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70
WellStructured Transition Systems Everywhere!
 THEORETICAL COMPUTER SCIENCE
, 1998
"... Wellstructured transition systems (WSTS's) are a general class of infinite state systems for which decidability results rely on the existence of a wellquasiordering between states that is compatible with the transitions. In this article, we provide an extensive treatment of the WSTS idea and ..."
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Cited by 250 (8 self)
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Wellstructured transition systems (WSTS's) are a general class of infinite state systems for which decidability results rely on the existence of a wellquasiordering 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 WSTS's.
Parameterized verification of infinitestate processes with global conditions
 In Proc. 19Ø�Int. Conf. on Computer Aided Verification
"... Abstract. We present a simple and effective approximated backward reachability algorithm for parameterized systems with existentially and universally quantified global conditions. The individual processes operate on unbounded local variables ranging over the natural numbers. In addition, processes m ..."
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Cited by 41 (11 self)
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Abstract. We present a simple and effective approximated backward reachability algorithm for parameterized systems with existentially and universally quantified global conditions. The individual processes operate on unbounded local variables ranging over the natural numbers. In addition, processes may communicate via broadcast, rendezvous and shared variables. We apply the algorithm to verify mutual exclusion for complex protocols such as Lamport’s bakery algorithm both with and without atomicity conditions, a distributed version of the bakery algorithm, and RicartAgrawala’s distributed mutual exclusion algorithm. 1
FORWARD ANALYSIS FOR WSTS, PART I: COMPLETIONS
, 2009
"... Wellstructured 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 theoretic ..."
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Cited by 18 (7 self)
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Wellstructured 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 downwardclosed 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.
Graph Grammar Modeling and Verification of Ad Hoc Routing Protocols (Extended Version)
"... Abstract. We present a technique for modeling and automatic verification of network protocols, based on graph transformation. It is suitable for protocols with a potentially unbounded number of nodes, in which the structure and topology of the network is a central aspect, such as routing protocols f ..."
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Cited by 15 (0 self)
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Abstract. We present a technique for modeling and automatic verification of network protocols, based on graph transformation. It is suitable for protocols with a potentially unbounded number of nodes, in which the structure and topology of the network is a central aspect, such as routing protocols for ad hoc networks. Safety properties are specified as a set of undesirable global configurations. We verify that there is no undesirable configuration which is reachable from an initial configuration, by means of symbolic backward reachability analysis. In general, the reachability problem is undecidable. We implement the technique in a graph grammar analysis tool, and automatically verify several interesting nontrivial examples. Notably, we prove loop freedom for the DYMO ad hoc routing protocol. DYMO is currently on the IETF standards track, to potentially become an Internet standard. 1
Forward analysis for WSTS, part II: Complete WSTS
 In ICALP’09, volume 5556 of LNCS
, 2009
"... Abstract. We describe a simple, conceptual forward analysis procedure for ∞complete WSTS S. This computes the clover of a state s0, i.e., a finite description of the closure of the cover of s0. When S is the completion of a WSTS X, the clover in S is a finite description of the cover in X. We show ..."
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Cited by 15 (5 self)
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Abstract. We describe a simple, conceptual forward analysis procedure for ∞complete WSTS S. This computes the clover of a state s0, i.e., a finite description of the closure of the cover of s0. When S is the completion of a WSTS X, the clover in S is a finite description of the cover in X. We show that this applies exactly when X is an ω 2WSTS, a new robust class of WSTS. We show that our procedure terminates in more cases than the generalized KarpMiller procedure on extensions of Petri nets. We characterize the WSTS where our procedure terminates as those that are cloverflattable. Finally, we apply this to wellstructured counter systems. 1
On (Omega)Regular Model Checking
, 2008
"... Checking infinitestate systems is frequently done by encoding infinite sets of states as regular languages. Computing such a regular representation of, say, the set of reachable states of a system requires acceleration techniques that can finitely compute the effect of an unbounded number of transi ..."
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Cited by 14 (3 self)
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Checking infinitestate systems is frequently done by encoding infinite sets of states as regular languages. Computing such a regular representation of, say, the set of reachable states of a system requires acceleration techniques that can finitely compute the effect of an unbounded number of transitions. Among the acceleration techniques that have been proposed, one finds both specific and generic techniques. Specific techniques exploit the particular type of system being analyzed, e.g. a system manipulating queues or integers, whereas generic techniques only assume that the transition relation is represented by a finitestate transducer, which has to be iterated. In this paper, we investigate the possibility of using generic techniques in cases where only specific techniques have been exploited so far. Finding that existing generic techniques are often not applicable in cases easily handled by specific techniques, we have developed a new approach to iterating transducers. This new approach builds on earlier work, but exploits a number of new conceptual and algorithmic ideas, often induced with the help of experiments, that give it a broad scope, as well as good performances.
Handling Parameterized Systems with NonAtomic Global Conditions
"... We consider verification of safety properties for parameterized systems with linear topologies. A process in the system is an extended automaton, where the transitions are guarded by both local and global conditions. The global conditions are nonatomic, i.e., a process allows arbitrary interleaving ..."
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Cited by 14 (9 self)
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We consider verification of safety properties for parameterized systems with linear topologies. A process in the system is an extended automaton, where the transitions are guarded by both local and global conditions. The global conditions are nonatomic, i.e., a process allows arbitrary interleavings with other transitions while checking the states of all (or some) of the other processes. We translate the problem into model checking of infinite transition systems where each configuration is a labeled finite graph. We derive an overapproximation of the induced transition system, which leads to a symbolic scheme for analyzing safety properties. We have implemented a prototype and run it on several nontrivial case studies, namely nonatomic versions of Burn’s protocol, Dijkstra’s protocol, the Bakery algorithm, Lamport’s distributed mutual exclusion protocol, and a twophase commit protocol used for handling transactions in distributed systems. As far as we know, these protocols have not previously been verified in a fully automated framework. 1
On the expressiveness of Mobile Synchronizing Petri Nets
 SecCo’05. ENTCS
, 2007
"... In recent papers we have introduced Mobile Synchronizing Petri Nets, a new model for mobility based on coloured Petri Nets. It allows the description of systems composed of a collection of (possibly mobile) hardware devices and mobile agents, both modelled in a homogenous way and abstracting from mi ..."
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Cited by 13 (7 self)
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In recent papers we have introduced Mobile Synchronizing Petri Nets, a new model for mobility based on coloured Petri Nets. It allows the description of systems composed of a collection of (possibly mobile) hardware devices and mobile agents, both modelled in a homogenous way and abstracting from middleware details. Our basic model introduced a colour to describe localities, but still lacked appropriate primitives to deal with security, and in fact it was equivalent to P/T nets. Then, we introduced the primitives to cope with security: a new colour for identifiers, basically corresponding to the natural numbers, that are created by means of a special transition. This mechanism allows us to deal with authentication issues. In this paper we discuss the expressiveness of the extended model with the authentication primitives. More specifically, we study several instances of the classical reachability and coverability problems. Finally, we also study a more abstract version of the mechanism to create identifiers, using abstract names, close to those in the πcalculus or the Ambient Calculus. We have proved that both models are strictly in between P/T nets and Turing machines.
Verifying infinite Markov chains with a finite attractor or the global coarseness property
 In Proc. LICS ’0521th IEEE Int. Symp. on Logic in Computer Science
, 2005
"... We consider infinite Markov chains which either have a finite attractor or satisfy the global coarseness property. Markov chains derived from probabilistic lossy channel systems (PLCS) or probabilistic vector addition systems with states (PVASS) are classic examples for these types, respectively. ..."
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Cited by 11 (3 self)
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We consider infinite Markov chains which either have a finite attractor or satisfy the global coarseness property. Markov chains derived from probabilistic lossy channel systems (PLCS) or probabilistic vector addition systems with states (PVASS) are classic examples for these types, respectively. We consider three different variants of the reachability problem and the repeated reachability problem: The qualitative problem, i.e., deciding if the probability is one (or zero); the approximate quantitative problem, i.e., computing the probability upto arbitrary precision; the exact quantitative problem, i.e., computing probabilities exactly. We express the qualitative problem in abstract terms for Markov chains with a finite attractor and for globally coarse Markov chains, and show an almost complete picture of its decidability of PLCS and PVASS. We also show that the path enumeration algorithm of [19] terminates for our types of Markov chain and can thus be used to solve the approximate quantitative reachability problem. Furthermore, a modified variant of this algorithm can solve the approximate quantitative repeated reachability problem for Markov chains with a finite attractor. Finally, we show that the exact probability of (repeated) reachability cannot be effectively expressed in the firstorder theory of the reals (IR; +; ;) for either PLCS or PVASS (unlike for other probabilistic models, e.g., probabilistic pushdown automata [14, 15, 13]). 1
COMPLEXITY HIERARCHIES BEYOND ELEMENTARY
, 2013
"... We introduce a hierarchy of fastgrowing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a nonelementary complexity, which occur naturally in logic, combinatorics, formal ..."
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Cited by 11 (4 self)
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We introduce a hierarchy of fastgrowing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a nonelementary complexity, which occur naturally in logic, combinatorics, formal languages, verification, etc., with complexities ranging from simple towers of exponentials to Ackermannian and beyond.