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We present optimal depth Boolean circuits (depth O(log n)) for integer division, powering, and multiple products. We also show that these three problems are of equivalent uniform depth and space complexity. In addition, we describe an algorithm for testing divisibility that is optimal for both depth and space. AMS(MOS) subject classification. 68Q 1.(More)
A B S T R A C T An object-oriented application framework provides a generic design within a given domain and a reusable implementation of that design. Frameworks have great potential for reuse, but that potential can only be achieved if the framework can be understood and used effectively by application developers. The complexity of the design and(More)
We present the Interaction Technique Markup Language (InTml), a profile on top of the core X3D that describes 3D interaction techniques (InTs) and hardware platforms. InTml makes 3D InTs easier to understand, compare, and integrate in complete virtual reality (VR) applications. InTml can be used as a front end for any VR toolkit, so InTml documents that(More)
to use journal articles in a variety of ways, limited only as required to insure fair attribution to authors and the journal, and to prohibit use in a competing commercial product. See the journal's World Wide Web site for further details. The Chicago Journal of Theoretical Computer Science is a peer-reviewed scholarly journal in theoretical computer(More)
In order to make frameworks easier to use we need to better understand the difficulties that programmers have with them. The questions that programmers ask give clues to the quality of design, documentation, and programmer practice. We describe the method and results of a study on the Java Swing framework. We collected and analyzed a sample of 300 newsgroup(More)
Deciding whether or not a framework ''ts' an application and provides an appropriate basis for development of the application is one of the key decisions developers make when choosing to use a new framework. In this paper we outline a three step process for helping to determine whether or not a framework is appropriate. The process looks at the limitations,(More)
Software developers often fail to respect the intentions of designers due to missing or ignored documentation of design intent. SCL (Structural Constraint Language) addresses this problem by enabling designers to formalize and confirm compliance with design intent. The designer expresses his intent as constraints on the program model using the SCL language.(More)