Passive Testing of Timed Systems

This paper presents a methodology to perform passive testing based on invariants for systems that present temporal restrictions. Invariants represent the most relevant expected properties of the implementation under test. Intuitively, an invariant expresses the fact that each time the implementation under test performs a given sequence of actions, then it must exhibit a behavior in a lapse of time reflected in the invariant. In particular, the algorithm presented in this paper are fully implemente

Passive Testing of Stochastic Timed Systems

In this paper we introduce a formal Methodology to perforin passive testing, based on invariants, for systems where the passing of time is represented in probabilistic terms by means of probability distributions functions. In our approach, invariants express the fact that each time the implementation under test performs a given sequence of actions, then it must exhibit a behavior according to the probability distribution functions reflected it? the invariant. We present algorithms to decide the correctness of the proposed invariants with respect to a given specification. Once we know that an invariant is correct, we check whether the execution traces observed from the implementation respect the invariant. In addition to the theoretical framework we have developed a tool., called PASTE, that helps in the automation of our passive testing approach. We have used the tool to obtain experimental results front the application of our methodology

Formal correctness of a passive testing approach for timed systems

In this paper we extend our previous work on passive testing of timed systems to establish a formal criterion to determine correctness of an implementation under test. In our framework, an invariant expresses the fact that if the implementation under test performs a given sequence of actions, then it must exhibit a behavior in a lapse of time reflected in the invariant. In a previous paper we gave an algorithm to establish the correctness of an invariant with respect to a specification. In this paper we continue the work by providing an algorithm to check the correctness of a log, recorded form the implementation under test, with respect to an invariant. We show the soundness of our method by relating it to an implementation relation. In addition to the theoretical framework we have developed a tool, called PASTE, that facilitates the automation of our passive testing approach

Markovian Testing Equivalence and Exponentially Timed Internal Actions

In the theory of testing for Markovian processes developed so far, exponentially timed internal actions are not admitted within processes. When present, these actions cannot be abstracted away, because their execution takes a nonzero amount of time and hence can be observed. On the other hand, they must be carefully taken into account, in order not to equate processes that are distinguishable from a timing viewpoint. In this paper, we recast the definition of Markovian testing equivalence in the framework of a Markovian process calculus including exponentially timed internal actions. Then, we show that the resulting behavioral equivalence is a congruence, has a sound and complete axiomatization, has a modal logic characterization, and can be decided in polynomial time

Runtime Verification Based on Executable Models: On-the-Fly Matching of Timed Traces

Runtime verification is checking whether a system execution satisfies or violates a given correctness property. A procedure that automatically, and typically on the fly, verifies conformance of the system's behavior to the specified property is called a monitor. Nowadays, a variety of formalisms are used to express properties on observed behavior of computer systems, and a lot of methods have been proposed to construct monitors. However, it is a frequent situation when advanced formalisms and methods are not needed, because an executable model of the system is available. The original purpose and structure of the model are out of importance; rather what is required is that the system and its model have similar sets of interfaces. In this case, monitoring is carried out as follows. Two "black boxes", the system and its reference model, are executed in parallel and stimulated with the same input sequences; the monitor dynamically captures their output traces and tries to match them. The main problem is that a model is usually more abstract than the real system, both in terms of functionality and timing. Therefore, trace-to-trace matching is not straightforward and allows the system to produce events in different order or even miss some of them. The paper studies on-the-fly conformance relations for timed systems (i.e., systems whose inputs and outputs are distributed along the time axis). It also suggests a practice-oriented methodology for creating and configuring monitors for timed systems based on executable models. The methodology has been successfully applied to a number of industrial projects of simulation-based hardware verification.Comment: In Proceedings MBT 2013, arXiv:1303.037

Process algebra for performance evaluation

This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resource-sharing systems – like large-scale computers, client–server architectures, networks – can accurately be described using such stochastic specification formalisms. The main emphasis of this paper is the treatment of operational semantics, notions of equivalence, and (sound and complete) axiomatisations of these equivalences for different types of Markovian process algebras, where delays are governed by exponential distributions. Starting from a simple actionless algebra for describing time-homogeneous continuous-time Markov chains, we consider the integration of actions and random delays both as a single entity (like in known Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS). In total we consider four related calculi and investigate their relationship to existing Markovian process algebras. We also briefly indicate how one can profit from the separation of time and actions when incorporating more general, non-Markovian distributions