The research on algorithmic verification methods for concurrent and parallel systems has mostly focussed on finite-state systems, with applications in e.g. communication protocols and hardware systems. For infinite-state systems, e.g. systems that operate on data from unbounded domains, algorithmic verification is more difficult, since most verification problems are in general undecidable. In this paper, we consider the verification of a particular class of infinite-state systems, namely systems consisting of finite-state processes that communicate via unbounded lossy FIFO channels. This class is able to model e.g. link protocols such as the Alternating Bit Protocol and HDLC. The unboundedness of the channels makes these systems infinite-state. For this class of systems, we show that several interesting verification problems are decidable by giving algorithms for verifying the following classes of properties.

) Bernard Boigelot Universit'e de Li`ege Institut Montefiore, B28 4000 Li`ege Sart-Tilman, Belgium Email: boigelot@montefiore.ulg.ac.be Patrice Godefroid Lucent Technologies -- Bell Laboratories 1000 E. Warrenville Road Naperville, IL 60566, U.S.A. Email: god@bell-labs.com Abstract We study the verification of properties of communication protocols modeled by a finite set of finite-state machines that communicate by exchanging messages via unbounded FIFO queues. It is well-known that most interesting verification problems, such as deadlock detection, are undecidable for this class of systems. However, in practice, these verification problems may very well turn out to be decidable for a subclass containing most "real" protocols. Motivated by this optimistic (and, we claim, realistic) observation, we present an algorithm that may construct a finite and exact representation of the state space of a communication protocol, even if this state space is infinite. Our algorithm performs a loo...

. We consider symbolic on-the-fly verification methods for systems of finite-state machines that communicate by exchanging messages via unbounded and lossy FIFO queues. We propose a novel representation formalism, called simple regular expressions (SREs), for representing sets of states of protocols with lossy FIFO channels. We show that the class of languages representable by SREs is exactly the class of downward closed languages that arise in the analysis of such protocols. We give methods for (i) computing inclusion between SREs, (ii) an SRE representing the set of states reachable by executing a single transition in a system, and (iii) an SRE representing the set of states reachable by an arbitrary number of executions of a control loop of a program. All these operations are rather simple and can be carried out in polynomial time. With these techniques, one can construct a semi-algorithm which explores the set of reachable states of a protocol, in order to check variou...

We consider the verification of a particular class of infinite-state systems, namely systems consisting of finite-state processes that communicate via unbounded lossy FIFO channels. This class is able to model e.g. link protocols such as the Alternating Bit Protocol and HDLC. In an earlier paper, we showed that the problems of checking reachability, safety properties, and eventuality properties are decidable for this class of systems. In this paper, we show that the following problems are undecidable, namely ffl The model checking problem in propositional temporal logics such as Propositional Linear Time Temporal Logic (PTL) and Computation Tree Logic (CTL). ffl The problem of deciding eventuality properties with fair channels: do all computations eventually reach a given set of states if the unreliable channels satisfy fairness assumptions. The results are obtained through a reduction from a variant of Post's Correspondence Problem. This research report is a revised and extended ...

Consider a system of finite state machines communicating with each other over unbounded FIFO buffers. Such a model of computation is, clearly, turing powerful. This model has been used as the backbone of ISO protocol specification languages Estelle and SDL, as it allows one to abstract away from the details, such as errors in communication, that occur at lower levels of the protocol stack. It has recently been shown (in the literature) that realistic models which implicitly model errors in the communication buffers are more tractable than models which assume perfect communication. In this paper, we propose to make the model more realistic by modeling the probability of loss in the buffers. Given specifications in such a model we provide algorithms for the probabilistic reachability problem and the probabilistic model-checking (against linear-time PTL requirements) problem.

We consider symbolic on-the-fly verification methods for systems of finite-state machines that communicate by exchanging messages via unbounded and lossy FIFO queues. We propose a novel representation formalism, called simple regular expressions (SREs), for representing sets of states of protocols with lossy FIFO channels. We show that the class of languages representable by SREs is exactly the class of downward closed languages that arise in the analysis of such protocols. We give methods for (i) computing inclusion between SREs, (ii) an SRE representing the set of states reachable by executing a single transition in a system, and (iii) an SRE representing the set of states reachable by an arbitrary number of executions of a control loop of a program. All these operations are rather simple and can be carried out in polynomial time. With these techniques, one can straightforwardly construct an algorithm which explores the set of reachable states of a protocol, in order t...

this paper on symbolic representations for the computation of the reachability set of FIFO automata --- a finite control with multiple unbounded FIFO channels. To the best of our knowledge, Pachl uses for the first time regular expressions to represent infinite sets of channel contents [31]. In [17], linear regular expressions have been defined and used. Boigelot et al. chosed a deterministic finite automata based representation, namely Queue-content Decision Diagrams [4] and afterwards Bouajjani et al. added Pressburger formulas, namely Constrained QDDs [5]. Simple regular expressions have been introduced for lossy FIFO automata [1]

Lossy channel systems model a set of finite state processes interacting with each other over unbounded, lossy FIFO channels. This computational model is an abstraction of protocols in the lower layers of the network protocol hierarchy. In spite of its unbounded FIFO queues the Lossy channel system model is not turing-powerful. It has been shown that the reachability problem is decidable [1]. However, the model-checking problem, against specifications in linear time temporal logic (LTL), is known to be undecidable [2]. Given that the rate of message loss in communication systems can be probabilistically characterized we consider a probabilistic version of Lossy channel systems. We show that the problem of checking whether a LTL requirement holds almost always. i.e., with probability 1, of probabilistic lossy channel systems (PLCS) is decidable. As can be expected the probability of message loss does not play a part in the model-checking procedure. 1 Introduction Finite state machines w...

We define a subclass of Petri nets called m \Gamma state n \Gamma cycle Petri nets, each of which can be thought of as a ring of n bounded (by m states) Petri nets using n potentially unbounded places as joins. Let Ring(n; l; m) be the class of m \Gamma state n \Gamma cycle Petri nets in which the largest integer mentioned can be represented in l bits (when the standard binary encoding scheme is used). As it turns out, both the reachability problem and the boundedness problem can be decided in O(n(l + log m)) nondeterministic space. Our results provide a slight improvement over previous results for the so-called cyclic communicating finite state machines. We also compare and contrast our results with that of V ASS(n; l; s), which represents the class of n-dimensional s-state VASSs where the largest integer mentioned can be described in l bits. Keywords: Communicating finite state machine, complexity, boundedness, Petri net, reachability, vector addition system with states. 1. Introdu...

We consider the verification of a class of infinite-state systems called lossy channel systems, which consist of finite-state processes communicating via unbounded but lossy FIFO channels. This class is able to model several interesting protocols, such as HDLC, the Alternating Bit Protocol, and other Sliding Window protocols. In earlier papers we have considered the decidability of various temporal properties for lossy channel systems. In this paper we study simulation and bisimulation relations between lossy channel systems and finite transition systems. More precisely, we show the decidability of (1) whether a state in a finite transition system simulates a state in a lossy channel system, and conversely, (2) whether a state in a finite transition system is bisimilar to a state in a lossy channel system, and (3) whether a state in a finite...