On the Two-Variable Fragment of the Equational Theory of the Max-Sum
Algebra of the Natural Numbers
Luca Aceto
August 1999 |

## 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 equational axiomatization modulo
trace equivalence
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