Unbounded Data Structures Research Articles

Bridging the semantic gap between qualitative and quantitative models of distributed systems

Today’s distributed systems must satisfy bothqualitativeandquantitativeproperties. These properties are analyzed using very different formal frameworks: expressive untimed and non-probabilistic frameworks, such as TLA+ and Hoare/separation logics, for qualitative properties; and timed/probabilistic-automaton-based ones, such as Uppaal and Prism, for quantitative ones. This requires developing two quite different models of the same system, without guarantees of semantic consistency between them. Furthermore, it is very hard or impossible torepresentintrinsic features of distributed object systems—such as unbounded data structures, dynamic object creation, and an unbounded number of messages—using finite automata.In this paper we bridge this semantic gap, overcome the problem of manually having to develop two different models of a system, and solve the representation problem by: (i) defining a transformation from a very general class of distributed systems (a generalization of Agha’s actor model) that maps an untimed non-probabilistic distributed system model suitable for qualitative analysis to a probabilistic timed model suitable for quantitative analysis; and (ii) proving the two models semantically consistent. We formalize our models in rewriting logic, and can therefore use the Maude tool to analyze qualitative properties, and statistical model checking with PVeStA to analyze quantitative properties. We have automated this transformation and integrated it, together with the PVeStA statistical model checker, into theActors2PMaudetool. We illustrate the expressiveness of our framework and our tool’s ease of use by automatically transforming untimed, qualitative models of numerous distributed system designs—including an industrial data store and a state-of-the-art transaction system—into quantitative models to analyze and compare the performance of different designs.

A Framework for the Verification of Parameterized Infinite-state Systems*

We present our tool, developed for the analysis and verification of parameterized infinite-state systems. The framework has been successfully applied in the verification of programs handling unbounded data-structures. In such application domain, being able to infer quantified invariants is a mandatory requirement for successful results. We will describe the techniques implemented in our system and discuss how they contribute in achieving important results in the analysis of parameterized distributed and timed systems, as well as of programs with arrays of unknown length.

Reachability results for timed automata with unbounded data structures

Systems of Data Management Timed Automata (SDMTAs) are networks of communicating timed automata with structures to store messages and functions to manipulate them. We prove the decidability of the reachability problem for a subclass of SDMTAs which assumes an unbounded knowledge, and we analyze the expressiveness of the model and the considered subclass. In particular, while SDMTAs can simulate a Turing machine, and hence the reachability problem is in general undecidable, the subclass for which reachability is decidable, when endowed with a concept of recognized language, accepts languages that are not regular. As an application, we model and analyze a variation of the Yahalom protocol.

Recent Advances in Real-Time Maude

This paper gives an overview of recent advances in Real-Time Maude. Real-Time Maude extends the Maude rewriting logic tool to support formal specification and analysis of object-based real-time systems. It emphasizes ease and generality of specification and supports a spectrum of analysis methods, including symbolic simulation, unbounded and time-bounded reachability analysis, and LTL model checking. Real-Time Maude can be used to specify and analyze many systems that, due to their unbounded features, such as unbounded data structures or dynamic object and message creation, cannot be modeled by current timed/hybrid automaton-based tools. We illustrate this expressiveness and generality by summarizing two case studies: (i) an advanced scheduling algorithm with unbounded queues; and (ii) a state-of-the-art wireless sensor network algorithm. Finally, we give some (often easily checkable) conditions that ensure that Real-Time Maude's analysis methods are complete, also for dense time, for object-based real-time systems. In practice, our result implies that Real-Time Maude's time-bounded search and model checking of LTL time-bounded formulas are complete decision procedures for a large and useful class of non-Zeno real-time systems that fall outside the scope of systems that can be modeled in decidable fragments of hybrid automata, including the sensor network case study discussed in this paper.

Analysis of pointers and structures

Compilers can make good use of knowledge about the shape of data structures and the values that pointers assume during execution. We present results which show how a compiler can automatically determine some of this information. We believe that practical analyses based on this work can be used in compilers for languages that provide linked data structures. The analysis we present obtains useful information about linked data structures. We summarize unbounded data structures by taking advantage of structure present in the original program. The worst-case time bounds for a naive algorithm are high-degree polynomial, but for the expected (sparse) case we have an efficient algorithm. Previous work has addressed time bounds rarely, and efficient algorithms not at all. The quality of information obtained by this analysis appears to be (generally) an improvement on what is obtained by existing techniques. A simple extension obtains aliasing information for entire data structures that previously was obtained only through declarations. Previous work has shown that this information, however obtained, allows worthwhile optimization.

Analyzing Automata with Presburger Arithmetic and Uninterpreted Function Symbols

We study a class of extended automata defined by guarded commands over Presburger arithmetic with uninterpreted functions. On the theoretical side, we show that the bounded reachability problem is decidable in this model. On the practical side, the class is useful for modeling programs with unbounded data structures, and the reachability procedure can be used for symbolic simulation, testing, and verification.

Networks of Processes with Parameterized State Space

In general, the verification of parameterized networks is undecidable. In recent years there has been a lot of research to identify subclasses of parameterized systems for which certain properties are decidable. Some of the results are based on finite abstractions of the parameterized system in order to use model-checking techniques to establish those properties. In a previous paper we presented a method which allows to compute abstractions of a parameterized system modeled in the decidable logic WS1S. These WS1S systems provide an intuitive way to describe parameterized systems of finite state processes. In practice however, the processes in the network themselves are infinite because of unbounded data structures. One source of unboundedness can be the usage of a parameterized data structure. Another typical source may be the presence of structures ranging over subsets of participating processes. E.g., this is the case for group membership or distributed shared memory consistency protocols. In this paper we use deductive methods to deal with such networks where the data structure is parameterized by the number of processes and an extra parameter. We show how to derive an abstract WS1S system which can be subject to algorithmic verification. For illustration of the method we verify the correctness of a distributed shared memory consistency protocol using PVS for the deductive verification part and the tools PAX and SMV for the algorithmic part.

Type-base flow analysis

We present a novel approach to scalable implementation of type-based flow analysis with polymorphic subtyping. Using a new presentation of polymorphic subytping with instantiation constraints, we are able to apply context-free language (CFL) reachability techniques to type-based flow analysis. We develop a CFL-based algorithm for computing flow-information in time O( n ³), where n is the size of the typed program. The algorithm substantially improves upon the best previously known algorithm for flow analysis based on polymorphic subtyping with complexity O( n 8 ). Our technique also yields the first demand-driven algorithm for polymorphic subtype-based flow-computation. It works directly on higher-order programs with structured data of finite type (unbounded data structures are incorporated via finite approximations), supports context-sensitive, global flow summariztion and includes polymorphic recursion.