Abstract
This analysis has shown that there are several levels of ideas used in categories of Park-Milner processes. First and foremost, the theory of exact categories provides the fundamental structures. Second, the idea of rooted processes means one is attempting to work in a bigpointed category. As this brief analysis shows, bipointed categories have a rather weak collection of nice properties—at least known to me. Third, additive idempotence introduces considerable additional structure, and it is here that the non-unital aspects of the A-modules play an important rôle.
Research supported in part by NSF grant MCS-8402305.
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M. A. Arbib and E. G. Manes, Fuzzy Machines in a Category, Bull. Austral. Math. Soc. 13, 1975, 169–210.
O. Ben-Shachar, Bisimulation of State Automata, MS thesis, Washington State University, 1986.
D. B. Benson, Counting Paths: Nondeterminism as Linear Algebra, IEEE Trans. Softw. Eng. SE-10, 1984, 785–794.
D. B. Benson, String Algebra and Coalgebra, Automata and Coautomata, ms.
D. B. Benson and O. Ben-Shachar, Bisimulation of State Automata, IEEE Symp. Logic in Computer Science, Cambridge, MA, 1986.
D. B. Benson and O. Ben-Shachar, Bisimulation of Automata, WSU Comput. Sci. Tech. Rpt. CS-87-162.
D. B. Benson and I. Guessarian, Iterative and Recursive Matrix Theories, J. Algebra 86, 1984, 302–314.
D. B. Benson and I. Guessarian, Algebraic Solutions to Recursion Equations, JCSS, to appear.
D. B. Benson and J. Tiuryn, Fixed Points in Free Process Algebras with Silent Events, Part I., WSU Comput. Sci. Tech. Rpt. CS-86-152.
J. A. Bergstra and J. W. Klop, Algebra of Communicating Processes with Abstraction, Theoret. Comput. Sci. 37, 1985, 77–121.
H.-B. Brinkmann and D. Puppe, Abelsche und Exakte Kategorien; Korrespondenzen, Springer-Verlag Lecture Notes in Mathematics 96, 1969.
H. Herrlich and G. E. Strecker, Category Theory, second edition, Heldermann-Verlag, Berlin, 1979.
W. Kuich and A. Salomaa, Semirings, Automata, Languages, Springer-Verlag, Berlin, 1986.
S. MacLane, Categories for the Working Mathematician, Springer-Verlag, New York, 1971.
M. G. Main, Demons, Catastropies and Communicating Processes, Univ. Colorado Tech. Rpt. CU-CS-343-86.
M. G. Main and D. B. Benson, Functional behavior of nondeterministic and concurrent programs, Inform. and Control 62, 1984, 144–189.
E. G. Manes, ed., Category Theory Applied to Computation and Control, Springer-Verlag LNCS 25, 1975.
E. G. Manes, A Class of Fuzzy Theories, J. Math. Analysis and Applications 85, 1982, 409–451.
E. G. Manes, Additive Domains, Springer-Verlag LNCS 239, 1986, 184–195.
E. G. Manes, Weakest preconditions: Categorical insights, Springer-Verlag LNCS 240, 1986, 182–197.
E. G. Manes, Assertional Categories, Proc. Third Workshop on Math. Found. Program. Semantics, Tulane, April 1987, to appear.
R. Milner, Calculi for Synchrony and Asynchrony, Theoret. Comput. Sci. 25, 1983, 267–310.
S. B. Niefield, Adjoints to Tensor for Graded Algebras and Coalgebras, J. Pure Appl. Alg. 41 1986, 255–261.
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© 1987 Springer-Verlag Berlin Heidelberg
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Benson, D.B. (1987). The category of Milner processes is exact. In: Pitt, D.H., Poigné, A., Rydeheard, D.E. (eds) Category Theory and Computer Science. Lecture Notes in Computer Science, vol 283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18508-9_21
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DOI: https://doi.org/10.1007/3-540-18508-9_21
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