Abstract.We study decision problems for parameterized verification of a formal model of ad hoc networks. We consider a model in which the network is composed of a set of processes connected to each other through a directed acyclic graph. Vertices of the graph represent states of individual processes. Adjacent vertices represent single-hop neighbors. The processes are finite-state machines with local and synchronized broadcast transitions. Reception of a broadcast is restricted to the immediate neighbors of the sender process. The underlying connectivity graph constrains communication pattern to only one direction. This allows to model typical communication patterns where data is propagated from a set of central nodes to the rest of the network, or alternatively collected in the other direction. For this model, we consider decidability of the control state reachability (coverability) problem, defined over two classes of architectures, namely the class of all acyclic networks (for which we show undecidability) and that of acyclic networks with a bounded depth (for which we show decidability). The decision problems are parameterized both by the size and by the topology of the underlying network.
Abstract. We study decidability and undecidability results for parameterized verification of a formal model of timed Ad Hoc network protocols. The communication topology is represented by a graph and the behavior of each node is represented by a timed automaton communicating with its neighbors via broadcast messages. We consider verification problems formulated in terms of reachability, starting from initial configurations of arbitrary size, of a configuration that contain at least one occurrence of a node in a certain state. We study the problem for dense and discrete time and compare the results with those obtained for (fully connected) networks of timed automata.
We propose a formalism to model database-driven systems, called database manipulating systems (DMS). The actions of a DMS modify the current instance of a relational database by adding new elements into the database, deleting tuples from the relations and adding tuples to the relations. The elements which are modified by an action are chosen by (full) first-order queries. DMS is a highly expressive model and can be thought of as a succinct representation of an infinite state relational transition system, in line with similar models proposed in the literature. We propose monadic second order logic (MSO-FO) to reason about sequences of database instances appearing along a run. Unsurprisingly, the linear-time model checking problem of DMS against MSO-FO is undecidable. Towards decidability, we propose under-approximate model checking of DMS, where the under-approximation parameter is the "bound on recency". In a k-recency-bounded run, only the most recent k elements in the current active domain may be modified by an action. More runs can be verified by increasing the bound on recency. Our main result shows that recency-bounded model checking of DMS against MSO-FO is decidable, by a reduction to the satisfiability problem of MSO over nested words.
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