Abstract
We propose an alternative characterisation of object-based distributed systems in terms of algebraic structures and topological spaces. Some examples are given in order to attest the adequacy of this approach to the subject. We also illustrate a method of transference of results from these mathematical theories that can further contribute to the advancement of distributed systems theory.
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References
Agha, G.: Actors: A Model of Concurrent Computation in Distributed Systems. MIT Press (1986)
Agha, G., Mason, I., Smith, S., Talcott, C.: A foundation for actor computation. Journal of Functional Programming 7(1), 1–72 (1997)
Alpern, B., Schneider, F.B.: Defining liveness. Information Processing Letters 21(4), 181–185 (1985)
Attiya, H., Snir, M., Warmuth, M.: Computing on an anonymous ring. Journal of the ACM 35(4), 845–876 (1988)
Barbosa, V., Gafni, E.: Concurrency in heavily loaded neighborhood-constrained systems. ACM Transactions on Programming Languages and Systems 11, 584–592 (1989)
Chandy, K.M., Misra, J.: Parallel Program Design, A Foundation. Addison-Wesley (1988)
Denker, G., Ehrich, H.D.: Specifying distributed information systems: Fundamentals of an object-oriented approach using distributed temporal logic. In: Bowman, H., Derrick, J. (eds.) Prof. 2nd IFIP Workshop on Formal Methods for Open Object-Based Distributed Systems Conference (FMOODS 1997), vol. 2, pp. 89–104. Chapman and Hall (1997)
Duarte, C.H.C.: A proof-theoretic approach to the design of object-based mobility. In: Bowman, H., Derrick, J. (eds.) Proc. 2nd IFIP Conference on Formal Methods for Open Object-Based Distributed Systems (FMOODS 1997), pp. 37–53. Chapman and Hall (July 1997)
Duarte, C.H.C., Maibaum, T.: A rely-guarantee discipline for open distributed systems design. Information Processing Letters 74(1-2), 55–63 (2000)
Duarte, C.H.C., Maibaum, T.: A branching-time logical system for open distributed systems development. Electronic Notes on Theoretical Computer Science 67 (2002)
Duarte, C.H.C., Talcott, C.: Clara: An actor language for high performance distributed computing. In: Proc. 12th Symposium on Computer Architecture and High Performance Computing (SBAC-PAD 2000), pp. 20–37 (October 2000)
Goguen, J.A., Burstall, R.M.: Institutions: Abstract model theory for specification and programming. Journal of the ACM 39(1), 95–146 (1992)
Hadzilacos, V., Toueg, S.: Fault-tolerant broadcasts and related problems. In: Distributed Systems, pp. 97–145. Addison-Wesley (1993), ch. 5 of [18]
Herlihy, M.P., Shavit, N.: The topological structure of asynchronous computation. Journal of the ACM 46, 856–923 (1999)
Lefschetz, S.: Algebraic Topology. American Mathematics Society (1942)
Lamport, L.: The temporal logic of actions. ACM Transactions on Programming Languages and Systems 16(3), 872–923 (1994)
Lynch, N.: Distributed Algorithms. Morgan Kaufmann (1996)
Mullender, S. (ed.): Distributed Systems, 2nd edn. Addison-Wesley (1993)
O. M. G. Unified Modelling Language Specification. Object Management Group — OMG, Version 1.3 (June 1999)
Nielsen, M., Plotkin, G., Winskel, G.: Petri-nets, event-structures and domains - part I. Theoretical Computer Science 13, 85–108 (1981)
Plotkin, G.: A structural approach to operational semantics. Technical Report DAIMI FN-19, Computer Science Department, University of Aahus (1981)
Ramanujam, R.: Locally linear time temporal logic. In: Proc. 11th IEEE Symposium on Logic in Computer Science, pp. 118–127. IEEE Computer Society Press (1996)
Saks, M., Zaharoglou, F.: Wait-free k-set agreement is impossible: The topology of public knowledge. Siam Journal on Computing 29, 1449–1483 (2000)
Schneider, F.B.: What good are models and what models are good. In: Distributed Systems, pp. 17–26. Addison-Wesley (1993), ch. 12 of [18]
Talcott, C.: Composable semantic models for actor theories. Higher-Order and Symbolic Computation 11(3), 281–343 (1998)
Tarski, A.: Logics, Semantics and Metamathematics. Oxford Publishing Company (1956)
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Duarte, C.H.C. (2011). Mathematical Models of Object-Based Distributed Systems. In: Agha, G., Danvy, O., Meseguer, J. (eds) Formal Modeling: Actors, Open Systems, Biological Systems. Lecture Notes in Computer Science, vol 7000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24933-4_4
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DOI: https://doi.org/10.1007/978-3-642-24933-4_4
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