Layered Fixed Point Logic

We present a logic for the specification of static analysis problems that goes beyond the logics traditionally used. Its most prominent feature is the direct support for both inductive computations of behaviors as well as co-inductive specifications of properties. Two main theoretical contributions are a Moore Family result and a parametrized worst case time complexity result. We show that the logic and the associated solver can be used for rapid prototyping and illustrate a wide variety of applications within Static Analysis, Constraint Satisfaction Problems and Model Checking. In all cases the complexity result specializes to the worst case time complexity of the classical methods

Discovering, quantifying, and displaying attacks

In the design of software and cyber-physical systems, security is often perceived as a qualitative need, but can only be attained quantitatively. Especially when distributed components are involved, it is hard to predict and confront all possible attacks. A main challenge in the development of complex systems is therefore to discover attacks, quantify them to comprehend their likelihood, and communicate them to non-experts for facilitating the decision process. To address this three-sided challenge we propose a protection analysis over the Quality Calculus that (i) computes all the sets of data required by an attacker to reach a given location in a system, (ii) determines the cheapest set of such attacks for a given notion of cost, and (iii) derives an attack tree that displays the attacks graphically. The protection analysis is first developed in a qualitative setting, and then extended to quantitative settings following an approach applicable to a great many contexts. The quantitative formulation is implemented as an optimisation problem encoded into Satisfiability Modulo Theories, allowing us to deal with complex cost structures. The usefulness of the framework is demonstrated on a national-scale authentication system, studied through a Java implementation of the framework.Comment: LMCS SPECIAL ISSUE FORTE 201

Termination analysis based on operational semantics

In principle termination analysis is easy: find a well-founded partial order and prove that calls decrease with respect to this order. In practice this often requires an oracle (or a theorem prover) for determining the well-founded order and this oracle may not be easily implementable. Our approach circumvents some of these problems by exploiting the inductive definition of algebraic data types and using pattern matching as in functional languages. We develop a termination analysis for a higher-order functional language; the analysis incorporates and extends polymorphic type inference and axiomatizes a class of well-founded partial orders for multiple-argument functions (as in Standard ML and Miranda). Semantics is given by means of operational (natural-style) semantics and soundness is proved; this involves making extensions to the semantic universe and we relate this to the techniques of denotational semantics. For dealing with the partiality aspects of the soundness proof, it suffices to incorporate approximations to the desired fixed points; for dealing with the totality aspects of the soundness proof, we also have to incorporate functions that are forced to terminate (in a way that might violate the monotonicity of denotational semantics)

From CML to process Algebras

Reppy's language CML extends Standard ML of Milner et al. with primitives for communication. It thus inherits a notion of strong polymorphic typing and may be equipped with a structural operational semantics. We formulate an effect system for statically expressing the communication behaviours of CML programs as these are not otherwise reflected in the types.We then show how types and behaviours evolve in the course of computation: types may decrease and behaviours may loose alternatives as well as decrease. It will turn out that the syntax of behaviours is rather similar to that of a process algebra; our main results may therefore be viewed as regarding the semantics of a process algebra as an abstraction of the semantics of an underlying programming language. This establishes a new kind of connection between ''realistic'' concurrent programming languages and ''theoretical'' process algebras