Hidden-Markov Program Algebra with iteration

We use Hidden Markov Models to motivate a quantitative compositional semantics for noninterference-based security with iteration, including a refinement- or "implements" relation that compares two programs with respect to their information leakage; and we propose a program algebra for source-level reasoning about such programs, in particular as a means of establishing that an "implementation" program leaks no more than its "specification" program. This joins two themes: we extend our earlier work, having iteration but only qualitative, by making it quantitative; and we extend our earlier quantitative work by including iteration. We advocate stepwise refinement and source-level program algebra, both as conceptual reasoning tools and as targets for automated assistance. A selection of algebraic laws is given to support this view in the case of quantitative noninterference; and it is demonstrated on a simple iterated password-guessing attack

Capturing and exploiting abstract views of states in OO verification

In this thesis, we study several implementation, specification and verification techniques for Object-Oriented (OO) programs. Our focus is on capturing conceptual structures in OO states in abstractions, and then exploiting such an abstract view of the state in specification and implementation approaches in a way that allows for formal verification. Generally, an OO state consists of many objects that reference each other in possibly complicated ways. At the same time, at any one point in the execution of the program, we can often reason about what is happening using an abstract view of the state that is much less complicated. To further improve the quality of implementations, better techniques must be developed for 1) specification of the abstract views that are used by the client and the programmer, and 2) the verification that an implementation satisfies its specification. This thesis contributes to that effort. We distinguish between client-level and programmer-level specification. A client-level specification acts as a contract between the client and the implementer. A programmer-level specification allows to reason formally about the implementation. We consider two specification formalisms that differ in the basic abstract view that is used: Algebraic Specification and OO Specification. We consider both client-level and programmer-level specifications based on algebraic specification. We contribute a novel syntax and semantics for the former, and we contribute an implementation approach for OO implementations based on the latter. We show that the implementation approach is suitable for problem-independent verification. We propose the programmer-level OO specification constructs inc and coop. The inc construct allows method specification to make explicit that a certain enumeration of invariants does not have to hold when that method is executed. The coop construct allows a field specification to make explicit that a certain enumeration of invariants might be invalidated when the field is updated. This allows for the specification and verification of OO designs in which in the process of updating one object, other objects with which it together implements a common purpose must be updated as well. We then generalize the inc and coop constructs by removing a restriction to enumerations of invariants. For instance, this is needed in the well-known Observer Pattern, where a Subject can have an arbitrary and dynamically changing number of Observers. A more general interpretation of invariants and accompanying proof system are provided as well. We contribute a programmer-level OO specification technique to capture layers in OO architectures, and we exploit these layers by providing a more liberal semantics of class invariants. We also provide a verification technique for the semantics. Layers are an abstraction at the architectural level in OO implementations that designate certain object structures in the design as sub-structures that are shared by other structures. An object in a higher layer is not relevant to the purpose of an object in the sub-structure. Given this intuition, an object in a higher layer is not part of the abstract view from an object in a lower layer. Therefore, the invariant of a higher layer object does not have to hold when a method of a lower-layer object is executing. Finally, we contribute a verification technique for pure methods and model fields, which are existing specification techniques for capturing an abstract view of the state in OO specifications. A method that is pure can be used as a function in predicates in class specifications. The function is axiomatized using the pre- and postcondition that are specified for the method. A model field abstracts part of the concrete state of an object into an abstract value. This too introduces an additional axiom in the underlying reasoning. The technique contributed establishes that such additional axioms do no introduce inconsistencies into the formal reasoning. It comes with heuristics that that make it amenable to automatic verification

Refinement by interpretation in {\pi}-institutions

The paper discusses the role of interpretations, understood as multifunctions that preserve and reflect logical consequence, as refinement witnesses in the general setting of pi-institutions. This leads to a smooth generalization of the refinement-by-interpretation approach, recently introduced by the authors in more specific contexts. As a second, yet related contribution a basis is provided to build up a refinement calculus of structured specifications in and across arbitrary pi-institutions.Comment: In Proceedings Refine 2011, arXiv:1106.348

The foundational legacy of ASL

Abstract. We recall the kernel algebraic specification language ASL and outline its main features in the context of the state of research on algebraic specification at the time it was conceived in the early 1980s. We discuss the most significant new ideas in ASL and the influence they had on subsequent developments in the field and on our own work in particular.