Alain Finkel

Well-structured transition systems everywhere!

Well-structured transition systems (WSTSs) are a general class of infinite-state systems for which decidability results rely on the existence of a well-quasi-ordering between states that is compatible with the transitions. In this article, we provide an extensive treatment of the WSTS idea and show several new results. Our improved definitions allow many examples of classical systems to be seen as instances of WSTSs.

Reset Nets Between Decidability and Undecidability

We study Petri nets with Reset arcs (also Transfer and Doubling arcs) in combination with other extensions of the basic Petri net model. While Reachability is undecidable in all these extensions (indeed they are Turing-powerful), we exhibit unexpected frontiers for the decidability of Termination, Coverability, Boundedness and place-Boundedness. In particular, we show counter-intuitive separations between seemingly related problems. Our main theorem is the very surprising fact that boundedness is undecidable for Petri nets with Reset arcs.

A direct symbolic approach to model checking pushdown systems

Abstract This paper gives a simple and direct algorithm for computing the always regular set of reachable states of a pushdown system. It then exploits this algorithm for obtaining model checking algorithms for linear-time temporal logic as well as for the logic CTL∗. For the latter, a new technical tool is introduced: pushdown automata with transitions conditioned on regular predicates on the stack content. Finally, this technical tool is also used to establish that CTL∗ model checking remains decidable when the formulas are allowed to include regular predicates on the stack content.

Unreliable Channels Are Easier to Verify Than Perfect Channels

We consider the problem of verifying correctness of finite state machines that communicate with each other over unbounded FIFO channels that are unreliable. Various problems of interest in verification of FIFO channels that can lose messages have been considered by Finkel and by Abdulla and Jonsson. We consider, in this paper, other possible unreliable behaviors of communication channels, viz., (a) duplication and (b) insertion errors. Furthermore, we also consider various combinations of duplication, insertion, and lossiness errors. Finite state machines that communicate over unbounded FIFO buffers are a model of computation that forms the backbone of the ISO standard protocol specification languages Estelle and SDL. While the assumption of a perfect communication medium is reasonable at the higher levels of the OSI protocol stack, the lower levels have to deal with an unreliable communication medium; hence our motivation for the present work. The verification problems that are of interest arereachability,unboundedness,deadlock, andmodel-checking against CTL*. All of these problems are undecidable for machines communicating over reliable unbounded FIFO channels. So it is perhaps surprising that some of these problems become decidable when unreliable channels are modeled. The contributions of this paper are (a) an investigation of solutions to these problems for machines with insertion errors, duplication errors, or a combination of duplication, insertion, and lossiness errors, and (b) a comparison of the relative expressive power of the various errors.

FAST: Fast Acceleration of Symbolic Transition Systems

fast is a tool for the analysis of infinite systems. This paper describes the underlying theory, the architecture choices that have been made in the tool design. The user must provide a model to analyse, the property to check and a computation policy. Several such policies are proposed as a standard in the package, others can be added by the user. fast capabilities are compared with those of other tools. A range of case studies from the literature has been investigated.

Reduction and covering of infinite reachability trees

Abstract We present a structure for transition systems with which the main decidability results on Petri nets can be generalized to structured transition systems. We define the reduced reachability tree of a structured transition system; it allows one to decide the finite reachability tree problem (also called the finite termination problem) and the finite reachability set problem. A general definition of the coverability set is given and the procedure of Karp and Miller is extended for well-structured transition systems. We show then that the coverability problem is a decidable problem in the framework of well-structured transition systems. Finally, we introduce structured set of terminal states and we show that the finite reachability tree problem and the finite reachability set problem are decidable. Coverability is an open problem for structured transition systems with a structured set of terminal states.

Decidability of the termination problem for completely specified protocols

SummaryIn this paper, we present a new class of protocols called completely specified protocols. Each protocol is represented as a system of Communicating Finite State Machines. The class of completely specified protocols is such that each message that can be received by a Finite State Machine, can also be received in every local state of the Finite State Machine. These protocols are important because they allow for modelling unbounded fifo channels and make it possible to decide the Termination Problem, that is whether the reachability tree is finite or not. An example of our techniques is given using a practical problem concerning link protocols.

Flat acceleration in symbolic model checking

Symbolic model checking provides partially effective verification procedures that can handle systems with an infinite state space. So-called “acceleration techniques” enhance the convergence of fixpoint computations by computing the transitive closure of some transitions. In this paper we develop a new framework for symbolic model checking with accelerations. We also propose and analyze new symbolic algorithms using accelerations to compute reachability sets.

FAST: acceleration from theory to practice

Fast acceleration of symbolic transition systems (Fast) is a tool for the analysis of systems manipulating unbounded integer variables. We check safety properties by computing the reachability set of the system under study. Even if this reachability set is not necessarily recursive, we use innovative techniques, namely symbolic representation, acceleration and circuit selection, to increase convergence. Fast has proved to perform very well on case studies. This paper describes the tool, from the underlying theory to the architecture choices. Finally, Fast capabilities are compared with those of other tools. A range of case studies from the literature is investigated.

Forward analysis for WSTS, Part I: Completions

Well-structured transition systems provide the right foundation to compute a finite basis of the set of predecessors of the upward closure of a state. The dual problem, to compute a finite representation of the set of successors of the downward closure of a state, is harder: Until now, the theoretical framework for manipulating downward-closed sets was missing. We answer this problem, using insights from domain theory (dcpos and ideal completions), from topology (sobrifications), and shed new light on the notion of adequate domains of limits.