On the Two-Variable Fragment of the Equational Theory of the Max-Sum Algebra of the Natural Numbers

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 the empty process, has no finite omega-complete equational
axiomatization modulo trace equivalence.

AMS Subject Classification (1991): 08A70, 08B05, 03C05, 68Q70.
ACM Computing Classification System (1998): F.4.1.
Keywords and Phrases: Equational logic, varieties, complete axiomatizations,
process algebra, trace equivalence.