This Article 
 Bibliographic References 
 Add to: 
Distributed Predicate Detection in Series-Parallel Systems
April 2002 (vol. 13 no. 4)
pp. 373-387

This paper addresses the problems of state space decomposition and predicate detection in a distributed computation involving asynchronous messages. We introduce a natural communication dependency which leads to the definition of the communication graph. This abstraction proves to be a useful tool to decompose the state lattice of a distributed computation into simpler structures, known as concurrent intervals. Efficient algorithms have been proposed in the literature to detect special classes of predicates, such as conjunctive predicates and bounded sum predicates. We show that more general classes of predicates can be detected when proper constraints are imposed on the underlying computations. In particular, we introduce a class of predicates, defined herein as separable predicates, that properly includes the above-mentioned classes. We show that separable predicates can be efficiently detected on distributed computations whose communication graphs satisfy the series-parallel constraint.

[1] M. Ahuja, A.D. Kshemkalyani, and T. Carlson, “A Basic Unit of Computation in Distributed Systems,” Proc. 10th Int'l Conf. Distributed Computation Systems, 1990.
[2] K.M. Chandy and L. Lamport, "Distributed Snapshots: Determining Global States of Distributed Systems," ACM Trans. Computer Systems, Feb. 1985.
[3] B. Charron-Bost, C. Delporte-Gallet, and H. Fauconnier, “Local and Temporal Predicates in Distributed Systems,” ACM Trans. Programming Languages and Systems, vol. 17, no. 1, pp. 157-179, 1995.
[4] C.M. Chase and V.K. Garg, “Detection of Global Predicates: Techniques and Their Limitations,” Distributed Computing, no. 11, pp. 191-201, 1998.
[5] C. Chase and V.K. Garg, "On Techniques and Their Limitations for the Global Predicate Detection Problem," in Proc. Workshop on Distributed Algorithms, Lecture Notes on Computer Science 971, Springer-Verlag, Berlin, 1995, pp. 303-317.
[6] G. Dumais, “Detection of Separable Predicates on Series-Parallel Systems,” MSc thesis, Concordia Univ., Montréal, Sept. 1998.
[7] D. Eppstein, “Parallel Recognition of Series-Parallel Graphs,” Information and Computation, no. 98, pp. 41-55, 1992.
[8] C.J. Fidge, "Logical Time in Distributed Computing Systems," Computer, pp. 28-33, Aug. 1991.
[9] E. Fromentin and M. Raynal, “Inevitable Global States: A Concept to Detect Properties of Distributed Computations in an Observer Independent Way,” Proc. Sixth IEEE Symp. Parallel and Distributed Processing, pp. 242-248, Oct. 1994.
[10] V.K. Garg and B. Waldecker, "Detection of Weak Unstable Predicates in Distributed Programs," IEEE Trans. Parallel and Distributed Systems, Mar. 1994, pp. 299-307.
[11] V.K. Garg and B. Waldecker, "Detection of Strong Unstable Predicates in Distributed Programs, IEEE Trans. Parallel and Distributed Systems, Dec. 1996, pp. 1323-1333.
[12] X. He and Y. Yesha, "Parallel Recognition and Decomposition of Two Terminal Series Parallel Graphs," Information and Computation, vol. 75, pp. 15-38, 1987.
[13] M. Hurfin, M. Mizuno, M. Raynal, and M. Singhal, “Efficient Distributed Detection of Conjunctions of Local Predicates,” IEEE Trans. Software Eng., vol. 24, no. 8, pp. 664-677, Aug. 1998.
[14] H.F. Li unpublished report, 1993.
[15] K. Marzullo and G. Neiger, “Detection of Global State Predicate,” Lectures Notes in Computer Science, vol. 59, pp. 254-272, Springer Verlag, 1991.
[16] F. Mattern, “Virtual Time and Global State of Distributed Systems,” Proc. Parallel and Distributed Algorithms Conf., M. Cosnbard, Y. Robert, P. Quinton, and M Raynal, pp. 215-226, 1988.
[17] A.I. Tomlinson and V.K. Garg, “Detecting Relational Global Predicates in Distributed Systems,” Proc. Third ACM/ONR Workshop Parallel and Distributed Debugging, pp. 21-31, May 1993.
[18] A.I. Tomlinson and V.K. Garg, "Monitoring Functions on Global States of Distributed Programs," J. Parallel and Distributed Computing, Mar. 1997, pp. 173-189.
[19] K. Takamizawa, T. Nishizeki, and N. Saito, “Linear-Time Computability of Combinatorial Problems on Series-Parallel Graphs,” J. ACM, vol. 29, pp. 623-641, July 1982.
[20] J. Valdes, R.E. Tarjan, and E.L. Lawler, “The Recognition of Series Parallel Digraphs,” SIAM J. Computing, vol. 11, pp. 298-313, 1982.

Index Terms:
distributed computation, predicate detection, state lattice, concurrent interval, communication graph, series-parallel structure, separable predicate
Guy Dumais, Hon F. Li, "Distributed Predicate Detection in Series-Parallel Systems," IEEE Transactions on Parallel and Distributed Systems, vol. 13, no. 4, pp. 373-387, April 2002, doi:10.1109/71.995818
Usage of this product signifies your acceptance of the Terms of Use.