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Symmetric quotients and domain constructions. (English) Zbl 0689.68095

We introduce the symmetric quotient of two relations as a new construct in abstract relational algebra generalizing the notion of a “noyau” of Riguet. After exhibiting the main properties of symmetric quotients we study applications in domain theory. In particular, we give a monomorphic characterization of powersets and function domains.

MSC:

68R99 Discrete mathematics in relation to computer science
68Q55 Semantics in the theory of computing
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References:

[1] Berghammer, R.; Schmidt, G.; Zierer, H., Symmetric quotients (1986), Techn. Univ. München
[2] Chin, L. H.; Taraki, A., Distributive and modular laws in the arithmetic of relation algebras, Univ. California Publ. Math., 1, 341-384 (1951)
[3] Riguet, J., Relations binaires, fermetures, correspondances de Galois, Bull. Soc. Math. France, 76, 114-155 (1984) · Zbl 0033.00603
[4] Schmidt, G.; Ströhlein, T., Relationen und Graphen (1988), Springer: Springer Berlin
[5] Zierer, H., Programming with function objects: Constructive generation of semantic domains and application to partial evaluation, (TUM-I8803 (1988)), Techn. Univ. München
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