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How to enforce serializable schedules? Option 1: run system, recording P(S); at end of day, check for P(S) cycles and declare if execution was good 2
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How to enforce serializable schedules? Option 1: run system, recording P(S); at end of day, check for P(S) cycles and declare if execution was good 2
How to enforce serializable schedules? Option 2: prevent P(S) cycles from occurring T1 T2 ….. Tn Scheduler DB 3
A locking protocol Two new actions: lock (exclusive): li (A) unlock: ui (A) T1 T2 lock scheduler table 4
Exercise: • What schedules are legal? What transactions are well-formed? S1 = l1(A)l1(B)r1(A)w1(B)l2(B)u1(A)u1(B) r2(B)w2(B)u2(B)l3(B)r3(B)u3(B) S2 = l1(A)r1(A)w1(B)u1(A)u1(B) l2(B)r2(B)w2(B)l3(B)r3(B)u3(B) S3 = l1(A)r1(A)u1(A)l1(B)w1(B)u1(B) l2(B)r2(B)w2(B)u2(B)l3(B)r3(B)u3(B) 7
Exercise: • What schedules are legal? What transactions are well-formed? S1 = l1(A)l1(B)r1(A)w1(B)l2(B)u1(A)u1(B) r2(B)w2(B)u2(B)l3(B)r3(B)u3(B) S2 = l1(A)r1(A)w1(B)u1(A)u1(B) l2(B)r2(B)w2(B)l3(B)r3(B)u3(B) S3 = l1(A)r1(A)u1(A)l1(B)w1(B)u1(B) l2(B)r2(B)w2(B)u2(B)l3(B)r3(B)u3(B) 8
Schedule F T1 T2 l1(A);Read(A) A A+100;Write(A);u1(A) l2(A);Read(A) A Ax2;Write(A);u2(A) l2(B);Read(B) B Bx2;Write(B);u2(B) l1(B);Read(B) B B+100;Write(B);u1(B) 9
Schedule F A B T1 T2 25 25 l1(A);Read(A) A A+100;Write(A);u1(A) 125 l2(A);Read(A) A Ax2;Write(A);u2(A) 250 l2(B);Read(B) B Bx2;Write(B);u2(B) 50 l1(B);Read(B) B B+100;Write(B);u1(B) 150 250 150 10
Rule #3 Two phase locking (2PL) for transactions Ti = ……. li(A) ………... ui(A) ……... no unlocks no locks 11
Schedule G T1 T2 l1(A);Read(A) A A+100;Write(A) l1(B); u1(A) delayed l2(A);Read(A) A Ax2;Write(A);l2(B) 13
Schedule G T1 T2 l1(A);Read(A) A A+100;Write(A) l1(B); u1(A) delayed l2(A);Read(A) A Ax2;Write(A);l2(B) Read(B);B B+100 Write(B); u1(B) 14
Schedule G T1 T2 l1(A);Read(A) A A+100;Write(A) l1(B); u1(A) l (A);Read(A) delayed 2 A Ax2;Write(A);l2(B) Read(B);B B+100 Write(B); u1(B) l2(B); u2(A);Read(B) B Bx2;Write(B);u2(B); 15
Schedule H (T2 reversed) T1 T2 l1(A); Read(A) l2(B);Read(B) A A+100;Write(A) B Bx2;Write(B) l1(B) l2(A) delayed delayed 16
• Assume deadlocked transactions are rolled back – They have no effect – They do not appear in schedule E.g., Schedule H = This space intentionally left blank! 17
Conflict rules for li(A), ui(A): • li(A), lj(A) conflict • li(A), uj(A) conflict Note: no conflict < ui(A), uj(A)>, < li(A), rj(A)>,... 19
Theorem Rules #1,2,3 conflict (2PL) serializable schedule To help in proof: Definition Shrink(Ti) = SH(Ti) = first unlock action of Ti 20
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