Abstract. We show that the the shift on the reduced C∗–algebras of RD–groups, including the free group on infinitely many generators, and the amalgamated free product C∗–algebras, enjoys the very strong ergodic property of the convergence to the equilibrium. Namely, the free shift converges, pointwise in the weak topology, to the conditional expectation onto the fixed–point subalgebra. Provided...

Abstract. We define a stronger property than unique ergodicity with respect to the fixed–point subalgebra firstly investigated in [1]. Such a property is denoted as F–strict weak mixing (F stands for the Markov projection onto the fixed–point operator system). Then we show that the free shifts on the reduced C–algebras of RD–groups, including the free group on infinitely many generators, and am...

Rewriting with non-symmetric relations can be considered as a computational model of many specification languages based on nonsymmetric relations. For instance, Logics of Inequalities, Ordered Algebras, Rewriting Logic, Order-Sorted Algebras, Subset Logic, Unified Algebras, taxonomies, subtypes, Refinement Calculus, all them use some kind of non-symmetric relation on expressions. We have develo...