution of T1, T2.