Local and global properties in networks of processors (Extended Abstract)

This paper attempts to get at some of the fundamental properties of distributed computing by means of the following question: “How much does each processor in a network of processors need to know about its own identity, the identities of other processors, and the underlying connection network in order for the network to be able to carry out useful functions?” The approach we take is to require that the processors be designed without any knowledge (or only very broad knowledge) of the networks they are to be used in, and furthermore, that all processors with the same number of communication ports be identical. Given a particular network function, e.g., setting up a spanning tree, we ask whether processors may be designed so that when they are embedded in any connected network and started in some initial configuration, they are guaranteed to accomplish the desired function.

[1]  Oscar H. IBARm.  Information and Control , 1957, Nature.

[2]  Journal of the Association for Computing Machinery , 1961, Nature.

[3]  John Mylopoulos.  On the Relation of Graph Grammars and Graph Automata , 1972, SWAT.

[4]  A. Gardiner.  Antipodal covering graphs , 1974 .

[5]  David L. Milgram,et al.  Web Automata , 1975, Inf. Control..

[6]  Azriel Rosenfeld,et al.  Networks of Automata: Some Applications , 1975, IEEE Transactions on Systems, Man, and Cybernetics.

[7]  D. A. Waller.  Double covers of graphs , 1976, Bulletin of the Australian Mathematical Society.

[8]  M. Blum,et al.  On the capability of finite automata in 2 and 3 dimensional space , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[9]  D. A. Waller,et al.  Kronecker Products and Local Joins of Graphs , 1977, Canadian Journal of Mathematics.

[10]  Jonathan L. Gross,et al.  Generating all graph coverings by permutation voltage assignments , 1977, Discret. Math..

[11]  Jonathan L. Gross.  Every connected regular graph of even degree is a Schreier coset graph , 1977, J. Comb. Theory, Ser. B.

[12]  Azriel Rosenfeld,et al.  Cellular Graph Automata , 1978, Graph-Grammars and Their Application to Computer Science and Biology.

[13]  Manuel Blum,et al.  On the power of the compass (or, why mazes are easier to search than graphs) , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[14]  Robin Milner,et al.  Concurrent Processes and Their Syntax , 1979, JACM.

[15]  Dexter Kozen,et al.  Automata and planar graphs , 1979, International Symposium on Fundamentals of Computation Theory.

[16]  Frank Harary,et al.  Some problems in topological graph theory , 1980, J. Graph Theory.

[17]  Nancy A. Lynch,et al.  On Describing the Behavior and Implementation of Distributed Systems , 1979, Theor. Comput. Sci..

[18]  Dana Angluin,et al.  Finite common coverings of pairs of regular graphs , 1981, J. Comb. Theory B.

[19]  R. Ho.  Algebraic Topology , 2022 .