180 research outputs found
Approaching the Coverability Problem Continuously
The coverability problem for Petri nets plays a central role in the
verification of concurrent shared-memory programs. However, its high
EXPSPACE-complete complexity poses a challenge when encountered in real-world
instances. In this paper, we develop a new approach to this problem which is
primarily based on applying forward coverability in continuous Petri nets as a
pruning criterion inside a backward coverability framework. A cornerstone of
our approach is the efficient encoding of a recently developed polynomial-time
algorithm for reachability in continuous Petri nets into SMT. We demonstrate
the effectiveness of our approach on standard benchmarks from the literature,
which shows that our approach decides significantly more instances than any
existing tool and is in addition often much faster, in particular on large
instances.Comment: 18 pages, 4 figure
Decision Problems for Petri Nets with Names
We prove several decidability and undecidability results for nu-PN, an
extension of P/T nets with pure name creation and name management. We give a
simple proof of undecidability of reachability, by reducing reachability in
nets with inhibitor arcs to it. Thus, the expressive power of nu-PN strictly
surpasses that of P/T nets. We prove that nu-PN are Well Structured Transition
Systems. In particular, we obtain decidability of coverability and termination,
so that the expressive power of Turing machines is not reached. Moreover, they
are strictly Well Structured, so that the boundedness problem is also
decidable. We consider two properties, width-boundedness and depth-boundedness,
that factorize boundedness. Width-boundedness has already been proven to be
decidable. We prove here undecidability of depth-boundedness. Finally, we
obtain Ackermann-hardness results for all our decidable decision problems.Comment: 20 pages, 7 figure
Safety verification of asynchronous pushdown systems with shaped stacks
In this paper, we study the program-point reachability problem of concurrent
pushdown systems that communicate via unbounded and unordered message buffers.
Our goal is to relax the common restriction that messages can only be retrieved
by a pushdown process when its stack is empty. We use the notion of partially
commutative context-free grammars to describe a new class of asynchronously
communicating pushdown systems with a mild shape constraint on the stacks for
which the program-point coverability problem remains decidable. Stacks that fit
the shape constraint may reach arbitrary heights; further a process may execute
any communication action (be it process creation, message send or retrieval)
whether or not its stack is empty. This class extends previous computational
models studied in the context of asynchronous programs, and enables the safety
verification of a large class of message passing programs
The ideal view on Rackoff's coverability technique
Rackoffâs small witness property for the coverability problem is the standard means to prove tight upper bounds in vector addition systems (VAS) and many extensions. We show how to derive the same bounds directly on the computations of the VAS instantiation of the generic backward coverability algorithm. This relies on a dual view of the algorithm using ideal decompositions of downwards-closed sets, which exhibits a key structural invariant in the VAS case. The same reasoning readily generalises to several VAS extensions
The Parametric Complexity of Lossy Counter Machines
The reachability problem in lossy counter machines is the best-known ACKERMANN-complete problem and has been used to establish most of the ACKERMANN-hardness statements in the literature. This hides however a complexity gap when the number of counters is fixed. We close this gap and prove F_d-completeness for machines with d counters, which provides the first known uncontrived problems complete for the fast-growing complexity classes at levels 3 < d < omega. We develop for this an approach through antichain factorisations of bad sequences and analysing the length of controlled antichains
Forward Analysis and Model Checking for Trace Bounded WSTS
We investigate a subclass of well-structured transition systems (WSTS), the
bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete
deterministic ones, which we claim provide an adequate basis for the study of
forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth.
Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered
previously for the termination of forward analysis, boundedness is decidable.
Boundedness turns out to be a valuable restriction for WSTS verification, as we
show that it further allows to decide all -regular properties on the
set of infinite traces of the system
Parameterized Verification of Safety Properties in Ad Hoc Network Protocols
We summarize the main results proved in recent work on the parameterized
verification of safety properties for ad hoc network protocols. We consider a
model in which the communication topology of a network is represented as a
graph. Nodes represent states of individual processes. Adjacent nodes represent
single-hop neighbors. Processes are finite state automata that communicate via
selective broadcast messages. Reception of a broadcast is restricted to
single-hop neighbors. For this model we consider a decision problem that can be
expressed as the verification of the existence of an initial topology in which
the execution of the protocol can lead to a configuration with at least one
node in a certain state. The decision problem is parametric both on the size
and on the form of the communication topology of the initial configurations. We
draw a complete picture of the decidability and complexity boundaries of this
problem according to various assumptions on the possible topologies.Comment: In Proceedings PACO 2011, arXiv:1108.145
The complexity of coverability in Μ-Petri nets
We show that the coverability problem in Îœ-Petri nets is complete for âdouble Ackermannâ time, thus closing an open complexity gap between an Ackermann lower bound and a hyper-Ackermann upper bound. The coverability problem captures the verification of safety properties in this nominal extension of Petri nets with name management and fresh name creation. Our completeness result establishes Îœ-Petri nets as a model of intermediate power among the formalisms of nets enriched with data, and relies on new algorithmic insights brought by the use of well-quasi-order ideals
Complexity Hierarchies Beyond Elementary
We introduce a hierarchy of fast-growing 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
non-elementary complexity, which occur naturally in logic, combinatorics,
formal languages, verification, etc., with complexities ranging from simple
towers of exponentials to Ackermannian and beyond.Comment: Version 3 is the published version in TOCT 8(1:3), 2016. I will keep
updating the catalogue of problems from Section 6 in future revision
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