Characteristic invariants in Hennessy-Milner logic

In this paper, we prove that Hennessy–Milner Logic (HML), despite its structural limitations, is sufficiently expressive to specify an initial property φ0 and a characteristic invariant χI for an arbitrary finite-state process P such that φ0∧AG(χI) is a characteristic formula for P. This means that a process Q, even if infinite state, is bisimulation equivalent to P iff Q⊨φ0∧AG(χI). It follows, in particular, that it is sufficient to check an HML formula for each state of a finite-state process to verify that it is bisimulation equivalent to P. In addition, more complex systems such as context-free processes can be checked for bisimulation equivalence with P using corresponding model checking algorithms. Our characteristic invariant is based on so called class-distinguishing formulas that identify bisimulation equivalence classes in P and which are expressed in HML. We extend Kanellakis and Smolka’s partition refinement algorithm for bisimulation checking in order to generate concise class-distinguishing formulas for finite-state processes

Program transformations using temporal logic side conditions

This paper describes an approach to program optimisation based on transformations, where temporal logic is used to specify side conditions, and strategies are created which expand the repertoire of transformations and provide a suitable level of abstraction. We demonstrate the power of this approach by developing a set of optimisations using our transformation language and showing how the transformations can be converted into a form which makes it easier to apply them, while maintaining trust in the resulting optimising steps. The approach is illustrated through a transformational case study where we apply several optimisations to a small program

CAESAR_SOLVE: A Generic Library for On-the-Fly Resolution of Alternation-Free Boolean Equation Systems

Boolean Equation Systems (BESs) provide a useful framework for modeling various verification problems on finite-state concurrent systems, such as equivalence checking and model checking. These problems can be solved on-the-fly (i.e., without constructing explicitly the state space of the system under analysis) by using a demand-driven construction and resolution of the corresponding BES. In this report, we present a generic software library dedicated to on-the-fly resolution of alternation-free BESs (i.e., without mutually recursive minimal and maximal fixed point equations). Four resolution algorithms are currently provided by the library: algorithms A1 and A2 are general, the latter being optimized to produce small-depth diagnostics, whereas algorithms A3 and A4 are specialized for handling acyclic and disjunctive/conjunctive BESs in a memory-efficient way. The library is developed within the CADP verification toolbox using the generic OPEN/CAESAR environment and is currently used for three purposes: on-the-fly equivalence checking modulo five widely-used equivalence relations, on-the-fly model checking of regular alternation-free mu-calculus, and on-the-fly reduction of state spaces based on tau-confluence