Graphical Encoding of a Spatial Logic for the pi-Calculus

This paper extends our graph-based approach to the verification of spatial properties of π-calculus specifications. The mechanism is based on an encoding for mobile calculi where each process is mapped into a graph (with interfaces) such that the denotation is fully abstract with respect to the usual structural congruence, i.e., two processes are equivalent exactly when the corresponding encodings yield isomorphic graphs. Behavioral and structural properties of π-calculus processes expressed in a spatial logic can then be verified on the graphical encoding of a process rather than on its textual representation. In this paper we introduce a modal logic for graphs and define a translation of spatial formulae such that a process verifies a spatial formula exactly when its graphical representation verifies the translated modal graph formula

Verifying Red-Black Trees

We show how to verify the correctness of insertion of elements into red-black trees--a form of balanced search trees--using analysis techniques developed for graph rewriting. We first model red-black trees and operations on them using hypergraph rewriting. Then we use the tool AUGUR, which computes approximated unfoldings, in order to show that insertion preserves the property that there are no two consecutive red nodes in a tree, a requirement for red-black trees. Furthermore, we prove that the tree remains balanced by exploiting a type system that can be obtained as an instance of a general framework

Verifying Red-Black Trees

Available as report RR-05-04 (Queen Mary, University of London