Blaise Genest

A Kleene theorem and model checking algorithms for existentially bounded communicating automata

The behavior of a network of communicating automata is called existentially bounded if communication events can be scheduled in such a way that the number of messages in transit is always bounded by a value that depends only on the machine, not the run itself. We show a Kleene theorem for existentially bounded communicating automata, namely the equivalence between communicating automata, globally cooperative compositional message sequence graphs, and monadic second order logic. Our characterization extends results for universally bounded models, where for each and every possible scheduling of communication events, the number of messages in transit is uniformly bounded. As a consequence, we give solutions in spirit of Madhusudan (2001) for various model checking problems on networks of communicating automata that satisfy our optimistic restriction.

Infinite-State High-Level MSCs: Model-Checking and Realizability

We consider three natural classes of infinite-state HMSCs: globally-cooperative, locally-cooperative and local-choice HMSCs. We show first that model-checking for globally-cooperative and locally-cooperative HMSCs has the same complexity as for the class of finite-state (bounded) HMSCs. Surprisingly, model-checking local-choice HMSCs turns out to be exponentially more efficient in space than for locally-cooperative HMSCs. We also show that locally-cooperative and local-choice HMSCs can be always implemented by communicating finite states machines, provided we allow some additional (bounded) message data. Moreover, the implementation of local-choice HMSCs is deadlock-free and of linear-size.

Infinite-state high-level MSCs: Model-checking and realizability

Message sequence charts (MSC) and High-level MSC (HMSC) is a visual notation for asynchronously communicating processes and a standard of the ITU. They usually represent incomplete specifications of required or forbidden properties of communication protocols. We consider in this paper two basic problems concerning the automated validation of HMSC specifications, namely model-checking and synthesis. We identify natural syntactic restrictions of HMSCs for which we can solve the above questions. We show first that model-checking for globally cooperative (and locally cooperative) HMSCs is decidable within the same complexity as for the restricted class of bounded HMSCs. Furthermore, model-checking local-choice HMSCs turns out to be as efficient as for finite-state (sequential) systems. The study of locally cooperative and local-choice HMSCs is motivated by the synthesis question, i.e., the question of implementing HMSCs through communicating finite-state machines (CFM) with additional message data. We show that locally cooperative and local-choice HMSCs are always implementable. Furthermore, the implementation of a local-choice HMSC is deadlock-free and of linear size.

Message Sequence Charts

Message sequence charts (MSC) are a graphical notation standardized by the ITU and used for the description of communication scenarios between asynchronous processes. This survey compares MSCs and communicating finite-state automata, presenting two fundamental validation problems on MSCs, model-checking and implementability.

Grey-Box checking

There are many cases where we want to verify a system that does not have a usable formal model: the model may be missing, out of date, or simply too big to be used. A possible method is to analyze the system while learning the model (black box checking). However, learning may be an expensive task, thus it needs to be guided, e.g., using the checked property or an inaccurate model (adaptive model checking). In this paper, we consider the case where some of the system components are completely specified (white boxes), while others are unknown (black boxes), giving rise to a grey box system. We provide algorithms and lower bounds, as well as experimental results for this model.

Specifying and Verifying Partial Order Properties Using Template MSCs

Message sequence charts (MSC) are a graphical language for the description of communication scenarios between asynchronous processes. Our starting point is to model systems using an assume-guarantee formalism, in the style of LSCs and Triggered MSCs. We enrich MSCs with the possibility of using gaps (template MSC), and show their expressivity. This formalism also allows to express logical formulas. We analyze the model-checking problem, whose complexity is linear in the size of the system, and ranges from PTIME to EXPSPACE in the size of the template formula.

Optimal Zielonka-type construction of deterministic asynchronous automata

Asynchronous automata are parallel compositions of finitestate processes synchronizing over shared variables. A deep theorem due to Zielonka says that every regular trace language can be represented by a deterministic asynchronous automaton. In this paper we improve the construction, in that the size of the obtained asynchronous automaton is polynomial in the size of a given DFA and simply exponential in the number of processes. We show that our construction is optimal within the class of automata produced by Zielonka-type constructions. In particular, we provide the first non trivial lower bound on the size of asynchronous automata.

Constructing exponential-size deterministic zielonka automata

The well-known algorithm of Zielonka describes how to transform automatically a sequential automaton into a deterministic asynchronous trace automaton. In this paper, we improve the construction of deterministic asynchronous automata from finite state automaton. Our construction improves the well-known construction in that the size of the asynchronous automaton is simply exponential in both the size of the sequential automaton and the number of processes. In contrast, Zielonkas algorithm gives an asynchronous automaton that is doubly exponential in the number of processes (and simply exponential in the size of the automaton)

Asynchronous games over tree architectures

We consider the distributed control problem in the setting of Zielonka asynchronous automata. Such automata are compositions of finite processes communicating via shared actions and evolving asynchronously. Most importantly, processes participating in a shared action can exchange complete information about their causal past. This gives more power to controllers, and avoids simple pathological undecidable cases as in the setting of Pnueli and Rosner. We show the decidability of the control problem for Zielonka automata over acyclic communication architectures. We provide also a matching lower bound, which is l-fold exponential, l being the height of the architecture tree.

Approximate Verification of the Symbolic Dynamics of Markov Chains

A finite state Markov chain M is often viewed as a probabilistic transition system. An alternative view - which we follow here - is to regard M as a linear transform operating on the space of probability distributions over its set of nodes. The novel idea here is to discretize the probability value space [0,1] into a finite set of intervals. A concrete probability distribution over the nodes is then symbolically represented as a tuple D of such intervals. The i-th component of the discretized distribution D will be the interval in which the probability of node i falls. The set of discretized distributions is a finite set and each trajectory, generated by repeated applications of M to an initial distribution, will induce a unique infinite string over this finite set of letters. Hence, given a set of initial distributions, the symbolic dynamics of M will consist of an infinite language L over the finite alphabet of discretized distributions. We investigate whether L meets a specification given as a linear time temporal logic formula whose atomic propositions will assert that the current probability of a node falls in an interval. Unfortunately, even for restricted Markov chains (for instance, irreducible and aperiodic chains), we do not know at present if and when L is an (omega)-regular language. To get around this we develop the notion of an epsilon-approximation, based on the transient and long term behaviors of M. Our main results are that, one can effectively check whether (i) for each infinite word in L, at least one of its epsilon-approximations satisfies the specification; (ii) for each infinite word in L all its epsilon approximations satisfy the specification. These verification results are strong in that they apply to all finite state Markov chains. Further, the study of the symbolic dynamics of Markov chains initiated here is of independent interest and can lead to other applications.