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.Comment: In Proceedings GRAPHITE 2014, arXiv:1407.767

Model Checking Paxos in Spin

We present a formal model of a distributed consensus algorithm in the executable specification language Promela extended with a new type of guards, called counting guards, needed to implement transitions that depend on majority voting. Our formalization exploits abstractions that follow from reduction theorems applied to the specific case-study. We apply the model checker Spin to automatically validate finite instances of the model and to extract preconditions on the size of quorums used in the election phases of the protocol.Comment: In Proceedings GandALF 2014, arXiv:1408.556

Supporting Domain-Specific State Space Reductions through Local Partial-Order Reduction

Model checkers offer to automatically prove safety and liveness properties of complex concurrent software systems, but they are limited by state space explosion. Partial-Order Reduction (POR) is an effective technique to mitigate this burden. However, applying existing notions of POR requires to verify conditions based on execution paths of unbounded length, a difficult task in general. To enable a more intuitive and still flexible application of POR, we propose local POR (LPOR). LPOR is based on the existing notion of statically computed stubborn sets, but its locality allows to verify conditions in single states rather than over long paths. As a case study, we apply LPOR to message-passing systems. We implement it within the Java Pathfinder model checker using our general Java-based LPOR library. Our experiments show significant reductions achieved by LPOR for model checking representative message-passing protocols and, maybe surprisingly, that LPOR can outperform dynamic POR. © 2011 IEEE

On efficient models for model checking message-passing distributed protocols

The complexity of distributed algorithms, such as state machine replication, motivates the use of formal methods to assist correctness verification. The design of the formal model of an algorithm directly affects the efficiency of the analysis. Therefore, it is desirable that this model does not add "unnecessary" complexity to the analysis. In this paper, we consider a general message-passing (MP) model of distributed algorithms and compare different ways of modeling the message traffic. We prove that the different MP models are equivalent with respect to the common properties of distributed algorithms. Therefore, one can select the model which is best suited for the applied verification technique. We consider MP models which differ regarding whether (1) the event of message delivery can be interleaved with other events and (2) a computation event must consume all messages that have been delivered after the last computation event of the same process. For generalized MP distributed protocols and especially focusing on fault-tolerance, we show that our proposed model (without interleaved delivery events and with relaxed semantics of computation events) is significantly more efficient for explicit state model checking. For example, the model size of the Paxos algorithm is 1/13 th that of existing equivalent MP models. © 2010 Springer-Verlag