Continuous Additive Algebras and Injective Simulations of Synchronization Trees

The (in)equational properties of t he least fixed point operation on ( -)continuous functions on ( -)complete partially ordered sets are captured by the axioms of (ordered) ite ration algebras, or iteration theories. We show that the inequational laws of the sum operation in conjunction w ith the least fixed point operation in continuous additive algebras have a finite axiomatization over the inequati ons of ordered iteration alg ebras. As a byproduct of this relative axiomatizability result, we obtain complete infinite in quational and finite impli cational axiomatizations. Along the way of proving these results, we give a concre te description of the free algebras in the corresponding variety of ordered iteration algebras. This description use s injective simulations of regular synchronization trees. Thus, our axioms are also sound and complete for the inject ve simulation (resource boundesimulation) of (regular) processes.

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