Structural Refinement for the Modal nu-Calculus

We introduce a new notion of structural refinement, a sound abstraction of logical implication, for the modal nu-calculus. Using new translations between the modal nu-calculus and disjunctive modal transition systems, we show that these two specification formalisms are structurally equivalent. Using our translations, we also transfer the structural operations of composition and quotient from disjunctive modal transition systems to the modal nu-calculus. This shows that the modal nu-calculus supports composition and decomposition of specifications.Comment: Accepted at ICTAC 201

Refinement Modal Logic

In this paper we present {\em refinement modal logic}. A refinement is like a bisimulation, except that from the three relational requirements only `atoms' and `back' need to be satisfied. Our logic contains a new operator 'all' in addition to the standard modalities 'box' for each agent. The operator 'all' acts as a quantifier over the set of all refinements of a given model. As a variation on a bisimulation quantifier, this refinement operator or refinement quantifier 'all' can be seen as quantifying over a variable not occurring in the formula bound by it. The logic combines the simplicity of multi-agent modal logic with some powers of monadic second-order quantification. We present a sound and complete axiomatization of multi-agent refinement modal logic. We also present an extension of the logic to the modal mu-calculus, and an axiomatization for the single-agent version of this logic. Examples and applications are also discussed: to software verification and design (the set of agents can also be seen as a set of actions), and to dynamic epistemic logic. We further give detailed results on the complexity of satisfiability, and on succinctness

Bounded Petri Net Synthesis from Modal Transition Systems is Undecidable

In this paper, the synthesis of bounded Petri nets from deterministic modal transition systems is shown to be undecidable. The proof is built from three components. First, it is shown that the problem of synthesising bounded Petri nets satisfying a given formula of the conjunctive nu-calculus (a suitable fragment of the mu-calculus) is undecidable. Then, an equivalence between deterministic modal transition systems and a language-based formalism called modal specifications is developed. Finally, the claim follows from a known equivalence between the conjunctive nu-calculus and modal specifications

Compositionality for Quantitative Specifications

We provide a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy. It is based on disjunctive modal transition systems where we allow actions to bear various types of quantitative information. Throughout the design process the actions can be further refined and the information made more precise. We show how to compute the results of standard operations on the systems, including the quotient (residual), which has not been previously considered for quantitative non-deterministic systems. Our quantitative framework has close connections to the modal nu-calculus and is compositional with respect to general notions of distances between systems and the standard operations

Completeness of Flat Coalgebraic Fixpoint Logics

Modal fixpoint logics traditionally play a central role in computer science, in particular in artificial intelligence and concurrency. The mu-calculus and its relatives are among the most expressive logics of this type. However, popular fixpoint logics tend to trade expressivity for simplicity and readability, and in fact often live within the single variable fragment of the mu-calculus. The family of such flat fixpoint logics includes, e.g., LTL, CTL, and the logic of common knowledge. Extending this notion to the generic semantic framework of coalgebraic logic enables covering a wide range of logics beyond the standard mu-calculus including, e.g., flat fragments of the graded mu-calculus and the alternating-time mu-calculus (such as alternating-time temporal logic ATL), as well as probabilistic and monotone fixpoint logics. We give a generic proof of completeness of the Kozen-Park axiomatization for such flat coalgebraic fixpoint logics.Comment: Short version appeared in Proc. 21st International Conference on Concurrency Theory, CONCUR 2010, Vol. 6269 of Lecture Notes in Computer Science, Springer, 2010, pp. 524-53

Analysing the Control Software of the Compact Muon Solenoid Experiment at the Large Hadron Collider

The control software of the CERN Compact Muon Solenoid experiment contains over 30,000 finite state machines. These state machines are organised hierarchically: commands are sent down the hierarchy and state changes are sent upwards. The sheer size of the system makes it virtually impossible to fully understand the details of its behaviour at the macro level. This is fuelled by unclarities that already exist at the micro level. We have solved the latter problem by formally describing the finite state machines in the mCRL2 process algebra. The translation has been implemented using the ASF+SDF meta-environment, and its correctness was assessed by means of simulations and visualisations of individual finite state machines and through formal verification of subsystems of the control software. Based on the formalised semantics of the finite state machines, we have developed dedicated tooling for checking properties that can be verified on finite state machines in isolation.Comment: To appear in FSEN'11. Extended version with details of the ASF+SDF translation of SML into mCRL

An analysis of the control hierarchy modeling of the CMS detector control system

The supervisory level of the Detector Control System (DCS) of the CMS experiment is implemented using Finite State Machines (FSM), which model the behaviours and control the operations of all the sub-detectors and support services. The FSM tree of the whole CMS experiment consists of more than 30.000 nodes. An analysis of a system of such size is a complex task but is a crucial step towards the improvement of the overall performance of the FSM system. This paper presents the analysis of the CMS FSM system using the micro Common Representation Language 2 (mcrl2) methodology. Individual mCRL2 models are obtained for the FSM systems of the CMS sub-detectors using the ASF+SDF automated translation tool. Different mCRL2 operations are applied to the mCRL2 models. A mCRL2 simulation tool is used to closer examine the system. Visualization of a system based on the exploration of its state space is enabled with a mCRL2 tool. Requirements such as command and state propagation are expressed using modal mu-calculus and checked using a model checking algorithm. For checking local requirements such as endless loop freedom, the Bounded Model Checking technique is applied. This paper discusses these analysis techniques and presents the results of their application on the CMS FSM system