61 research outputs found
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 -calculus or CTL has received little attention. It is known that
parity games, which are closely related to the modal -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 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
Timed Lossy Channel Systems
Lossy channel systems are a classical model with applications ranging from the modeling of communication protocols to programs running on weak memory models. All existing work assume that messages traveling inside the channels are picked from a finite alphabet. In this paper, we extend the model by assuming that each message is equipped with a clock representing the age of the message, thus obtaining the model of Timed Lossy Channel Systems (TLCS). The main contribution of the paper is to show that the control state reachability problem is decidable for TLCS
Data Multi-Pushdown Automata
We extend the classical model of multi-pushdown systems by considering systems that operate on a finite set of variables ranging over natural numbers. The conditions on variables are defined via gap-order constraints that allow to compare variables for equality, or to check that the gap between the values of two variables exceeds a given natural number. Furthermore, each message inside a stack is equipped with a data item representing its value. When a message is pushed to the stack, its value may be defined by a variable. When a message is popped, its value may be copied to a variable. Thus, we obtain a system that is infinite in multiple dimensions, namely we have a number of stacks that may contain an unbounded number of messages each of which is equipped with a natural number.
It is well-known that the verification of any non-trivial property of multi-pushdown systems is undecidable, even for two stacks and for a finite data-domain. In this paper, we show the decidability of the reachability problem for the classes of data multi-pushdown system that admit a bounded split-width (or equivalently a bounded tree-width). As an immediate consequence, we obtain decidability for several subclasses of data multi-pushdown systems. These include systems with single stacks, restricted ordering policies on stack operations, bounded scope, bounded phase, and bounded context switches
On the Upward/Downward Closures of Petri Nets
We study the size and the complexity of computing finite state automata (FSA) representing and approximating the downward and the upward closure of Petri net languages with coverability as the acceptance condition.
We show how to construct an FSA recognizing the upward closure of a Petri net language in doubly-exponential time, and therefore the size is at most doubly exponential.
For downward closures, we prove that the size of the minimal automata can be non-primitive recursive.
In the case of BPP nets, a well-known subclass of Petri nets, we show that an FSA accepting the downward/upward closure can be constructed in exponential time.
Furthermore, we consider the problem of checking whether a simple regular language is included in the downward/upward closure of a Petri net/BPP net language.
We show that this problem is EXPSPACE-complete (resp. NP-complete) in the case of Petri nets (resp. BPP nets).
Finally, we show that it is decidable whether a Petri net language is upward/downward closed
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