Philipp Niemann

Filmstripping and Unrolling: A Comparison of Verification Approaches for UML and OCL Behavioral Models

Guaranteeing the essential properties of a system early in the design process is an important as well as challenging task. Modeling languages such as the UML allow for a formal description of structure and behavior by employing OCL class invariants and operation pre- and postconditions. This enables the verification of a system description prior to implementation. For this purpose, first approaches have recently been put forward. In particular, solutions relying on the deductive power of constraint solvers are promising. Here, complementary approaches of how to formulate and transform respective UML and OCL verification tasks into corresponding solver tasks have been proposed. However, the resulting methods have not yet been compared to each other. In this contribution, we consider two verification approaches for UML and OCL behavioral models and compare their methods and the respective workflows with each other. By this, a better understanding of the advantages and disadvantages of these verification methods is achieved.

Assisted generation of frame conditions for formal models

Modeling languages such as UML or SysML allow for the validation and verification of the structure and the behavior of designs even in the absence of a specific implementation. However, formal models inherit a severe drawback: Most of them hardly provide a comprehensive and determinate description of transitions from one system state to another. This problem can be addressed by additionally specifying so-called frame conditions. However, only naive “workarounds” based on trivial heuristics or completely relying on a manual creation have been proposed for their generation thus far. In this work, we aim for a solution which neither leaves the burden of generating frame conditions entirely on the designer (avoiding the introduction of another time-consuming and expensive design step) nor is completely automatic (which, due to ambiguities, is not possible anyway). For this purpose, a systematic design methodology for the assisted generation of frame conditions is proposed.

QMDDs: Efficient Quantum Function Representation and Manipulation

Quantum mechanical phenomena such as phase shifts, superposition, and entanglement show promise in use for computation. Suitable technologies for the modeling and design of quantum computers and other information processing techniques that exploit quantum mechanical principles are in the range of vision. Quantum algorithms that significantly speed up the process of solving several important computation problems have been proposed in the past. The most common representation of quantum mechanical phenomena are transformation matrices. However, the transformation matrices grow exponentially with the size of a quantum system and, thus, pose significant challenges for efficient representation and manipulation of quantum functionality. In order to address this problem, first approaches for the representation of quantum systems in terms of decision diagrams have been proposed. One very promising approach is given by Quantum Multiple-Valued Decision Diagrams (QMDDs) which are able to efficiently represent transformation matrices and also inherently support multiple-valued basis states offered by many physical quantum systems. However, the initial proposal of QMDDs was lacking in a formal basis and did not allow, e.g., the change of the variable order-an established core functionality in decision diagrams which is crucial for determining more compact representations. Because of this, the full potential of QMDDs or decision diagrams for quantum functionality in general has not been fully exploited yet. In this paper, we present a refined definition of QMDDs for the general quantum case. Furthermore, we provide significantly improved computational methods for their use and manipulation and show that the resulting representation satisfies important criteria for a decision diagram, i.e., compactness and canonicity. An experimental evaluation confirms the efficiency of QMDDs.

Extracting frame conditions from operation contracts

In behavioral modeling, operation contracts defined by pre- and postconditions describe the effects on model properties (i.e., model elements such as attributes, links, etc.) that are enforced by an operation. However, it is usually omitted which model properties should not be modified. Defining so-called frame conditions can fill this gap. But, thus far, these have to be defined manually - a time-consuming task. In this work, we propose a methodology which aims to support the modeler in the definition of the frame conditions by extracting suggestions based on an automatic analysis of operation contracts provided in OCL. More precisely, the proposed approach performs a structural analysis of pre- and postconditions together with invariants in order to categorize which class and object properties are clearly “variable” or “unaffected” - and which are “ambiguous”, i.e. indeed require a more thorough inspection. The developed concepts are implemented as a prototype and evaluated by means of several example models known from the literature.

Efficient synthesis of quantum circuits implementing clifford group operations

Quantum circuits established themselves as a promising emerging technology and, hence, attracted considerable attention in the domain of computer-aided design. As a result, many approaches for synthesis of corresponding netlists have been proposed in the last decade. However, as the design of quantum circuits faces serious obstacles caused by phenomena such as superposition, entanglement, and phase shifts, automatic synthesis still represents a significant challenge. In this paper, we propose an automatic synthesis approach for quantum circuits that implement Clifford Group operations. These circuits are essential for many quantum applications and cover core aspects of quantum functionality. The proposed approach exploits specific properties of the unitary transformation matrices that are associated to quantum operations. Furthermore, Quantum Multiple-Valued Decision Diagrams (QMDDs) are employed for an efficient representation of these matrices. Experimental results confirm that this enables a compact realization of the respective quantum functionality.

Synthesis of Quantum Circuits for Dedicated Physical Machine Descriptions

Quantum computing has been attracting increasing attention in recent years because of the rapid advancements that have been made in quantum algorithms and quantum system design. Quantum algorithms are implemented with the help of quantum circuits. These circuits are inherently reversible in nature and often contain a sizeable Boolean part that needs to be synthesized. Consequently, a large body of research has focused on the synthesis of corresponding reversible circuits and their mapping to the quantum operations supported by the quantum system. However, reversible circuit synthesis has usually not been performed with any particular target technology in mind, but with respect to an abstract cost metric. When targeting actual physical implementations of the circuits, the adequateness of such an approach is unclear. In this paper, we explicitly target synthesis of quantum circuits at selected quantum technologies described through their Physical Machine Descriptions (PMDs). We extend the state-of-the-art synthesis flow in order to realize quantum circuits based on just the primitive quantum operations supported by the respective PMDs. Using this extended flow, we evaluate whether the established reversible circuit synthesis methods and metrics are still applicable and adequate for PMD-specific implementations.

Frame conditions in symbolic representations of UML/OCL models

Verification and validation of UML/OCL models is a crucial task in the design of complex software/hardware systems. The behavior in those models is expressed in terms of operations with pre- and postconditions. These, however, are often not precise enough to describe what may or may not be modified in a transition between two system states. This frame problem is commonly addressed by providing additional constraints in terms of so-called frame conditions and has already been considered in different research areas in the last decades - except for UML/OCL where corresponding approaches have been investigated only recently. Besides that, several approaches for the verification of the behavior specified in UML/OCL models have been proposed. They rely on a symbolic representation of all possible system states and transitions between them. But here, frame conditions have not been considered yet - a significant drawback for the underlying verification approaches. In this paper, we describe how to integrate frame conditions to symbolic representations. This enables designers to verify the behavior of UML/OCL models while, at the same time, respecting the given frame conditions.

From UML/OCL to Base Models: Transformation Concepts for Generic Validation and Verification

Modeling languages such as UML and OCL find more and more application in the early stages of todays system design. Validation and verification, i.e.i¾źchecking the correctness of the respective models, gains interest. Since these languages offer various description means and a huge set of constructs, existing approaches for this purpose only support a restricted subset of constructs and often focus on dedicated description means as well as verification tasks. To overcome this, we follow the idea of using model transformations to unify different description means to a base model. In the course of these transformation, complex language constructs are expressed by means of a small subset of so-called core elements in order to interface with a wide range of verification engines with complementary strengths and weaknesses. In this paper, we provide a detailed introduction of the proposed base model and its core elements as well as corresponding model transformations.

On the Q in QMDDs: efficient representation of quantum functionality in the QMDD data-structure

The Quantum Multiple-valued Decision Diagram (QMDD) data-structure has been introduced as a means for an efficient representation and manipulation of transformation matrices realized by quantum or reversible logic circuits. A particular challenge is the handling of arbitrary complex numbers as they frequently occur in quantum functionality. These numbers are represented through edge weights which, however, represent a severe obstacle with respect to canonicity, modifiability, and applicability of QMDDs. Previously introduced approaches did not provide a satisfactory solution to these obstacles. In this paper, we propose an improved factorization scheme for complex numbers that ensures a canonical representation while, at the same time, allows for local changes. We demonstrate how the proposed solution can be exploited to improve the data-structure itself (e.g. through variable re-ordering enabled by the advanced modifiability) and how applications such as equivalence checking benefit from that.

Equivalence Checking in Multi-level Quantum Systems

Motivated by its superiority compared to conventional solutions in many applications, quantum computation has intensely been investigated from a theoretical, physical, and design perspective. While these investigations mainly focused on two-level quantum systems, recently also advantages and benefits of higher-level quantum systems became evident. Though this led to several approaches for the representation and realization of quantum functionality in different dimensions, no efficient solution for verifying their equivalence has been proposed yet. In the present paper, we address this problem. We propose a scheme which is capable of verifying the equivalence of two quantum operations regardless of the dimension of their underlying quantum system. The proposed scheme can be incorporated into data-structures such as Quantum Multiple-Valued Decision Diagrams (QMDD) particularly suited for the representation of quantum functionality and, by this, enables an efficient verification. Experiments confirm the efficiency of the proposed approach.