An Automata-Theoretic Approach to the Verification of Distributed Algorithms

We introduce an automata-theoretic method for the verification of distributed algorithms running on ring networks. In a distributed algorithm, an arbitrary number of processes cooperate to achieve a common goal (e.g., elect a leader). Processes have unique identifiers (pids) from an infinite, totally ordered domain. An algorithm proceeds in synchronous rounds, each round allowing a process to perform a bounded sequence of actions such as send or receive a pid, store it in some register, and compare register contents wrt. the associated total order. An algorithm is supposed to be correct independently of the number of processes. To specify correctness properties, we introduce a logic that can reason about processes and pids. Referring to leader election, it may say that, at the end of an execution, each process stores the maximum pid in some dedicated register. Since the verification of distributed algorithms is undecidable, we propose an underapproximation technique, which bounds the number of rounds. This is an appealing approach, as the number of rounds needed by a distributed algorithm to conclude is often exponentially smaller than the number of processes. We provide an automata-theoretic solution, reducing model checking to emptiness for alternating two-way automata on words. Overall, we show that round-bounded verification of distributed algorithms over rings is PSPACE-complete.Comment: 26 pages, 6 figure

Distributed Graph Automata and Verification of Distributed Algorithms

Combining ideas from distributed algorithms and alternating automata, we introduce a new class of finite graph automata that recognize precisely the languages of finite graphs definable in monadic second-order logic. By restricting transitions to be nondeterministic or deterministic, we also obtain two strictly weaker variants of our automata for which the emptiness problem is decidable. As an application, we suggest how suitable graph automata might be useful in formal verification of distributed algorithms, using Floyd-Hoare logic.Comment: 26 pages, 6 figures, includes a condensed version of the author's Master's thesis arXiv:1404.6503. (This version of the article (v2) is identical to the previous one (v1), except for minor changes in phrasing.

On Zone-Based Analysis of Duration Probabilistic Automata

We propose an extension of the zone-based algorithmics for analyzing timed automata to handle systems where timing uncertainty is considered as probabilistic rather than set-theoretic. We study duration probabilistic automata (DPA), expressing multiple parallel processes admitting memoryfull continuously-distributed durations. For this model we develop an extension of the zone-based forward reachability algorithm whose successor operator is a density transformer, thus providing a solution to verification and performance evaluation problems concerning acyclic DPA (or the bounded-horizon behavior of cyclic DPA).Comment: In Proceedings INFINITY 2010, arXiv:1010.611

Advanced SPIN Tutorial

Spin [9] is a model checker for the verification of distributed systems software. The tool is freely distributed, and often described as one of the most widely used verification systems. The Advanced Spin Tutorial is a sequel to [7] and is targeted towards intermediate to advanced Spin users

Applying Formal Methods to Networking: Theory, Techniques and Applications

Despite its great importance, modern network infrastructure is remarkable for the lack of rigor in its engineering. The Internet which began as a research experiment was never designed to handle the users and applications it hosts today. The lack of formalization of the Internet architecture meant limited abstractions and modularity, especially for the control and management planes, thus requiring for every new need a new protocol built from scratch. This led to an unwieldy ossified Internet architecture resistant to any attempts at formal verification, and an Internet culture where expediency and pragmatism are favored over formal correctness. Fortunately, recent work in the space of clean slate Internet design---especially, the software defined networking (SDN) paradigm---offers the Internet community another chance to develop the right kind of architecture and abstractions. This has also led to a great resurgence in interest of applying formal methods to specification, verification, and synthesis of networking protocols and applications. In this paper, we present a self-contained tutorial of the formidable amount of work that has been done in formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial

Platform Dependent Verification: On Engineering Verification Tools for 21st Century

The paper overviews recent developments in platform-dependent explicit-state LTL model checking.Comment: In Proceedings PDMC 2011, arXiv:1111.006