Abstracts of talks at the Braga IFIP WG1.3 meeting

Abstracts of talks at the Braga IFIP WG1.3 meeting (March 23-24, 2007)

1 - Narciso MARTI-OLIET
Algebraic simulations (slides)
(joint work with Jose Meseguer and Miguel Palomino)

In the first part of the talk we describe generalizations of simulations in three directions. First, by avoiding negation we relax the condition on preservation of atomic properties from equality to containment; second, we consider stuttering simulations, which are useful to relate concurrent systems with different levels of atomicity; third, we allow different alphabets AP and AP' of atomic propositions so that an atomic proposition in AP is mapped to a state formula over AP'. A categorical viewpoint is the most natural to understand and organize these generalized simulations.

In the second part of the talk we prove several representability results showing that any Kripke structure can be represented by a rewrite theory, and that any generalized simulation can be represented by a rewrite relation. We consider four increasingly more general ways of defining simulations in rewriting logic: equational abstractions, theory interpretations, simulation maps as equationally defined functions, and simulations given by rewrite relations. The first two techniques have been studied in detail in previous papers. The third one is illustrated here by means of an example showing that a stack machine correctly implements the operational semantics for a simple functional language. The fourth one is also illustrated by means of a communication protocol example proving in-order delivery of messages in the presence of an unreliable medium.

References:
J. Meseguer, M. Palomino, and N. Marti-Oliet. Equational abstractions (extended version)
J. Meseguer, M. Palomino, and N. Marti-Oliet. Algebraic Simulations

Both are available from http://maude.sip.ucm.es/~miguelpt

2 - Laure PETRUCCI
Modular construction of symbolic observation graph
(joint work with Kais Klai)

Model checking for Linear Time Logic (LTL) is usually based on converting the property into a Buchi automaton (or tableau), composing the automaton and the model, and finally checking for emptiness of the language of the composed system. The last step is the crucial stage of the verification process because of the state explosion problem, i.e. the exponential increase of the number of states w.r.t. the number of system components.
In this work, we present a symbolic and modular solution which builds, in a modular way, an observation graph represented in a non-symbolic way but where the nodes are essentially symbolic sets of states and the edges either labelled by events occurring in the formula or by synchronisation actions between the system components. Due to the small number of events to be observed in a typical formula, this graph has a very moderate size and thus the complexity time of verification is negligible w.r.t. the time to build the observation graph.
The preliminary evaluations we have achieved on standard examples show that our method outperforms both a non modular generation of the symbolic graph and the pure symbolic methods.

4 - Marie-Claude GAUDEL
Uniform random sampling of traces in very large models
(joint work with Alain Denise, Sandrine-Dominique Gouraud, Richard Lassaigne, Sylvain Peyronnet)

This talk presents some first results on how to perform uniform random walks (where every trace has the same probability to occur) in very large models. The models considered here are described in a succinct way as a set of communicating reactive modules. The method relies upon techniques for counting and drawing uniformly at random words in regular languages. Each module is considered as an automaton defining such a language. It is shown how it is possible to combine local uniform drawings of traces, and to obtain some global uniform random sampling, without construction of the global model.

5 - Stefania GNESI web page
A model checking approach for designing asynchronous extension of SOAP
(joint work with Maurice ter Beek, and Franco Mazzanti)

In this talk an action-state based logical framework for the analysis and verification of complex systems that relies on the definition of doubly labeled transition systems. The defined logic combines the action paradigm, classically used for describing systems using labeled transitions systems together with the predicates that are true over states as captured using Kripke structures as semantic model. An efficient model checker for this logic has been realized exploiting an on the fly algorithm. In the end of the talk the use of the logic and its model checker in the design phase of an asynchronous extension of SOAP is shown.

7 - Luis Soares BARBOSA slides and web page
Revisiting invariants
(joint work with José N. Oliveira and Alexandra Silva )

We discuss the usefulness of reasoning about invariants for software components coalgebraically in the allegory of binary relations.
The novelty of our approach consists in establishing a synergy between a relational construct, Reynolds' Çrelation on functionsÈ involved in his abstraction theorem (traditionally employed in explaining and reasoning about parametric polymorphism), and the coalgebraic approach to bisimulations and invariants.

This synergy arises from the fact that, once pointfree-transformed, formulae in one domain Çlook likeÈ others in the other domain. We stress on this syntactic aspect of formal reasoning, a kind of "let-the-symbols-do-the-work" style of calculation, often neglected by too much emphasis on domain-specific, semantic concerns.

9 - Alexander KURZ
A characterisation of modal logics of rank 1
(joint work with J. Rosicky)

We show that a functor on a variety has a finitary presentation by operations and equations if and only if this functor preserves sifted colimits. Moreover, from the proof it follows that this presentation is by equations of rank 1 (an equation is of rank 1 if each variable is in the scope of precisely one modal operator). We also remark that on the variety of Boolean algebras sifted colimit preserving functors and filtered colimit preserving functors (almost) coincide.

This is joint work with J. Rosicky and one of the results of our paper on Strongly complete logics for coalgebras, available from my home page.

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== Saturday, March 24rd, 2007
13 - Till MOSSAKOWSKI
Heterogeneous proof scripts

The heterogeneous tool set integrates various languages, logics and proof tools. So far, proof management has been session based, using a graphical user interface. A proof script language (like the ones used by current interactive theorem provers) has the advantage that proof developments are made explicit and can be re-used for later developments. We introduce such as proof script language for Hets. It combines proof commands for the structured level (using the development graph calculus) with local theorem provers for specific logics. Proof scripts for the latter can be embedded into the scripts for Hets, such that we arrive at heterogeneous proof scripts.

Hets is available under: here