Approximating Petri Net Reachability Along Context-free Traces

We investigate the problem asking whether the intersection of a context-free language (CFL) and a Petri net language (PNL) is empty. Our contribution to solve this long-standing problem which relates, for instance, to the reachability analysis of recursive programs over unbounded data domain, is to identify a class of CFLs called the finite-index CFLs for which the problem is decidable. The k-index approximation of a CFL can be obtained by discarding all the words that cannot be derived within a budget k on the number of occurrences of non-terminals. A finite-index CFL is thus a CFL which coincides with its k-index approximation for some k. We decide whether the intersection of a finite-index CFL and a PNL is empty by reducing it to the reachability problem of Petri nets with weak inhibitor arcs, a class of systems with infinitely many states for which reachability is known to be decidable. Conversely, we show that the reachability problem for a Petri net with weak inhibitor arcs reduces to the emptiness problem of a finite-index CFL intersected with a PNL.Comment: 16 page

Model-Checking of Ordered Multi-Pushdown Automata

We address the verification problem of ordered multi-pushdown automata: A multi-stack extension of pushdown automata that comes with a constraint on stack transitions such that a pop can only be performed on the first non-empty stack. First, we show that the emptiness problem for ordered multi-pushdown automata is in 2ETIME. Then, we prove that, for an ordered multi-pushdown automata, the set of all predecessors of a regular set of configurations is an effectively constructible regular set. We exploit this result to solve the global model-checking which consists in computing the set of all configurations of an ordered multi-pushdown automaton that satisfy a given w-regular property (expressible in linear-time temporal logics or the linear-time \mu-calculus). As an immediate consequence, we obtain an 2ETIME upper bound for the model-checking problem of w-regular properties for ordered multi-pushdown automata (matching its lower-bound).Comment: 31 page

Adding Time to Pushdown Automata

In this tutorial, we illustrate through examples how we can combine two classical models, namely those of pushdown automata (PDA) and timed automata, in order to obtain timed pushdown automata (TPDA). Furthermore, we describe how the reachability problem for TPDAs can be reduced to the reachability problem for PDAs.Comment: In Proceedings QFM 2012, arXiv:1212.345

Zenoness for Timed Pushdown Automata

Timed pushdown automata are pushdown automata extended with a finite set of real-valued clocks. Additionaly, each symbol in the stack is equipped with a value representing its age. The enabledness of a transition may depend on the values of the clocks and the age of the topmost symbol. Therefore, dense-timed pushdown automata subsume both pushdown automata and timed automata. We have previously shown that the reachability problem for this model is decidable. In this paper, we study the zenoness problem and show that it is EXPTIME-complete.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

Model checking Branching-Time Properties of Multi-Pushdown Systems is Hard

We address the model checking problem for shared memory concurrent programs modeled as multi-pushdown systems. We consider here boolean programs with a finite number of threads and recursive procedures. It is well-known that the model checking problem is undecidable for this class of programs. In this paper, we investigate the decidability and the complexity of this problem under the assumption of bounded context-switching defined by Qadeer and Rehof, and of phase-boundedness proposed by La Torre et al. On the model checking of such systems against temporal logics and in particular branching time logics such as the modal $\mu$-calculus or CTL has received little attention. It is known that parity games, which are closely related to the modal $\mu$-calculus, are decidable for the class of bounded-phase systems (and hence for bounded-context switching as well), but with non-elementary complexity (Seth). A natural question is whether this high complexity is inevitable and what are the ways to get around it. This paper addresses these questions and unfortunately, and somewhat surprisingly, it shows that branching model checking for MPDSs is inherently an hard problem with no easy solution. We show that parity games on MPDS under phase-bounding restriction is non-elementary. Our main result shows that model checking a $k$ context bounded MPDS against a simple fragment of CTL, consisting of formulas that whose temporal operators come from the set {\EF, \EX}, has a non-elementary lower bound

CARET analysis of multithreaded programs

Dynamic Pushdown Networks (DPNs) are a natural model for multithreaded programs with (recursive) procedure calls and thread creation. On the other hand, CARET is a temporal logic that allows to write linear temporal formulas while taking into account the matching between calls and returns. We consider in this paper the model-checking problem of DPNs against CARET formulas. We show that this problem can be effectively solved by a reduction to the emptiness problem of B\"uchi Dynamic Pushdown Systems. We then show that CARET model checking is also decidable for DPNs communicating with locks. Our results can, in particular, be used for the detection of concurrent malware.Comment: Pre-proceedings paper presented at the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur, Belgium, 10-12 October 2017 (arXiv:1708.07854

Localisation osseuse sternale et claviculaire d’une amylose

Un homme de 46 ans, sans antécédents pathologiques notables, est hospitalisé pour une altération de l'état général avec troubles de la marche évoluant depuis 6 mois. On constate à l'examen physique des ecchymoses périorbitaires droites et une tuméfaction de l'extrémité interne de la clavicule droite et du sternum. L'imagerie standard ainsi que la tomodensitométrie thoraco-abdominale révèle un aspect hétérogène diffus à toute la trame osseuse avec une fracture pathologique de l'extrémité externe de la clavicule (A) et une masse lytique sternale (B) dont la biopsie conclu à la présence de dépôts amyloïdes. On notait par ailleurs à la biologie une hypercalcémie à 2,8 mmol/l et une anémie normochrome normocytaire à 10 g/l. L'électrophorèse des protides était normale et le myélogramme ne montre pas d'infiltration par des plasmocytes dystrophiques . A La biopsie ostéomédullaire on note la présence d'une amylose médullaire et à l'échographie cardiaque, un aspect infiltré tigré du myocarde, un trouble restrictif et une lame d'épanchement péricardique. L'évolution était rapidement fatale avant le typage de l'amylose. La localisation osseuse de l'amylose, révélatrice chez ce patient, est rare. Elle réalise un tableau clinique de tuméfaction osseuse ou de fracture pathologique avec atteinte essentiellement vertébrale. Le principal diagnostic différentiel est celui de lésion tumorale maligne primitive ou secondaire