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Removing semantics of transaction in the determination of serializability

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• Serializable due to "luck"
  • Consider the following 2 (different) transactions:

    T1 T3 ================================= READ(A, t) READ(A, s) t = t + 100 s = s + 200 WRITE(A, t) WRITE(A, s) READ(B, t) READ(B, s) t = t + 100 s = s + 200 WRITE(B, t) WRITE(B, s)

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  • Consider the following schedule for these 2 transactions:

    T1 T3 ================================= READ(A, t) t = t + 100 WRITE(A, t) READ(A, s) s = s + 200 WRITE(A, s) READ(B, s) s = s + 200 WRITE(B, s) READ(B, t) t = t + 100 WRITE(B, t)

    (It's exactly the same as the previous example, but the operations in T₃ is different....

    The addition in T₃ and T₁ commutes !!!)

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  • The interleaved execution will now result in a consistent database state:

    T1 T3 A B ======================================================= READ(A, t) c c t = t + 100 WRITE(A, t) --------------------> c+100 READ(A, s) s = s + 200 WRITE(A, s) ----> c+300 READ(B, s) s = s + 200 WRITE(B, s) -------------> c+200 READ(B, t) t = t + 100 WRITE(B, t) ------------------------------> c+300

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  • Now compare the result against the execution of T₁ and T₂ that was have seen previously:

    T1 T2 A B ======================================================= READ(A, t) c c t = t + 100 WRITE(A, t) --------------------> c+100 READ(A, s) s = 2×s WRITE(A, s) ----> 2c+200 READ(B, s) s = 2×s WRITE(B, s) -------------> 2c READ(B, t) t = t + 100 WRITE(B, t) ------------------------------> 2c+100

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  • Conclusion:

    The schedule of T1 and T3: T1 T3 A B ======================================================= READ(A, t) c c t = t + 100 WRITE(A, t) --------------------> c+100 READ(A, s) s = s + 200 WRITE(A, s) ----> c+300 READ(B, s) s = s + 200 WRITE(B, s) -------------> c+200 READ(B, t) t = t + 100 WRITE(B, t) ------------------------------> c+300 is serializable because: Addition is communitative          ( c + 100 ) + 200 = ( c + 200 ) + 100

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  • Observation:

    The schedule preserved consistency because of luck !!!

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  • Fact:

    We cannot rely on the semantics of a transaction to determine whether a schedule is Serializable           or        Not serializable....

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• Determinant of serializable behavior

  • Determinant of serializability:

    To determine whether an interleaved execution of transaction is serializable: We must discard the semantics (= operations performed) of the transaction The serializable of an interleaved execution of transaction is only determined by the interleaving of their: READ(...) operations          and         WRITE(...) operations

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  • Example 1:

    The schedule of T1 and T3: T1 T3 A B ======================================================= READ(A, t) c c t = t + 100 WRITE(A, t) --------------------> c+100 READ(A, s) s = s + 200 WRITE(A, s) ----> c+300 READ(B, s) s = s + 200 WRITE(B, s) -------------> c+200 READ(B, t) t = t + 100 WRITE(B, t) ------------------------------> c+300 The schedule without semantics: T1 T3 ====================================== | READ(A, t) | WRITE(A, t) | READ(A, s) | WRITE(A, s) | | READ(B, s) | WRITE(B, s) | READ(B, t) | WRITE(B, t) V time

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  • Example 2:

    The schedule of T1 and T2: T1 T2 A B ======================================================= READ(A, t) c c t = t + 100 WRITE(A, t) --------------------> c+100 READ(A, s) s = 2×s WRITE(A, s) ----> 2c+200 READ(B, s) s = 2×s WRITE(B, s) -------------> 2c READ(B, t) t = t + 100 WRITE(B, t) ------------------------------> 2c+100 The schedule without semantics: T1 T2 ====================================== READ(A, t) WRITE(A, t) READ(A, s) WRITE(A, s) READ(B, s) WRITE(B, s) READ(B, t) WRITE(B, t)

    Notice that:

    The schedules without semantics (= meaningful operations) in example 1 and example 2 are identical !!!

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  • Fact:

    The criteria to decide if a schedule is Serializable           or         Not serializable must be based solely on the ordering of the READ( ) and WRITE( ) operations in the schedule

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• Notation for a schedule
  • Notation:

    ri(X) = transaction Ti reads the DB element X wi(X) = transaction Ti writes the DB element X

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  • Example: notation for a schedule

    Schedule: T1 T2 ====================================== READ(A, t) WRITE(A, t) READ(A, s) WRITE(A, s) READ(B, s) WRITE(B, s) READ(B, t) WRITE(B, t) Notation: r1(A) w1(A) r2(A) w2(A) r2(B) w2(B) r1(B) w1(B)