Pairs of Languages Closed under Shuffle Projection

Shuffle projection is motivated by the verification of safety properties of special parameterized systems. Basic definitions and properties, especially related to alphabetic homomorphisms, are presented. The relation between iterated shuffle products and shuffle projections is shown. A special class of multi-counter automata is introduced, to formulate shuffle projection in terms of computations of these automata represented by transductions. This reformulation of shuffle projection leads to construction principles for pairs of languages closed under shuffle projection. Additionally, it is shown that under certain conditions these transductions are rational, which implies decidability of closure against shuffle projection. Decidability of these conditions is proven for regular languages. Finally, without additional conditions, decidability of the question, whether a pair of regular languages is closed under shuffle projection, is shown. In an appendix the relation between shuffle projection and the shuffle product of two languages is discussed. Additionally, a kind of shuffle product for computations in S-automata is defined

Security properties of self-similar uniformly parameterised systems of cooperations

Abstract-Uniform parameterisations of cooperations are defined in terms of formal language theory, such that each pair of partners cooperates in the same manner, and that the mechanism (schedule) to determine how one partner may be involved in several cooperations, is the same for each partner. Generalising each pair of partners cooperating in the same manner, for such systems of cooperations a kind of selfsimilarity is formalised. From an abstracting point of view, where only actions of some selected partners are considered, the complex system of all partners behaves like the smaller subsystem of the selected partners. For verification purposes, so called uniformly parameterised safety properties are defined. Such properties can be used to express privacy policies as well as security and dependability requirements. It is shown, how the parameterised problem of verifying such a property is reduced by self-similarity to a finite state problem. Keywords-cooperations as prefix closed languages; abstractions of system behaviour; self-similarity in systems of cooperations; privacy policies; uniformly parameterised safety properties

The SH-Verification Tool

The sh-verification tool supports a verification method for cooperating systems based on formal languages. It comprises computing abstractions of finite-state behaviour representations as well as automata and temporal logic based verification approaches. A small but typical example shows the steps for analysing its dynamic behaviour using the sh-verification tool

Abstraction Based Verification of a Parameterised Policy Controlled System

Abstract. Safety critical and business critical systems are usually controlled by policies with the objective to guarantee a variety of safety, liveness and security properties. Traditional model checking techniques allow a verification of the required behaviour only for systems with very few components. To be able to verify entire families of systems, independent of the exact number of replicated components, we developed an abstraction based approach to extend our current tool supported verification techniques to such families of systems that are usually parameterised by a number of replicated identical components. We demonstrate our technique by an exemplary verification of security and liveness properties of a simple parameterised collaboration scenario. Verification results for configurations with fixed numbers of components are used to choose an appropriate property preserving abstraction that provides the basis for an inductive proof that generalises the results for a family of systems with arbitrary settings of parameters. Key words: Formal analysis of security and liveness properties, security modelling and simulation, security policies, parameterised models.

Deterministic omega-Regular Liveness Properties

A major drawback for the use of automated verification techniques is the complexity of verification algorithms in general. One of the sources of the algorithms' complexity is the difference between the language classes accepted by deterministic and nondeterministic Büchi-automata respectively. This difference causes the problem of complementing Büchi-automata and hence deciding subset conditions on regular !-languages to be PSPACE-complete. We investigate in this paper whether nontrivial property classes exist that can be characterized by deterministic Büchi-automata and hence be complemented rather easily. Since the class of safety properties is known to be representable deterministically, taking into account that safety properties are the closed sets in the Cantor topology, it suffices for us to identify nontrivial deterministic !-regular liveness properties