Fully Abstract Models for Nondeterministic Regular Expressions

Regular expressions and Kleene Algebras have been a direct inspiration for many constructs and axiomatizations for concurrency models. These, however, put a different stress on nondeterminism. With concurrent interpretations in mind, we study the effect of removing the idempotence law X+X=X and distribution law X·(Y+Z)=X·Y +X·Z from Kleene Algebras. We propose an operational semantics that is sound and complete w.r.t. the new set of axioms and is fully abstract w.r.t. a denotational semantic based on trees. The operational semantics is based on labelled transition systems that keep track of the performed choices and on a preorder relation (we call it resource simulation) that takes also into account the number of states reachable via every action.An important property we exhibit is that resource bisimulation equivalence can be obtained as the kernel of resource simulation