845 research outputs found
A Generic Framework for Reasoning about Dynamic Networks of Infinite-State Processes
We propose a framework for reasoning about unbounded dynamic networks of
infinite-state processes. We propose Constrained Petri Nets (CPN) as generic
models for these networks. They can be seen as Petri nets where tokens
(representing occurrences of processes) are colored by values over some
potentially infinite data domain such as integers, reals, etc. Furthermore, we
define a logic, called CML (colored markings logic), for the description of CPN
configurations. CML is a first-order logic over tokens allowing to reason about
their locations and their colors. Both CPNs and CML are parametrized by a color
logic allowing to express constraints on the colors (data) associated with
tokens. We investigate the decidability of the satisfiability problem of CML
and its applications in the verification of CPNs. We identify a fragment of CML
for which the satisfiability problem is decidable (whenever it is the case for
the underlying color logic), and which is closed under the computations of post
and pre images for CPNs. These results can be used for several kinds of
analysis such as invariance checking, pre-post condition reasoning, and bounded
reachability analysis.Comment: 29 pages, 5 tables, 1 figure, extended version of the paper published
in the the Proceedings of TACAS 2007, LNCS 442
Mechanizing a Process Algebra for Network Protocols
This paper presents the mechanization of a process algebra for Mobile Ad hoc
Networks and Wireless Mesh Networks, and the development of a compositional
framework for proving invariant properties. Mechanizing the core process
algebra in Isabelle/HOL is relatively standard, but its layered structure
necessitates special treatment. The control states of reactive processes, such
as nodes in a network, are modelled by terms of the process algebra. We propose
a technique based on these terms to streamline proofs of inductive invariance.
This is not sufficient, however, to state and prove invariants that relate
states across multiple processes (entire networks). To this end, we propose a
novel compositional technique for lifting global invariants stated at the level
of individual nodes to networks of nodes.Comment: This paper is an extended version of arXiv:1407.3519. The
Isabelle/HOL source files, and a full proof document, are available in the
Archive of Formal Proofs, at http://afp.sourceforge.net/entries/AWN.shtm
Parameterized Synthesis
We study the synthesis problem for distributed architectures with a
parametric number of finite-state components. Parameterized specifications
arise naturally in a synthesis setting, but thus far it was unclear how to
detect realizability and how to perform synthesis in a parameterized setting.
Using a classical result from verification, we show that for a class of
specifications in indexed LTL\X, parameterized synthesis in token ring networks
is equivalent to distributed synthesis in a network consisting of a few copies
of a single process. Adapting a well-known result from distributed synthesis,
we show that the latter problem is undecidable. We describe a semi-decision
procedure for the parameterized synthesis problem in token rings, based on
bounded synthesis. We extend the approach to parameterized synthesis in
token-passing networks with arbitrary topologies, and show applicability on a
simple case study. Finally, we sketch a general framework for parameterized
synthesis based on cutoffs and other parameterized verification techniques.Comment: Extended version of TACAS 2012 paper, 29 page
Structural Invariants for the Verification of Systems with Parameterized Architectures
We consider parameterized concurrent systems consisting of a finite but
unknown number of components, obtained by replicating a given set of finite
state automata. Components communicate by executing atomic interactions whose
participants update their states simultaneously. We introduce an interaction
logic to specify both the type of interactions (e.g.\ rendez-vous, broadcast)
and the topology of the system (e.g.\ pipeline, ring). The logic can be easily
embedded in monadic second order logic of finitely many successors, and is
therefore decidable.
Proving safety properties of such a parameterized system, like deadlock
freedom or mutual exclusion, requires to infer an inductive invariant that
contains all reachable states of all system instances, and no unsafe state. We
present a method to automatically synthesize inductive invariants directly from
the formula describing the interactions, without costly fixed point iterations.
We experimentally prove that this invariant is strong enough to verify safety
properties of a large number of systems including textbook examples (dining
philosophers, synchronization schemes), classical mutual exclusion algorithms,
cache-coherence protocols and self-stabilization algorithms, for an arbitrary
number of components.Comment: preprint; to be published in the proceedings of TACAS2
First-order logic for safety verification of hedge rewriting systems
In this paper we deal with verification of safety properties of hedge rewriting systems and their generalizations. The verification problem is translated to a purely logical problem of finding a finite countermodel for a first-order formula, which is further tackled by a generic finite model finding procedure. We show that the proposed approach is at least as powerful as the methods using regular invariants. At the same time the finite countermodel method is shown to be efficient and applicable to the wide range of systems, including the protocols operating on unranked trees
Structural Invariants for the Verification of Systems with Parameterized Architectures
We consider parameterized concurrent systems consisting of a finite but unknown number of components, obtained by replicating a given set of finite state automata. Components communicate by executing atomic interactions whose participants update their states simultaneously. We introduce an interaction logic to specify both the type of interactions (e.g. rendezvous , broadcast) and the topology of the system (e.g. pipeline, ring). The logic can be easily embedded in monadic second logic of κ ≥ 1 successors (WSκS), and is therefore decidable. Proving safety properties of such a parameterized system, like deadlock freedom or mutual exclusion, requires to infer an inductive invariant that contains all reachable states of all system instances, and no unsafe state. We present a method to automatically synthesize inductive invariants directly from the formula describing the interactions , without costly fixed point iterations. We experimentally prove that this invariant is strong enough to verify many textbook examples, such as dining philosophers, mutual exclusion protocols, and concurrent systems with preemption and priorities, for an arbitrary number of components
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