Partitioning Interpolant-Based Verificationfor effective Unbounded Model Checking

Interpolant-based model checking has been shown to be effective on large verification instances, as it efficiently combines automated abstraction and reachability fixed-point checks. On the other hand, methods based on variable quantification have proved their ability to remove free inputs, thus projecting the search space over state variables. In this paper we propose an integrated approach which combines the abstraction power of interpolation with techniques that rely on AIG and/or BDD representations of states, directly supporting variable quantification and fixed-point checks. The underlying idea of this combination is to adopt AIG- or BDD-based quantifications to limit and restrict the search space and the complexity of the interpolant-based approach. The exploited strategies, most of which are individually well-known, are integrated with a new flavor, specifically designed to improve their effectiveness on difficult verification instances. Experimental results, specifically oriented to hard-to-solve verification problems, show the robustness of our approach

Multi-stage languages in hardware design

As circuits increase in size and complexity, hardware description techniques have been trying to adopt features already well- established in software languages. In this paper, we investigate how different hardware description languages implement levels of abstraction over the hardware designs, and we examine how improvements have lead to features like parameterised circuits and generic descriptions, that enable users to efficiently model and reason about large regular-shaped structures and connection patterns. Nonetheless, the ability to include non-functional properties of circuits in the same description is still an open issue. Lately, proposed solutions are looking into meta-functional languages and multi-staging techniques. We examine how hardware description languages can benefit from the capabilities of meta-functional languages, which are able to reason about, and transform the circuit generators as data objects, thus providing a means to access both the functional and non-functional aspects of the generated circuits.peer-reviewe

JINC - A Multi-Threaded Library for Higher-Order Weighted Decision Diagram Manipulation

Ordered Binary Decision Diagrams (OBDDs) have been proven to be an efficient data structure for symbolic algorithms. The efficiency of the symbolic methods de- pends on the underlying OBDD library. Available OBDD libraries are based on the standard concepts and so far only differ in implementation details. This thesis introduces new techniques to increase run-time and space-efficiency of an OBDD library. This thesis introduces the framework of Higher-Order Weighted Decision Diagrams (HOWDDs) to combine the similarities of different OBDD variants. This frame- work pioneers the basis for the new variant Toggling Algebraic Decision Diagrams (TADDs) which has been shown to be a space-efficient HOWDD variant for sym- bolic matrix representation. The concept of HOWDDs has been use to implement the OBDD library JINC. This thesis also analyzes the usage of multi-threading techniques to speed-up OBDD manipulations. A new reordering framework ap- plies the advantages of multi-threading techniques to reordering algorithms. This approach uses an abstraction layer so that the original reordering algorithms are not touched. The challenge that arise from a straight forward algorithm is that the computed-tables and the garbage collection are not as efficient as in a single- threaded environment. We resolve this problem by developing a new multi-operand APPLY algorithm that eliminates the creation of temporary nodes which could occur during computation and thus reduces the need for caching or garbage collection. The HOWDD framework leads to an efficient library design which has been shown to be more efficient than the established OBDD library CUDD. The HOWDD instance TADD reduces the needed number of nodes by factor two compared to ordinary ADDs. The new multi-threading approaches are more efficient than single-threading approaches by several factors. In the case of the new reordering framework the speed- up almost equals the theoretical optimal speed-up. The novel multi-operand APPLY algorithm reduces the memory usage for the n-queens problem by factor 50 which enables the calculation of bigger problem instances compared to the traditional APPLY approach. The new approaches improve the performance and reduce the memory footprint. This leads to the conclusion that applications should be reviewed whether they could benefit from the new multi-threading multi-operand approaches introduced and discussed in this thesis

Doctor of Philosophy

dissertationAbstraction plays an important role in digital design, analysis, and verification, as it allows for the refinement of functions through different levels of conceptualization. This dissertation introduces a new method to compute a symbolic, canonical, word-level abstraction of the function implemented by a combinational logic circuit. This abstraction provides a representation of the function as a polynomial Z = F(A) over the Galois field F2k , expressed over the k-bit input to the circuit, A. This representation is easily utilized for formal verification (equivalence checking) of combinational circuits. The approach to abstraction is based upon concepts from commutative algebra and algebraic geometry, notably the Grobner basis theory. It is shown that the polynomial F(A) can be derived by computing a Grobner basis of the polynomials corresponding to the circuit, using a specific elimination term order based on the circuits topology. However, computing Grobner bases using elimination term orders is infeasible for large circuits. To overcome these limitations, this work introduces an efficient symbolic computation to derive the word-level polynomial. The presented algorithms exploit i) the structure of the circuit, ii) the properties of Grobner bases, iii) characteristics of Galois fields F2k , and iv) modern algorithms from symbolic computation. A custom abstraction tool is designed to efficiently implement the abstraction procedure. While the concept is applicable to any arbitrary combinational logic circuit, it is particularly powerful in verification and equivalence checking of hierarchical, custom designed and structurally dissimilar Galois field arithmetic circuits. In most applications, the field size and the datapath size k in the circuits is very large, up to 1024 bits. The proposed abstraction procedure can exploit the hierarchy of the given Galois field arithmetic circuits. Our experiments show that, using this approach, our tool can abstract and verify Galois field arithmetic circuits up to 1024 bits in size. Contemporary techniques fail to verify these types of circuits beyond 163 bits and cannot abstract a canonical representation beyond 32 bits

Software Product Line

The Software Product Line (SPL) is an emerging methodology for developing software products. Currently, there are two hot issues in the SPL: modelling and the analysis of the SPL. Variability modelling techniques have been developed to assist engineers in dealing with the complications of variability management. The principal goal of modelling variability techniques is to configure a successful software product by managing variability in domain-engineering. In other words, a good method for modelling variability is a prerequisite for a successful SPL. On the other hand, analysis of the SPL aids the extraction of useful information from the SPL and provides a control and planning strategy mechanism for engineers or experts. In addition, the analysis of the SPL provides a clear view for users. Moreover, it ensures the accuracy of the SPL. This book presents new techniques for modelling and new methods for SPL analysis

Assessing and improving the quality of model transformations

Software is pervading our society more and more and is becoming increasingly complex. At the same time, software quality demands remain at the same, high level. Model-driven engineering (MDE) is a software engineering paradigm that aims at dealing with this increasing software complexity and improving productivity and quality. Models play a pivotal role in MDE. The purpose of using models is to raise the level of abstraction at which software is developed to a level where concepts of the domain in which the software has to be applied, i.e., the target domain, can be expressed e??ectively. For that purpose, domain-speci??c languages (DSLs) are employed. A DSL is a language with a narrow focus, i.e., it is aimed at providing abstractions speci??c to the target domain. This makes that the application of models developed using DSLs is typically restricted to describing concepts existing in that target domain. Reuse of models such that they can be applied for di??erent purposes, e.g., analysis and code generation, is one of the challenges that should be solved by applying MDE. Therefore, model transformations are typically applied to transform domain-speci??c models to other (equivalent) models suitable for di??erent purposes. A model transformation is a mapping from a set of source models to a set of target models de??ned as a set of transformation rules. MDE is gradually being adopted by industry. Since MDE is becoming more and more important, model transformations are becoming more prominent as well. Model transformations are in many ways similar to traditional software artifacts. Therefore, they need to adhere to similar quality standards as well. The central research question discoursed in this thesis is therefore as follows. How can the quality of model transformations be assessed and improved, in particular with respect to development and maintenance? Recall that model transformations facilitate reuse of models in a software development process. We have developed a model transformation that enables reuse of analysis models for code generation. The semantic domains of the source and target language of this model transformation are so far apart that straightforward transformation is impossible, i.e., a semantic gap has to be bridged. To deal with model transformations that have to bridge a semantic gap, the semantics of the source and target language as well as possible additional requirements should be well understood. When bridging a semantic gap is not straightforward, we recommend to address a simpli??ed version of the source metamodel ??rst. Finally, the requirements on the transformation may, if possible, be relaxed to enable automated model transformation. Model transformations that need to transform between models in di??erent semantic domains are expected to be more complex than those that merely transform syntax. The complexity of a model transformation has consequences for its quality. Quality, in general, is a subjective concept. Therefore, quality can be de??ned in di??erent ways. We de??ned it in the context of model transformation. A model transformation can either be considered as a transformation de??nition or as the process of transforming a source model to a target model. Accordingly, model transformation quality can be de??ned in two di??erent ways. The quality of the de??nition is referred to as its internal quality. The quality of the process of transforming a source model to a target model is referred to as its external quality. There are also two ways to assess the quality of a model transformation (both internal and external). It can be assessed directly, i.e., by performing measurements on the transformation de??nition, or indirectly, i.e., by performing measurements in the environment of the model transformation. We mainly focused on direct assessment of internal quality. However, we also addressed external quality and indirect assessment. Given this de??nition of quality in the context of model transformations, techniques can be developed to assess it. Software metrics have been proposed for measuring various kinds of software artifacts. However, hardly any research has been performed on applying metrics for assessing the quality of model transformations. For four model transformation formalisms with di??fferent characteristics, viz., for ASF+SDF, ATL, Xtend, and QVTO, we de??ned sets of metrics for measuring model transformations developed with these formalisms. While these metric sets can be used to indicate bad smells in the code of model transformations, they cannot be used for assessing quality yet. A relation has to be established between the metric sets and attributes of model transformation quality. For two of the aforementioned metric sets, viz., the ones for ASF+SDF and for ATL, we conducted an empirical study aiming at establishing such a relation. From these empirical studies we learned what metrics serve as predictors for di??erent quality attributes of model transformations. Metrics can be used to quickly acquire insights into the characteristics of a model transformation. These insights enable increasing the overall quality of model transformations and thereby also their maintainability. To support maintenance, and also development in a traditional software engineering process, visualization techniques are often employed. For model transformations this appears as a feasible approach as well. Currently, however, there are few visualization techniques available tailored towards analyzing model transformations. One of the most time-consuming processes during software maintenance is acquiring understanding of the software. We expect that this holds for model transformations as well. Therefore, we presented two complementary visualization techniques for facilitating model transformation comprehension. The ??rst-technique is aimed at visualizing the dependencies between the components of a model transformation. The second technique is aimed at analyzing the coverage of the source and target metamodels by a model transformation. The development of the metric sets, and in particular the empirical studies, have led to insights considering the development of model transformations. Also, the proposed visualization techniques are aimed at facilitating the development of model transformations. We applied the insights acquired from the development of the metric sets as well as the visualization techniques in the development of a chain of model transformations that bridges a number of semantic gaps. We chose to solve this transformational problem not with one model transformation, but with a number of smaller model transformations. This should lead to smaller transformations, which are more understandable. The language on which the model transformations are de??ned, was subject to evolution. In particular the coverage visualization proved to be bene??cial for the co-evolution of the model transformations. Summarizing, we de??ned quality in the context of model transformations and addressed the necessity for a methodology to assess it. Therefore, we de??ned metric sets and performed empirical studies to validate whether they serve as predictors for model transformation quality. We also proposed a number of visualizations to increase model transformation comprehension. The acquired insights from developing the metric sets and the empirical studies, as well as the visualization tools, proved to be bene??cial for developing model transformations