Equational Axioms for Probabilistic Bisimilarity (Preliminary Report)

This paper gives an equational axiomatization of probabilistic bisimulation equivalence for a class of finite-state agents previously studied by Stark and Smolka ((2000) Proof, Language, and Interaction: Essays in Honour of Robin Milner, pp. 571-595). The axiomatization is obtained by extending the general axioms of iteration theories (or iteration algebras), which characterize the equational properties of the fixed point operator on (omega-)continuous or monotonic functions, with three axiom schemas that express laws that are specific to probabilistic bisimilarity. Hence probabilistic bisimilarity (over finite-state agents) has an equational axiomatization relative to iteration algebras

On flowchart theories Part I. The deterministic case

AbstractWe give a calculus for the classes of deterministic flowchart schemes with respect to the strong equivalence relation, similar to the calculus of the classes of polynomials with respect to the reduction of similar terms. The algebraic structure involved is a strong iteration theory, i.e., an iteration theory (defined by Bloom, Elgot, and Wright, SIAM J. Comput. 9 (1980), 525–540) satisfying a “functorial dagger implication.