Classification of Weak Correctness Criteria for Real-Time Database Applications Lee, Kyu-Woong and Park, Seog Sogang Univ., Seoul, Korea

Contents Introduction and Motivation Forms of Database Consistency VSR and Relaxed Serializability Statewise Serializability(SSR) Algorithm for SSR Comparisons to Other Criteria Conclusion

Introductory Example n the example – that the final state of schedule H 0 is correct with respect to the situation in the real world schedule H 0 : W 1 (x) R 2 (x) W 2 (x) R 3 (z) W 3 (y) W 1 (y) But, the final state is the same as the serial schedule T 3 T 1 T 2 At this time, one of transactions should be aborted to satisfy the conflict serializability.

Forms of Database Consistency strong consistency weak consistency update consistency write consistency state consistency strict consistency

Forms of Database Consistency o weak consistency [GW82]  multiple query cycles are allowed o update consistency [BC92]  single query cycles are allowed if they can be broken by removing the single read-write edge between update transactions U1 U3 Q2Q4 U2U3 Q1 single read-write edge

o write consistency  single query cycles are allowed  update transaction cycles are not allowed  Epsilon-serializability [WYP92] o state consistency  update transaction cycle are restrictively allowed Forms of Database Consistency U1 Q2 U1U2 U3 write-write

Motivation VSR n possibility –All of non-VSR schedule produce the inconsistent state ? –It is possible that the non-view serializable schedules produce a correct(consistent) state CSR serialcorrect states possible range of relaxed serializability

View Serializability [BH 87] n A schedule H is said to be view-serializable if it is view-equivalent to some serial schedule n Two schedules H 1 and H 2 are view equivalent 1. They are over the same set of transactions and same set of operations 2. for any data item x, if T i reads x from T j in H 1, then T i reads x from T j in H for each data item x, if the write operation W i (x) is the final write of x in H 1, then it is also the final write of x in H 2.

the schedules that produce the correct states (the same final write) The Range of Relaxed SR CSR VSR all possible schedules : final states are consistent : final states are inconsistent schedules that have the same read-from relationships as some serial schedule

Invalid Read Operation n invalid read operation –A read operation R invalid in the schedule H is invalid iff R invalid is different from the read-from relationship of a serial schedule that produces the same database state as the result of schedule H. n example of invalid read operation – schedule H 1 : W 1 (a) R 2 (a) W 2 (b) W 3 (b) W 3 (c) R 1 (c) abc T 1 W T 2 RW T 3 WW T 1 R an invalid read operation final state of schedule H 1 is the same as the serial schedule T 1 T 2 T 3

Statewise Serializability n [definition] A schedule is statewise serializable if and only if (1) A schedule has the same result as at least one serial schedule and (2) If there exists invalid read operations R invalid, they do not reflect any changes on the database state n problem – How can we find the invalid read operations ? – NP problem

Algorithm for Relaxed SR n data structures – W edge : the set of write-write conflict edges – W set i : the set of data item that is written by T i n algorithm TjTj TiTi T i+1 TkTk T k-1 W W W set i ⊇ W set j

Example of Proposed Algorithm schedule H 2 : W 1 (a) R 2 (a) W 2 (b) R 3 (b) W 3 (c) W 1 (c) abc T 1 W T 2 RW T 3 RW T 1 W final state is the same as a serial schedule T 3 T 1 T 2 T1T1 T2T2 T3T3 w R w w w R the set of write data item W set 1 : { a, c} the set of write data item W set 3 : { c} ∪

SSR(statewise serializability) VSR CSR Comparison to Other Criteria serial

Conclusion n our contribution for real-time database system – provides the higher degree of concurrency – reduces the abort ratio of transaction with urgent deadline – utilizes for other application with semantic transaction n further research – extendibility for applying the relaxed serializability to distributed database system