Kernel Implements Processes The relationship between the abstract kernel and an individual task is pictured in Figure 4, and is formalized by the theorem AK-IMPLEMENTS-PARALLEL-TASKS. Intuitively, this theorem says that for a given good abstract kernel state AK and abstract kernel oracle ORACLE, the final state reached by task I can equivalently be achieved by running TASK-PROCESSOR on the initial task state, with an oracle constructed by the function CONTROL-ORACLE. The oracle constructed for TASK-PROCESSOR accounts for the precise sequence of delays to task I in the abstract kernel. Task project AK Figure 4: AK Implements Parallel Tasks THEOREM AK-IMPLEMENTS-PARALLEL-TASKS (IMPLIES (AND (GOOD-AK AK) (FINITE-NUMBERP I (LENGTH (AK-PSTATES AK)))) (EQUAL (PROJECT I (AK-PROCESSOR AK ORACLE)) (TASK-PROCESSOR (PROJECT I AK) I (CONTROL-ORACLE I AK ORACLE)))) 6. The Target Machine The target machine TM is a simple von Neumann computer. It is not based on an existing physical machine becaus...

Over the past decade, software architecture research has emerged as the principled study of the overall structure of software systems, especially the relations among subsystems and components. From its roots in qualitative descriptions of useful system organizations, software architecture has matured to encompass broad explorations of notations, tools, and analysis techniques. Whereas initially the research area interpreted software practice, it now offers concrete guidance for complex software design and development. We can understand the evolution and prospects of software architecture research by examining the research paradigms used to establish its results. These are, for the most part, the paradigms of software engineering. We advance our fundamental understanding by posing research questions of several kinds and applying appropriate research techniques, which differ from one type of problem to another, yield correspondingly different kinds of results, and require different methods of validation. Unfortunately, these paradigms are not recognized explicitly and are often not carried out correctly; indeed not all are consistently accepted as valid. This retrospective on a decade-plus of software architecture research examines the maturation of the software architecture research area by tracing the types of research questions and techniques used at various stages. We will see how early qualitative results set the stage for later precision, formality, and automation and how results build up over time. This generates advice to the field and projections about future impact. Keywords: Software architecture, research paradigms 1.

Data Types and Software Validation ," Communications of the ACM, Vol. 21, No. 12, 1978, pp. 1048-1064.

We define algebraic systems called concurrent regular expressions which provide a modular description of languages of Petri nets. Concurrent regular expressions are extension of regular expressions with four operators - interleaving, interleaving closure, synchronous composition and renaming. This alternative characterization of Petri net languages gives us a flexible way of specifying concurrent systems. Concurrent regular expressions are modular and hence easier to use for specification. The proof of equivalence also provides a natural decomposition method for Petri nets. 1 Introduction Formal models proposed for specification and analysis of concurrent systems can be categorized roughly into two groups: algebra based and transition based. The algebra based models specify all possible behaviors of concurrent systems by means of expressions that consist of algebraic operators and primitive behaviors. Examples of such models are path expressions[3], behavior expressions[21] and extend...

This article presents an example of correct circuit design through interactive transformation. Interactive transformation differs from traditional hardware design transformation frameworks in that it focuses on the issue of finding suitable hardware architecture for the specified system and the issue of architecture correctness. The transformation framework divides every transformation in designs into two steps. The first step is to find a proper architecture implementation. Although the framework does not guarantee existence of such an implementation, nor its discovery, it does provide a characterization of architectural implementation so that the question "is this a correct implementation?" can be answered by equational rewriting. The framework allows a correct architecture implementation to be automatically incorporated with control descriptions to obtain a new system description. The significance of this transformation framework lies in the fact that it requires simpler mechanism o...

this paper, we propose an algebraic model called concurrent regular expressions for modeling of concurrent systems. These expressions can be converted automatically to Petri nets, and thus all analysis techniques that are applicable to Petri nets can be used. Conversely, any Petri net can be converted to a concurrent regular expression providing further insights into its language

One of the main reasons why constructing deductive proofs that programs satisfy their specifications can be very expensive in practice is the absence of reusable problem domain theories. These theories contain functions that define relevant concepts in the application area of the program, and they contain properties that are deduced from these definitions. Presently, the cost of proving programs is highly inflated by the fact that we usually have to build a new problem domain theory for each new application. If we can develop reusable problem domain theories, the cost of specifying and proving programs in actual practice can be greatly reduced. The development of these theories also would have significant benefits for other aspects of computing science. This paper discusses the composition of problem domain theories and their relation to program specification and proof. REUSABLE PROBLEM DOMAIN THEORIES 2 Acknowledgements During its eight year existence, well over 50 people have contr...

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