Abstract
A fundamental problem in debugging and monitoring distributed computations is to detect whether a state of the system satisfies some predicate. Cooper and Marzullo defined this problem as Possibly(Φ).
This paper presents the first on-line algorithm using linear space which solves this problem in the general case, improving all existing algorithms both in time and space. It is particularly interesting for the detection of Possibly(Φ) on potentially infinite computations. To our knowledge, it is also the only algorithm which do not use vectors of timestamps.
The presented algorithm is based on structural properties of the consistent cuts lattice, leading to a new structure which seems promising for the study distributed computations: the consistent cuts tree.
This work is partially supported by the Région Rhône-Alpes project “Modélisation et Algorithmes massivement parallèles pour les problèmes industriels”
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References
S. Alagar and S. Venkatesan. Techniques to tackle state explosion in global predicate detection. In Proc. IEEE International Conference on Parallel and Distributed Systems, pp 412–417, Taiwan, December 1994.
M.O. Ball and J.S. Provan. Calculating bounds on reachability and connectedness in stochastic networks. Networks, 13 (1), 253–278, 1983.
G. Birkhoff. Lattice Theory, volume 25 of Coll. Publ. XXV. American Mathematical Society, Providence, 3rd edition, 1967.
R. Bonnet and M. Pouzet. Extensions et stratifications d’ensembles dispersés. C.R. Acad. Sci., t. 268-Série A: 1512–1515, 1969.
J.P. Bordat. Calcul des idéaux d’un ordonné fini. Recherche Opérationnelle/Operations Research, 25 (3): 265–275, 1991.
B. Charron-Bost, C. Delporte-Gallet, and H. Fauconnier. Local and temporal predicates in distributed systems. Technical Report LITP 92.36, Institut Blaise Pascal, Université Paris 7, France, April 1992.
R. Cooper and K. Marzullo. Consistent detection of global predicates. In Proc. ACM/ONR Workshop on Parallel and Distributed Debugging, pp 163–173, Santa Cruz, California, May 1991.
C. Diehl, C. Jard, and J.-X. Rampon. Reachability analysis on distributed executions. In Jouannaud Gaudel (ed), TAPS OFT, Springer-Verlag, Orsay (France), 1993, pp 629–643 (LNCS 688).
C.J. Fidge. Timestamps in message-passing systems that preserve the partial ordering. In Proc. 11th Australian Computer Science Conference, pp 55–66, University of Queensland, Australia, February 1988.
V.K. Garg and B. Waldecker. Detection of unstable predicates in distributed programs. In Proc. of 12th Conference on the Foundations of Software Technology & Theoretical Computer Science, 1992, Springer Verlag, pp 253–264, (LNCS 652).
V.K. Garg and B. Waldecker. Detection of weak unstable predicates in distributed programs. IEEE Transactions on Parallel and Distributed Systems, To appear.
M. Habib and L. Nourine. Tree structures for distributive lattice and its application. Research report, LIRMM, Montpellier, France, October 1993.
J.-M. Helary and M. Raynal. Towards the construction of distributed detection programs with an application to distributed termination. Research Report 1460, INRIA, Rennes, France, Juin 1991.
C. Jard, G.-V. Jourdan, and J.-X. Rampon. Some ‘on-line’ computations of the ideal lattice of posets. Internal Publication PI-773, IRISA, Rennes, France, October 1993.
L. Lamport. Time, clocks, and the ordering of events in a distributed system. Communications of the ACM, 21 (7): 558–565, July 1978.
F. Mattern. Virtual time and global states of distributed systems. In M. Cosnard et al. (ed), Parallel and Distributed Algorithms, pp 215–226. Elsevier/North- Holland, 1989.
R. Medina. Incremental Garbage Collection for Causal Relationship Computation in Distributed Systems. In Proc. 5th IEEE Symposium on Parallel and Distributed Processing, pp 650–655, Dallas (Texas), 1993.
R. Medina and L. Nourine. Growing and pruning the consistent cuts tree. Research Report 93–074, LIRMM, Montpellier, France, December 1993.
R. Medina and L. Nourine. Algorithme efficace de génération des idéaux d’un ensemble ordonné. C.R. Acad. Sci., t. 319-Série 1: 1115–1120, 1994.
L. Nourine. Quelques propriétés algorithmiques des treillis. PhD thesis, Université Montpellier II, Montpellier, France, June 1993.
R. Schwarz and F. Mattern. Detecting causal relationships in distributed computations - in search of the holy grail. Distributed Computing, 7 (3): 149–174, 1994.
G. Steiner. An algorithm for generating the ideals of a partial order. Operations Res. Lett., 5: 317–320, 1986.
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© 1995 British Computer Society
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Jégou, R., Medina, R., Nourine, L. (1995). Linear Space Algorithm for On-line Detection of Global Predicates. In: Desel, J. (eds) Structures in Concurrency Theory. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3078-9_12
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DOI: https://doi.org/10.1007/978-1-4471-3078-9_12
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