A CTL Specification of Serializability for Transactions Accessing Uniform Data

Existing work in temporal logic on representing the execution of infinitely many transactions, uses linear-time temporal logic (LTL) and only models two-step transactions. In this paper, we use the comparatively efficient branching-time computational tree logic CTL and extend the transaction model to a class of multistep transactions, by introducing distinguished propositional variables to represent the read and write steps of n multi-step transactions accessing m data items infinitely many times. We prove that the well known correspondence between acyclicity of conflict graphs and serializability for finite schedules, extends to infinite schedules. Furthermore, in the case of transactions accessing the same set of data items in (possibly) different orders, serializability corresponds to the absence of cycles of length two. This result is used to give an efficient encoding of the serializability condition into CTL.

Authors:

• Rafat Alshorman
• Walter Hussak

Keywords:

• computational tree logic
• serializability
• multi-step transactions.

References:

[1] R.Alshorman and W.Hussak, Multi-step transactions specification and
verification in a mobile database community, in 3rd IEEE International
Conference on Information Technologies: from Theory to Applications,
IEEE, ICTTA 08, Damacus, Syria, IEEE Computer Society Press, 2008,
pp. 1407-1412.
[2] A. Cimatti, E. Clarke, F. Giunchiglia, and M. Roveri, NuSMV: a new
symbolic model verifier, Lecture Notes in Computer Science 1633
(1999), pp. 495-499.
[3] E. Clarke, O. Grumberg and D. Peled, Model checking, MIT Press, 1999.
[4] M.P. Fle and G. Roucairol, On serializability of iterated transactions,
Proc, 1st ACM SIGACT-SIGOPS Symp. on Principles of Distributed
Computing, 1982, pp. 194-200.
[5] W. Hussak, Serializable histories in Quantified Propositional Temporal
Logic, International Journal of Computer Mathematics, vol. 81, issue 10
(2004), pp. 1203-1211.
[6] W. Hussak, Specifying strict serializability of iterated transactions in
Propositional Temporal Logic, International Journal of Computer Science,
vol. 2, issue 2 (2007), pp. 150-156 (at www.waset.org/ijcs)
[7] W.Hussak, The serializability problem for a temporal logic of transaction
queries, Journal of Applied Non-Classical Logics, vol. 18, issue 1
(2008), pp. 67-78.
[8] C.H. Papadimitriou, The serializability of concurrent database updates,
Journal of the ACM, vol. 26 (1979), pp. 631-653.
[9] C.H. Papadimitriou, The Theory of Database Concurrency Control,
Computer Science Press, Pockville, Maryland, 1986.
[10] D. Peled and A. Pnueli, Proving partial order properties, Theoretical
Computer Science, vol. 126 (1994), pp. 143-182.
[11] D.Peled, S.Katz, and A.Pnueli. Specifying and proving serializability
in temporal logic in Proceedings LICS 1991, IEEE Computer Society
Press, 1991, pp. 232-245.