Counter Attack on Byzantine Generals: Parameterized Model Checking of Fault-tolerant Distributed Algorithms

We introduce an automated parameterized verification method for fault-tolerant distributed algorithms (FTDA). FTDAs are parameterized by both the number of processes and the assumed maximum number of Byzantine faulty processes. At the center of our technique is a parametric interval abstraction (PIA) where the interval boundaries are arithmetic expressions over parameters. Using PIA for both data abstraction and a new form of counter abstraction, we reduce the parameterized problem to finite-state model checking. We demonstrate the practical feasibility of our method by verifying several variants of the well-known distributed algorithm by Srikanth and Toueg. Our semi-decision procedures are complemented and motivated by an undecidability proof for FTDA verification which holds even in the absence of interprocess communication. To the best of our knowledge, this is the first paper to achieve parameterized automated verification of Byzantine FTDA

Revisiting Reachability in Timed Automata

We revisit a fundamental result in real-time verification, namely that the binary reachability relation between configurations of a given timed automaton is definable in linear arithmetic over the integers and reals. In this paper we give a new and simpler proof of this result, building on the well-known reachability analysis of timed automata involving difference bound matrices. Using this new proof, we give an exponential-space procedure for model checking the reachability fragment of the logic parametric TCTL. Finally we show that the latter problem is NEXPTIME-hard

Quantitative Robustness Analysis of Flat Timed Automata

Whereas formal verification of timed systems has become a very active field of research, the idealized mathematical semantics of timed automata cannot be faithfully implemented. Recently, several works have studied a parametric semantics of timed automata related to implementability: if the specification is met for some positive value of the parameter, then there exists a correct implementation. In addition, the value of the parameter gives lower bounds on sufficient resources for the implementation. In this work, we present a symbolic algorithm for the computation of the parametric reachability set under this semantics for flat timed automata. As a consequence, we can compute the largest value of the parameter for a timed automaton to be safe

Parametric model checking timed automata under non-Zenoness assumption

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Decomposition of Decidable First-Order Logics over Integers and Reals

We tackle the issue of representing infinite sets of real- valued vectors. This paper introduces an operator for combining integer and real sets. Using this operator, we decompose three well-known logics extending Presburger with reals. Our decomposition splits a logic into two parts : one integer, and one decimal (i.e. on the interval [0,1]). We also give a basis for an implementation of our representation

Re-verification of a Lip Synchronization Algorithm using robust reachability

The timed automata formalism is an important model for specifying and analysing real-time systems. Robustness is the correctness of the model in the presence of small drifts on clocks or imprecision in testing guards. A symbolic algorithm for the analysis of the robustness of timed automata has been implemented. In this paper we re-analyse an industrial case lip synchronization protocol using the new robust reachability algorithm.This lip synchronization protocol is an interesting case because timing aspect are crucial for the correctness of the protocol. Several versions of the model are considered, with an ideal video stream, with anchored jitter, and with non-anchored jitter