Giorgio Delzanno

Parameterized verification of ad hoc networks

We study decision problems for parameterized verification of a formal model of Ad Hoc Networks with selective broadcast and spontaneous movement. 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 verification problems that can be expressed as reachability of configurations with one node (resp. all nodes) in a certain state from an initial configuration with an arbitrary number of nodes and unknown topology. We draw a complete picture of the decidability boundaries of these problems according to different assumptions on communication graphs, namely static, mobile, and bounded path topology.

On the power of cliques in the parameterized verification of Ad Hoc networks

We study decision problems for parameterized verification of protocols for ad hoc networks. The problem we consider is control state reachability for networks of arbitrary size. We restrict our analysis to topologies that approximate the notion of bounded diameter often used in ad hoc networks for optimizing broadcast communication. We show that restricting to graphs with bounded diameter is not sufficient to make control state reachability decidable, but the problem turns out to be decidable when considering an additionally restricted class of graphs that still includes cliques. Although decidable, the problem is already Ackermann-hard over clique graphs.

On the Decidability Status of Reachability and Coverability in Graph Transformation Systems

We study decidability issues for reachability problems in graph transformation systems, a powerful infinite-state model. For a fixed initial configuration, we consider reachability of an entirely specified configuration and of a configuration that satisfies a given pattern (coverability). The former is a fundamental problem for any computational model, the latter is strictly related to verification of safety properties in which the pattern specifies an infinite set of bad configurations. In this paper we reformulate results obtained, e.g., for context-free graph grammars and concurrency models, such as Petri nets, in the more general setting of graph transformation systems and study new results for classes of models obtained by adding constraints on the form of reduction rules.

On the Complexity of Parameterized Reachability in Reconfigurable Broadcast Networks

We investigate the impact of dynamic topology reconfiguration on the complexity of verification problems for models of protocols with broadcast communication. We first consider reachability of a configuration with a given set of control states and show that parameterized verification is decidable with polynomial time complexity. We then move to richer queries and show how the complexity changes when considering properties with negation or cardinality constraints.

Verification of ad hoc networks with node and communication failures

We investigate the impact of node and communication failures on the decidability and complexity of parametric verification of a formal model of ad hoc networks. We start by considering three possible types of node failures: intermittence, restart, and crash. Then we move to three cases of communication failures: nondeterministic message loss, message loss due to conflicting emissions, and detectable conflicts. Interestingly, we prove that the considered decision problem (reachability of a control state) is decidable for node intermittence and message loss (either nondeterministic or due to conflicts) while it turns out to be undecidable for node restart/crash, and conflict detection.

On the verification of timed ad hoc networks

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.

Parameterized Verification and Model Checking for Distributed Broadcast Protocols

We report on recent research lines related to parameterized verification and model checking applied to formal models of distributed algorithms. Both approaches are based on graph rewriting and graph transformation systems. Case-studies include distributed mutual exclusion protocols like Ricart-Agrawala, routing protocols like link reversal, and distributed consensus protocols like Paxos. Verification algorithms for restricted classes of models exploit finite-state abstractions, symbolic representations based on graph orderings, the theory of well-structured transition systems, and reachability algorithms based on labeling procedures.

Parameterized Verification of Safety Properties in Ad Hoc Network Protocols

We summarize the main results proved in recent work on the parameterized verification of safetyproperties for ad hoc network protocols. We consider a model in which the communication topologyof a network is represented as a graph. Nodes represent states of individual processes. Adjacentnodes represent single-hop neighbors. Processes are finite state automata that communicate via se-lective broadcast messages. Reception of a broadcast is restricted to single-hop neighbors. For thismodel we consider a decision problem that can be expressed as the verification of the existence ofan initial topology in which the execution of the protocol can lead to a configuration with at leastone node in a certain state. The decision problem is parametric both on the size and on the form ofthe communication topology of the initial configurations. We draw a complete picture of the decid-ability and complexity boundaries of this problem according to various assumptions on the possibletopologies.

Reachability analysis of mobile ambients in fragments of AC term rewriting

In this paper we investigate the connection between fragments of associative-commutative Term Rewriting and fragments of Mobile Ambients, a powerful model for mobile and distributed computations. The connection can be used to transfer decidability and undecidability results for important computational properties like reachability from one formalism to the other. Furthermore, it can be viewed as a vehicle to apply tools based on rewriting for the simulation and validation of specifications given in Mobile Ambients.

Graph- versus Vector-Based Analysis of a Consensus Protocol

The Paxos distributed consensus algorithm is a challenging case-study for standard, vector-based model checking techniques. Due to asynchronous communication, exhaustive analysis may generate very large state spaces already for small model instances. In this paper, we show the advantages of graph transformation as an alternative modelling technique. We model Paxos in a rich declarative transformation language, featuring (among other things) nested quantifiers, and we validate our model using the GROOVE model checker, a graph-based tool that exploits isomorphism as a natural way to prune the state space via symmetry reductions. We compare the results with those obtained by the standard model checker Spin on the basis of a vector-based encoding of the algorithm.