Continuous Additive Algebras and Injective Simulations of Synchronization Trees

Zoltán Ésik
2000 BRICS Report Series  
<p>The (in)equational properties of the least fixed point operation on<br />(omega-)continuous functions on (omega-)complete partially ordered sets are<br />captured by the axioms of (ordered) iteration algebras, or iteration<br />theories. We show that the inequational laws of the sum operation in<br />conjunction with the least fixed point operation in continuous additive<br />algebras have a finite axiomatization over the inequations of ordered<br />iteration algebras. As a byproduct of this
more » ... relative axiomatizability <br />result, we obtain complete infinite inequational and finite implicational<br />axiomatizations. Along the way of proving these results, we give a <br />concrete description of the free algebras in the corresponding variety of<br />ordered iteration algebras. This description uses injective simulations of <br />regular synchronization trees. Thus, our axioms are also sound and<br />complete for the injective simulation (resource bounded simulation) of<br />(regular) processes.</p><p><br />Keywords: equational logic, fixed points, synchronization trees, simulation.</p>
doi:10.7146/brics.v7i25.20153 fatcat:x24emoenbzfkrla2g2rzpfsnzu