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Abstract: This paper shows that the collection of identities in two variables which hold in the algebra N of the natural numbers with constant zero, and binary operations of sum and maximum does not have a finite equational axiomatization. This gives an alternative proof of the non-existence of a finite basis for N - a result previously obtained by the authors. As an application of the main theorem, it is shown that the language of Basic Process Algebra (over a singleton set of actions), with or without... (Update)
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...do not give an equational axiomatization of either. Remark 4. 3 Another view of the non existence of a finite basis for the is o#ered in [1]. Ibidem we show that the collection of equations in two variables that hold in has no finite equational axiomatization. 5 The Models...
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BibTeX entry: (Update)
L. Aceto, Z. Esik, and A. Ing olfsd ottir, On the two-variable fragment of the equational theory of the max-sum algebra of the natural numbers, in Proceedings of the 17th STACS, H. Reichel and S. Tison, eds., vol. 1770 of Lecture Notes in Computer Science, Springer-Verlag, Feb. 2000, pp. 267--278. http://citeseer.ist.psu.edu/aceto00twovariable.html More
@article{ aceto00twovariable,
author = "Luca Aceto and Zolt{\'a}n {\'E}sik and Anna Ing{\'o}lfsd{\'o}ttir",
title = "On the Two-Variable Fragment of the Equational Theory of the Max-Sum Algebra of the Natural Numbers",
journal = "Lecture Notes in Computer Science",
volume = "1770",
pages = "267+",
year = "2000",
url = "citeseer.ist.psu.edu/aceto00twovariable.html" }
Citations (may not include all citations):2732 Communicating Sequential Processes (context) - Hoare - 1985
266 Cambridge Tracts in Theoretical Computer Science (context) - Baeten, Weijland et al. - 1990
83 A Course in Universal Algebra - Burris, Sankappanavar - 1981
27 Fixed point semantics (context) - Bergstra, Klop - 1982
20 Universal Algebra (context) - Gr - 1979
18 The algebra of communicating processes with empty process (context) - Vrancken
8 Equational logic (context) - Taylor
1 The Max-Sum Algebra of the Natural Numbers has no Finite Equ.. (context) - Aceto, Esik et al. - 1999
1 A eld guide to equational logic (context) - McNulty - 1992
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