Three Notes on Distributed Property Testing

In this paper we present distributed property-testing algorithms for graph properties in the CONGEST model, with emphasis on testing subgraph-freeness. Testing a graph property P means distinguishing graphs G = (V,E) having property P from graphs that are epsilon-far from having it, meaning that epsilon|E| edges must be added or removed from G to obtain a graph satisfying P. We present a series of results, including: - Testing H-freeness in O(1/epsilon) rounds, for any constant-sized graph H containing an edge (u,v) such that any cycle in H contain either u or v (or both). This includes all connected graphs over five vertices except K_5. For triangles, we can do even better when epsilon is not too small. - A deterministic CONGEST protocol determining whether a graph contains a given tree as a subgraph in constant time. - For cliques K_s with s >= 5, we show that K_s-freeness can be tested in O(m^(1/2-1/(s-2)) epsilon^(-1/2-1/(s-2))) rounds, where m is the number of edges in the network graph. - We describe a general procedure for converting epsilon-testers with f(D) rounds, where D denotes the diameter of the graph, to work in O((log n)/epsilon)+f((log n)/epsilon) rounds, where n is the number of processors of the network. We then apply this procedure to obtain an epsilon-tester for testing whether a graph is bipartite and testing whether a graph is cycle-free. Moreover, for cycle-freeness, we obtain a corrector of the graph that locally corrects the graph so that the corrected graph is acyclic. Note that, unlike a tester, a corrector needs to mend the graph in many places in the case that the graph is far from having the property. These protocols extend and improve previous results of [Censor-Hillel et al. 2016] and [Fraigniaud et al. 2016]

Oracles for distributed testing

Copyright @ 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.The problem of deciding whether an observed behaviour is acceptable is the oracle problem. When testing from a finite state machine (FSM) it is easy to solve the oracle problem and so it has received relatively little attention for FSMs. However, if the system under test has physically distributed interfaces, called ports, then in distributed testing we observe a local trace at each port and we compare the set of local traces with the set of allowed behaviours (global traces). This paper investigates the oracle problem for deterministic and non-deterministic FSMs and for two alternative definitions of conformance for distributed testing. We show that the oracle problem can be solved in polynomial time for the weaker notion of conformance but is NP-hard for the stronger notion of conformance, even if the FSM is deterministic. However, when testing from a deterministic FSM with controllable input sequences the oracle problem can be solved in polynomial time and similar results hold for nondeterministic FSMs. Thus, in some cases the oracle problem can be efficiently solved when using stronger notion of conformance and where this is not the case we can use the decision procedure for weaker notion of conformance as a sound approximation

A Static Verification Framework for Secure Peer-to-Peer Applications

In this paper we present a static verification framework to support the design and verification of secure peer-to-peer applications. The framework supports the specification, modeling, and analysis of security aspects together with the general characteristics of the system, during early stages of the development life-cycle. The approach avoids security issues to be taken into consideration as a separate layer that is added to the system as an afterthought by the use of security protocols. The main functionality supported by the framework are concerned with the modeling of the system together with its security aspects by using an extension of UML, modeling of abuse cases to represent scenarios of attackers and assist with the identification of properties to be verified, specification of properties to be verified in a graphical template language, verification of the models against the properties, and visualization of the results of the verification process

Uncovering Bugs in Distributed Storage Systems during Testing (not in Production!)

Testing distributed systems is challenging due to multiple sources of nondeterminism. Conventional testing techniques, such as unit, integration and stress testing, are ineffective in preventing serious but subtle bugs from reaching production. Formal techniques, such as TLA+, can only verify high-level specifications of systems at the level of logic-based models, and fall short of checking the actual executable code. In this paper, we present a new methodology for testing distributed systems. Our approach applies advanced systematic testing techniques to thoroughly check that the executable code adheres to its high-level specifications, which significantly improves coverage of important system behaviors. Our methodology has been applied to three distributed storage systems in the Microsoft Azure cloud computing platform. In the process, numerous bugs were identified, reproduced, confirmed and fixed. These bugs required a subtle combination of concurrency and failures, making them extremely difficult to find with conventional testing techniques. An important advantage of our approach is that a bug is uncovered in a small setting and witnessed by a full system trace, which dramatically increases the productivity of debugging

Statistical Model Checking : An Overview

Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with respect to such logics is typically solved by a numerical approach that iteratively computes (or approximates) the exact measure of paths satisfying relevant subformulas; the algorithms themselves depend on the class of systems being analyzed as well as the logic used for specifying the properties. Another approach to solve the model checking problem is to \emph{simulate} the system for finitely many runs, and use \emph{hypothesis testing} to infer whether the samples provide a \emph{statistical} evidence for the satisfaction or violation of the specification. In this short paper, we survey the statistical approach, and outline its main advantages in terms of efficiency, uniformity, and simplicity.Comment: non

COST Action IC 1402 ArVI: Runtime Verification Beyond Monitoring -- Activity Report of Working Group 1

This report presents the activities of the first working group of the COST Action ArVI, Runtime Verification beyond Monitoring. The report aims to provide an overview of some of the major core aspects involved in Runtime Verification. Runtime Verification is the field of research dedicated to the analysis of system executions. It is often seen as a discipline that studies how a system run satisfies or violates correctness properties. The report exposes a taxonomy of Runtime Verification (RV) presenting the terminology involved with the main concepts of the field. The report also develops the concept of instrumentation, the various ways to instrument systems, and the fundamental role of instrumentation in designing an RV framework. We also discuss how RV interplays with other verification techniques such as model-checking, deductive verification, model learning, testing, and runtime assertion checking. Finally, we propose challenges in monitoring quantitative and statistical data beyond detecting property violation