Continuous Additive Algebras and Injective Simulations of
Synchronization Trees
Zoltán Ésik September 2000 |

## Abstract:
The (in)equational properties of the least fixed point
operation on (-)continuous functions on (-)complete
partially ordered sets are captured by the axioms of (ordered) iteration
algebras, or iteration theories. We show that the inequational laws of the
sum operation in conjunction with the least fixed point operation in
continuous additive algebras have a finite axiomatization over the
inequations of ordered iteration algebras. As a byproduct of this relative
axiomatizability result, we obtain complete infinite inequational and finite
implicational axiomatizations. Along the way of proving these results, we
give a concrete description of the free algebras in the corresponding variety
of ordered iteration algebras. This description uses injective simulations of
regular synchronization trees. Thus, our axioms are also sound and complete
for the injective simulation (resource bounded simulation) of (regular)
processes
Available as |

Last modified: 2003-06-08 by webmaster.