The Serializability Theorem
A history is SR if and only if SG(H) is acyclic.
Proof: (if) SG(H) is acyclic. So let Hs be a serial history consistent with SG(H). Each pair of conflicting ops in H induces an edge in SG(H). Since conflicting ops in Hs and H are in the same order, Hs?H, so H is SR.
(only if) H is SR. Let Hs be a serial history equivalent to H. Claim that if Ti ? Tk in SG(H), then Ti precedes Tk in Hs (else Hs?H). If SG(H) had a cycle, T1?T2?…?Tn?T1, then T1 precedes T1 in Hs,a contradiction. So SG(H) is acyclic.