Notion Of Refinement Research Articles

Fault-based refinement-testing for CSP

The process algebra CSP has been studied as a notation for model-based testing. Theoretical and practical work has been developed using its trace and failure semantics, and their refinement notions as conformance relations. Two sets of tests have been defined and proved to be exhaustive, in the sense that they can identify any SUT that is non-conforming with respect to the relevant refinement relation. However, these sets are usually infinite, and in this case, it is obviously not possible to apply them to verify the conformity of an SUT. Some classical selection criteria based on models have been studied. In this paper, we propose a procedure for online test generation for selection of finite test sets for traces refinement from CSP models. It is based on the notion of fault domains, focusing on the set of faulty implementations of interest. We investigate scenarios where the verdict of a test campaign can be reached after a finite number of test executions. We illustrate the usage of the procedure with some case studies.

MEDIA REPRESENTATIONS of the NOUVEAUX RICHES and the CULTURAL CONSTITUTION of the GLOBAL MIDDLE CLASS

The article offers a distinctive account of how the nouveaux riches serve as an anchor for a range of upper- middle- class ambivalences and anxieties associated with transformations of capitalism and shifting global hierarchies. Reflecting the long- term association of middle- class symbolic boundaries with notions of refinement and respectability, it examines how the discourse of civility shapes how the nouveaux riches are represented to the upper middle class, identifying a number of recurrent media frames and narrative tropes related to vulgarity, civility, and order. The author argues that these representations play a central role in the reproduction of the Western professional middle class, and in the cultural constitution of a global middle class — professional, affluent, urban, and affiliated by an aesthetic regime of civility that transcends national borders. The findings underline the significance of representations of the new super- rich as devices through which the media accomplish the global circulation of an upper- middle- class repertoire of cultural capital, which is used both to police shifting class boundaries and to establish a legitimate preserve for univorous snobbishness.

Correct and Efficient Antichain Algorithms for Refinement Checking

The notion of refinement plays an important role in software engineering. It is the basis of a stepwise development methodology in which the correctness of a system can be established by proving, or computing, that a system refines its specification. Wang et al. describe algorithms based on antichains for efficiently deciding trace refinement, stable failures refinement and failures-divergences refinement. We identify several issues pertaining to the soundness and performance in these algorithms and propose new, correct, antichain-based algorithms. Using a number of experiments we show that our algorithms outperform the original ones in terms of running time and memory usage. Furthermore, we show that additional run time improvements can be obtained by applying divergence-preserving branching bisimulation minimisation.

Refinement Modal Logic Based on Finite Approximation of Covariant-Contravariant Refinement

The notion of covariant-contravariant refinement (CC-refinement) is a generalization of the notions of bisimulation and refinement, which is coinductively defined to describe behavior relation, i.e., two related processes are required to be always able to provide matched transitions each other. The notion of CC-n-refinement, where n is a natural number, presented in this paper, finitely approximates the notion of CC-refinement through weakening the above-mentioned requirement. A process is said to CC-n-refine another process whenever they can, within n-steps, match the transitions each other, and a CC-n-refinement relation may be considered to be a CC-refinement relation if n is big enough. Based on this kind of finite approximation, this paper presents CC-n-refinement modal logic (nCCRML) obtained from the modal system K by adding CC-n-refinement quantifiers, establishes an axiom system for nCCRML, and explores some important properties of this axiom system: soundness, completeness, and decidability. CC-n-refinement quantifiers can be used to formalize some interesting problems in the field of formal method.

The Extension of Bisimulation Quantified Modal Logic Based on Covariant-Contravariant Refinement

The notion of covariant-contravariant refinement (CC-refinement, for short) is a generalization of the notions of bisimulation and refinement. This paper interprets semantically a CC-refinement as bisimulation plus model restriction, that is, a CC-refinement model of a given model may be obtained from one bisimilar duplicate of this model by adding some transitions labelled by covariant actions and removing some transitions labelled by contravariant actions. By using certain proposition letter to witness a contravariant action, the standard bisimulation quantified modal logic is able to capture the characterization of this action, however, this fails for covariant actions. This paper, based on the notion of CC-refinement, introduces an extended bisimulation quantified modal logic with the universal modality (EBQML), describes syntactically CC-refinement quantification as the extended bisimulation quantification plus relativization, and establishes a translation from the language of CC-refinement modal μ-calculus to the language of EBQML such that every CC-refinement modal μ-formula is equivalent to its translation. The language of EBQML may be considered as a specification language for describing the properties of a system referring to reactive and generative actions, which are represented respectively by covariant and contravariant actions, and may be used to formalize some interesting problems in the field of formal methods.

Ordering Strict Partial Orders to Model Behavioral Refinement

Software is now ubiquitous and involved in complex interactions with the human users and the physical world in so-called cyber-physical systems where the management of time is a major issue. Separation of concerns is a key asset in the development of these ever more complex systems. Two different kinds of separation exist: a first one corresponds to the different steps in a development leading from the abstract requirements to the system implementation and is qualified as vertical. It matches the commonly used notion of refinement. A second one corresponds to the various components in the system architecture at a given level of refinement and is called horizontal. Refinement has been studied thoroughly for the data, functional and concurrency concerns while our work focuses on the time modeling concern. This contribution aims at providing a formal construct for the verification of refinement in time models, through the definition of an order between strict partial orders used to relate the different instants in asynchronous systems. This relation allows the designer at the concrete level to distinguish events that are coincident at the abstract level while preserving the properties assessed at the abstract level. This work has been conducted using the proof assistant Agda and is connected to a previous work on the asynchronous language CCSL, which has also been modelled using the same tool.

Fast predictive multi-fidelity prediction with models of quantized fidelity levels

In this paper, we introduce a novel approach for the construction of multi-fidelity surrogate models with “discrete” fidelity levels. The notion of a discrete level of fidelity is in contrast to a mathematical model, for which the notion of refinement towards a high-fidelity model is relevant to sending a discretization parameter toward zero in a continuous way. Our notion of discrete fidelity levels encompasses cases for which there is no notion of convergence in terms of a fidelity parameter that can be sent to zero or infinity. The particular choice of how levels of fidelity are defined in this framework paves the way for using models that may have no apparent physical or mathematical relationship to the target high-fidelity model. However, our approach requires that models can produce results with a common set of parameters in the target model. Hence, fidelity level in this work is not directly representative of the degree of similarity of a low-fidelity model to a target high-fidelity model. In particular, we show that our approach is applicable to competitive ecological systems with different numbers of species, discrete-state Markov chains with a different number of states, polymer networks with a different number of connections, and nano-particle plasmonic arrays with a different number of scatterers. The results of this study demonstrate that our procedure boasts computational efficiency and accuracy for a wide variety of models and engineering systems.

Basic behavioral models for software product lines: Revisited

In Beohar et al. (2016) [9] , we established an expressiveness hierarchy and studied the notions of refinement and testing for three fundamental behavioral models for software product lines. These models were featured transition systems, product line labeled transition systems, and modal transition systems. It turns out that our definition of product line labeled transition systems is more restrictive than the one introduced by Gruler, Leucker, and Scheidemann. Adopting the original and more liberal notion changes the expressiveness results, as we demonstrate in this paper. Namely, we show that the original notion of product line labeled transition systems and featured transition systems are equally expressive. As an additional result, we show that there are featured transition systems for which the size of the corresponding product line labeled transition system, resulting from any sound encoding, is exponentially larger than the size of the original model. Furthermore, we show that each product line labeled transition system can be encoded into a featured transition system, such that the size of featured transition system is linear in terms of the size of the corresponding model. To summarize, featured transition systems are equally expressive as, but exponentially more succinct than, product line labeled transition systems. • An encoding from FTSs into PL-LTSs is proposed. • Result of comparing expressive power shows FTSs and PL-LTSs are equally expressive. • Succinctness analysis shows FTSs are exponentially more succinct than PL-LTSs.

Refined cyclic sieving on words for the major index statistic

Reiner–Stanton–White (Reiner et al., 2004) defined the cyclic sieving phenomenon (CSP) associated to a finite cyclic group action and a polynomial. A key example arises from the length generating function for minimal length coset representatives of a parabolic quotient of a finite Coxeter group. In type A, this result can be phrased in terms of the natural cyclic action on words of fixed content.There is a natural notion of refinement for many CSP’s. We formulate and prove a refinement, with respect to the major index statistic, of this CSP on words of fixed content by also fixing the cyclic descent type. The argument presented is completely different from Reiner–Stanton–White’s representation-theoretic approach. It is combinatorial and largely, though not entirely, bijective in a sense we make precise with a “universal” sieving statistic on words, flex.A building block of our argument involves cyclic sieving for shifted subset sums, which also appeared in Reiner–Stanton–White. We give an alternate, largely bijective proof of a refinement of this result by extending some ideas of Wagon–Wilf (Wagon and Wilf, 1994).

Belief Update within Propositional Fragments

Belief change within the framework of fragments of propositional logic is one of the main and recent challenges in the knowledge representation research area. While previous research works focused on belief revision, belief merging, and belief contraction, the problem of belief update within fragments of classical logic has not been addressed so far. In the context of revision, it has been proposed to refine existing operators so that they operate within propositional fragments, and that the result of revision remains in the fragment under consideration. This approach is not restricted to the Horn fragment but also applicable to other propositional fragments like Krom and affine fragments. We generalize this notion of refinement to any belief change operator. We then focus on a specific belief change operation, namely belief update. We investigate the behavior of the refined update operators with respect to satisfaction of the KM postulates and highlight differences between revision and update in this context.

Securing a compiler transformation

A compiler optimization may be correct and yet be insecure. This work focuses on the common optimization that removes dead (i.e., useless) store instructions from a program. This operation may introduce new information leaks, weakening security while preserving functional equivalence. This work presents a polynomial-time algorithm for securely removing dead stores. The algorithm is necessarily approximate, as it is shown that determining whether new leaks have been introduced by dead store removal is undecidable in general. The algorithm uses taint and control-flow information to determine whether a dead store may be removed without introducing a new information leak. A notion of secure refinement is used to establish the security preservation properties of other compiler transformations. The important static single assignment optimization is, however, shown to be inherently insecure.

Reasoning about firewall policies through refinement and composition

An algebra is proposed for constructing and reasoning about anomaly-free firewall policies. Based on the notion of refinement as safe replacement, the algebra provides operators for sequential composition, union and intersection of policies. The algebra is used to specify and reason about iptables firewall policy configurations. A prototype policy management toolkit has been implemented.

Using Coq to write fast and correct Haskell

Correctness and performance are often at odds in the field of systems engineering, either because correct programs are too costly to write or impractical to execute, or because well-performing code involves so many tricks of the trade that formal analysis is unable to isolate the main properties of the algorithm. As a prime example of this tension, Coq is an established proof environment that allows writing correct, dependently-typed code, but it has been criticized for exorbitant development times, forcing the developer to choose between optimal code or tractable proofs. On the other side of the divide, Haskell has proven itself to be a capable, well-typed programming environment, yet easy-to-read, straightforward code must all too often be replaced by highly optimized variants that obscure the author's original intention. This paper builds on the existing Fiat refinement framework to bridge this divide, demonstrating how to derive a correct-by-construction implementation that meets (or exceeds) the performance characteristics of highly optimized Haskell, starting from a high-level Coq specification. To achieve this goal, we extend Fiat with a stateful notion of refinement of abstract data types and add support for extracting stateful code via a free monad equipped with an algebra of heap-manipulating operations. As a case study, we reimplement a subset of the popular bytestring library, with little to no loss of performance, while retaining a high guarantee of program correctness.

Control refinement for discrete-time descriptor systems: a behavioural approach via simulation relations

The analysis of industrial processes, modelled as descriptor systems, is often computationally hard due to the presence of both algebraic couplings and difference equations of high order. In this paper, we introduce a control refinement notion for these descriptor systems that enables analysis and control design over related reduced-order systems. Utilising the behavioural framework, we extend upon the standard hierarchical control refinement for ordinary systems and allow for algebraic couplings inherent to descriptor systems.

Metabolic systems biology: a brief primer.

In the early to mid-20th century, reductionism as a concept in biology was challenged by key thinkers, including Ludwig von Bertalanffy. He proposed that living organisms were specific examples of complex systems and, as such, they should display characteristics including hierarchical organisation and emergent behaviour. Yet the true study of complete biological systems (for example, metabolism) was not possible until technological advances that occurred 60years later. Technology now exists that permits the measurement of complete levels of the biological hierarchy, for example the genome and transcriptome. The complexity and scale of these data require computational models for their interpretation. The combination of these - systems thinking, high-dimensional data and computation - defines systems biology, typically accompanied by some notion of iterative model refinement. Only sequencing-based technologies, however, offer full coverage. Other 'omics' platforms trade coverage for sensitivity, although the densely connected nature of biological networks suggests that full coverage may not be necessary. Systems biology models are often characterised as either 'bottom-up' (mechanistic) or 'top-down' (statistical). This distinction can mislead, as all models rely on data and all are, to some degree, 'middle-out'. Systems biology has matured as a discipline, and its methods are commonplace in many laboratories. However, many challenges remain, especially those related to large-scale data integration.

Relating trace refinement and linearizability

Abstract In the late 1980’s, Back extended the notion of stepwise refinement of sequential systems to concurrent systems. By doing so he provided a definition of what it means for a concurrent system to be correct with respect to an abstract (potentially sequential) specification. This notion of refinement, referred to as trace refinement , was also independently proposed by Abadi and Lamport and has found widespread acceptance and application within the refinement community. Around the same time as Back’s work, Herlihy and Wing proposed linearizability as the correctness notion for concurrent objects. Linearizability has also found widespread acceptance being regarded as the standard notion of correctness for concurrent objects in the concurrent-algorithms community. In this paper, we provide a formal link between trace refinement and linearizability. This allows us to compare the two correctness conditions. Our comparisons show that trace refinement implies linearizability, but that linearizability does not imply trace refinement in general. However, linearizability does imply trace refinement under certain conditions. These conditions relate to (i) the fact that trace refinement can be used to prove both safety and liveness properties, whereas linearizability can only be used to prove safety properties, and (ii) the fact that trace refinement depends on the identification of when operations in the implementation are observed to occur. We discuss the consequences of these differences in the context of verifying concurrent objects.

Big Data Refinement

"Big data" has become a major area of research and associated funding, as well as a focus of utopian thinking. In the still growing research community, one of the favourite optimistic analogies for data processing is that of the oil refinery, extracting the essence out of the raw data. Pessimists look for their imagery to the other end of the petrol cycle, and talk about the "data exhausts" of our society. Obviously, the refinement community knows how to do "refining". This paper explores the extent to which notions of refinement and data in the formal methods community relate to the core concepts in "big data". In particular, can the data refinement paradigm can be used to explain aspects of big data processing?

A logic for n-dimensional hierarchical refinement

Hierarchical transition systems provide a popular mathematical structure to represent state-based software applications in which different layers of abstraction are represented by inter-related state machines. The decomposition of high level states into inner sub-states, and of their transitions into inner sub-transitions is common refinement procedure adopted in a number of specification formalisms. This paper introduces a hybrid modal logic for k-layered transition systems, its first-order standard translation, a notion of bisimulation, and a modal invariance result. Layered and hierarchical notions of refinement are also discussed in this setting.

ASM-based formal design of an adaptivity component for a Cloud system

AbstractThe request of formal methods for the specification and analysis of distributed systems is nowadays increasing, especially when considering the development of Cloud systems and Web applications. This is due to the fact that modeling languages currently used in these areas have informal definitions and ambiguous semantics, and therefore their use may be unreliable. Thanks to their mathematical foundation, formal methods can guarantee rigorous system design, leading to precise models where requirements can be validated and properties can be assured, already at the early stages of the system development. In this paper, we present a rigorous engineering process for distributed systems, based on the Abstract State Machines (ASM) formal method. We rely on the foundational notions of ASM ground model and model refinement to obtain a precise model for a client-server application for Cloud systems. This application has been proposed to tackle the problem of making Cloud services usable to different end-devices by adapting on-the-fly the content coming from the Cloud to the different devices contexts. The ASM-based modeling process is supported by a number of validation and verification activities that have been exploited on the component under development to guarantee consistency, correctness, and reliability properties.

Log-based Evaluation of Label Splits for Process Models

Process mining techniques aim to extract insights in processes from event logs. One of the challenges in process mining is identifying interesting and meaningful event labels that contribute to a better understanding of the process. Our application area is mining data from smart homes for elderly, where the ultimate goal is to signal deviations from usual behavior and provide timely recommendations in order to extend the period of independent living. Extracting individual process models showing user behavior is an important instrument in achieving this goal. However, the interpretation of sensor data at an appropriate abstraction level is not straightforward. For example, a motion sensor in a bedroom can be triggered by tossing and turning in bed or by getting up. We try to derive the actual activity depending on the context (time, previous events, etc.). In this paper we introduce the notion of label refinements, which links more abstract event descriptions with their more refined counterparts. We present a statistical evaluation method to determine the usefulness of a label refinement for a given event log from a process perspective. Based on data from smart homes, we show how our statistical evaluation method for label refinements can be used in practice. Our method was able to select two label refinements out of a set of candidate label refinements that both had a positive effect on model precision.