Abstract
Ternary algebra has been used for detection of hazards in logic circuits since 1948. Process spaces have been introduced in 1995 as abstract models of concurrent processes. Surprisingly, process spaces turned out to be special ternary algebras. We study symmetry in process spaces; this symmetry is analoguous to duality, but holds among three algebras. An important role is played here by the uncertainty partial order, which has been used since 1972 in algebras dealing with ambiguity. We prove that each process space consists of three isomorphic Boolean algebras and elements related to partitions of a set into three blocks.
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References
Balbes, R., Dwinger, P.: Distributive Lattices. University of Missouri Press (1974)
Brzozowski, J.A.: De Morgan Bisemilattices. In: Proc. 30th Int. Symp. on Multiple-Valued Logic, pp. 173–178. IEEE Comp. Soc, Los Alamitos (2000)
Brzozowski, J.A.: Involuted Semilattices and Uncertainty in Ternary Algebras. Int. J. Algebra and Comput (2004) (to appear)
Brzozowski, J.A., Ésik, Z., Iland, Y.: Algebras for hazard detection. In: Fitting, M., Orłowska, E. (eds.) Beyond Two: Theory and Applications of Multiple-Valued Logic, pp. 3–24. Physica-Verlag (2003)
Brzozowski, J.A., Lou, J.J., Negulescu, R.: A Characterization of Finite Ternary Algebras. Int. J. Algebra and Comput. 7(6), 713–721 (1997)
Brzozowski, J.A., Seger, C.-J.H.: Asynchronous Circuits. Springer, Heidelberg (1995)
Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1990)
Eichelberger, E.B.: Hazard detection in combinational and sequential circuits. IBM J. Res. and Dev. 9, 90–99 (1965)
Ésik, Z.: A Cayley Theorem for Ternary Algebras. Int. J. Algebra and Comput. 8(3), 311–316 (1998)
Goto, M.: Application of Three-Valued Logic to Construct the Theory of Relay Networks (in Japanese). In: Proc. IEE, IECE, and I. of Illum. E. of Japan (1948)
Kleene, S.C.: Introduction to Metamathematics. North-Holland, Amsterdam (1952)
Mukaidono, M.: On the B-Ternary Logical Function—A Ternary Logic Considering Ambiguity. Trans. IECE, Japan 55–D(6), 355–362 (1972), In English in Systems, Computers, Controls 3 (3), 27–36 (1972)
Negulescu, R.: Process Spaces. Technical Report CS-95-48, Dept. of Comp. Science, University of Waterloo, ON, Canada (1995)
Negulescu, R.: Process Spaces and Formal Verification of Asynchronous Circuits. PhD Thesis, Dept. of Comp. Science, University of Waterloo, ON, Canada (1998)
Negulescu, R.: Process Spaces. In: Proc. 11th Int. Conf. on Concurrency Theory, pp. 196–210 (2000)
Negulescu, R.: Generic Transforms on Incomplete Specifications of Asynchronous Interfaces. In: Proc. 19th Conf. on Math. Found. of Programming Semantics (2003)
Troelstra, A.S.: Lectures on Linear Logic, Center for the Study of Language and Information, Stanford University, Stanford, CA (1992)
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Brzozowski, J., Negulescu, R. (2004). Duality for Three: Ternary Symmetry in Process Spaces. In: Karhumäki, J., Maurer, H., Păun, G., Rozenberg, G. (eds) Theory Is Forever. Lecture Notes in Computer Science, vol 3113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27812-2_1
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DOI: https://doi.org/10.1007/978-3-540-27812-2_1
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