Embedded systems are targeted for specific applications under constraints on relative timing of their actions. For such systems, use of predesigned reprogrammable components such as microprocessors provides an effective way to reduce system cost by implementing part of the functionality as a program running on the processor. Dedicated hardware is often necessary to achieve requisite timing performance. Analysis of timing constraints is key to determination of an efficient hardware-software implementation. In this paper, we present a methodology to achieve embedded system realizations as co-synthesis of interacting hardware and software components. This co-synthesis is based on synthesis techniques for digital hardware and software compilation under constraints. We present operation-level timing constraints and develop the notion of satisfiability of constraints by a given implementation. Constraint analysis is then used to define hardware and software portions of functionality...

An intelligent mathematical environment must enable symbolic mathematical computation and sophisticated reasoning techniques on the underlying mathematical laws. This paper disscusses different possible levels of interaction between a symbolic calculator based on algebraic algorithms and a theorem prover. A high level of interaction requires a common knowledge representation of the mathematical knowledge of the two systems. We describe a model for such a knowledge base mainly consisting of type and algorithm schemata, algebraic algorithms and theorems.

Adaptive and honest plotting are two techniques to improve the quality of curve and surface visualization packages. Beyond honest plotting, we investigate a number of alternative techniques in order to improve correctness and completeness of 2D and 3D plotting, increase efficiency, and achieve better usability. We refer to these techniques as intelligent plotting as most of them transparently take advantage of the numerical and/or symbolic capabilities available from some mathematical engine in order to provide better and faster graphical displays. We implemented these techniques inside two very different packages: the Graphing Calculator and IZIC which we used as testbeds for our experiments. 1 Introduction Most general purpose Computer Algebra (CA) systems include more and more sophisticated 2D and 3D plotting facilities. Axiom, Macsyma, Maple, and Mathematica, for example, all include options to change graphical parameters such as colors, labels, viewpoint, or painting style. In a...

ion in itself is not the goal: for Whitehead [117]"it is the large generalisation, limited by a happy particularity, which is the fruitful conception." As an example consider the theorem in ring theory, which states that if R is a ring, f(x) is a polynomial over R and f(r) = 0 for every element of r of R then R is commutative. Special cases of this, for example f(x) is x 2 \Gamma x or x 3 \Gamma x, can be given a first order proof in a few lines of symbol manipulation. The usual proof of the general result [20] (which takes a semester's postgraduate course to develop from scratch) is a corollary of other results: we prove that rings satisfying the condition are semi-simple artinian, apply a theorem which shows that all such rings are matrix rings over division rings, and eventually obtain the result by showing that all finite division rings are fields, and hence commutative. This displays von Neumann's architectural qualities: it is "deep" in a way in which the symbol manipulati...

For a class of two-dimensional boundary value problems including diffusion and elasticity problems it is proved that the constants in the corresponding strengthened Cauchy-Buniakowski-Schwarz (C.B.S.) inequality in the cases of h-hierarchical and p-hierarchical finite element discretizations with triangular meshes differ by the factor 0.75. For plane linear elasticity problems and triangulations with right isosceles triangles formulas are presented that show the dependence of the constant in the C.B.S. inequality on the Poisson's ratio. Furthermore, numerically determined bounds of the constant in the C.B.S. inequality are given for three-dimensional elasticity problems discretized by means of tetrahedral elements. Finally, the robustness of iterative solvers for elasticity problems is discussed briefly.

In an earlier report the authors developed an initial value algorithm for one class of exponential sum least squares fitting problems. As a natural extension of that problem the authors in this paper develop an initial value algorithm for a slightly different model in the class of exponential models, f (t) = P p i=1 a i (1 \Gamma exp (\Gammab i t)), which occurs in radiophysics in medicin. A method of generalized interpolation will provide initial values a = [a 1 ; :::; a p ] ; b = [b 1 ; :::; b p ] and these are refined by iterative least squares algorithms. New initial value algorithms are developed. For data equidistant in time, generalized interpolation gives explicit expressions for p 2 and a semi-heuristic solution for p 3. For data not equidistant in time, the numerical derivatives are estimated. The derivative is another exponential sum for which the authors earlier have developed an initial value algorithm for arbitrary number of terms and data not equidistant in time...

Exponential sum models f (t) = P p i=1 a i exp (\Gammab i t) are used frequently: In heat diffusion, diffusion of chemical compounds, time series in medicine, economics and the physical sciences and technology. As the fitting of an exponential sum by e.g. a least squares criterion is difficult, good initial values for the parameters a = [a 1 ; :::; a p ] ; b = [b 1 ; :::; b p ] are needed. Interpolation methods will provide initial values and these are then refined by general least squares algorithms. New initial value algorithms are developed. For data equidistant in time, generalized interpolation gives explicit expressions for p 2, and a numerically solvable one-variable equation for 3 p 4. For p ? 4 we use a heuristic algorithm to get rough initial values. For data not equidistant in time a two point interpolation by a exp (\Gammabt) will generate artificial data points equidistant in time. The least squares refinement is not using the artificial data. Numerical results are p...

this article. The Matlab M-files we used are available from http://www.spelman.edu/~colm.

We describe an approach for formally verifying the linkage between a symbolic state enumeration system and a theorem proving system. This involves the following three stages of proof. Firstly we prove theorems about the correctness of the translation part of the symbolic state system. It interfaces between low level decision diagrams and high level description languages. We ensure that the semantics of a program is preserved in those of its translated form. Secondly we prove linkage theorems: theorems that justify introducing a result from a state enumeration system into a proof system. Finally we combine the translator correctness and linkage theorems. The resulting new linkage theorems convert results to a high level language from the low level decision diagrams that the result was actually proved about in the state enumeration system.They justify importing low-level external verification results into a theorem prover. We use a linkage between the HOL system and a simplified version of the MDG system to illustrate the ideas and consider a small example that integrates two applications from MDG and HOL to illustrate the linkage theorems.

We present a verifiable symbolic de nite integral table lookup: a system which matches a query, comprising a definite integral with parameters and side conditions, against an entry in a verifiable table and uses a call to a library of facts about the reals in the theorem prover PVS to aid in the transformation of the table entry into an answer. Our system is able to obtain correct answers in cases where standard techniques implemented in computer algebra systems fail. We present the full model of such a system as well as a description of our prototype implementation showing the efficacy of such a system: for example, the prototype is able to obtain correct answers in cases where computer algebra systems [CAS] do not. We extend upon Fateman's web-based table by including parametric limits of integration and queries with side conditions.