34,944 research outputs found
A probabilistic algorithm to test local algebraic observability in polynomial time
The following questions are often encountered in system and control theory.
Given an algebraic model of a physical process, which variables can be, in
theory, deduced from the input-output behavior of an experiment? How many of
the remaining variables should we assume to be known in order to determine all
the others? These questions are parts of the \emph{local algebraic
observability} problem which is concerned with the existence of a non trivial
Lie subalgebra of the symmetries of the model letting the inputs and the
outputs invariant. We present a \emph{probabilistic seminumerical} algorithm
that proposes a solution to this problem in \emph{polynomial time}. A bound for
the necessary number of arithmetic operations on the rational field is
presented. This bound is polynomial in the \emph{complexity of evaluation} of
the model and in the number of variables. Furthermore, we show that the
\emph{size} of the integers involved in the computations is polynomial in the
number of variables and in the degree of the differential system. Last, we
estimate the probability of success of our algorithm and we present some
benchmarks from our Maple implementation.Comment: 26 pages. A Maple implementation is availabl
Tarski's influence on computer science
The influence of Alfred Tarski on computer science was indirect but
significant in a number of directions and was in certain respects fundamental.
Here surveyed is the work of Tarski on the decision procedure for algebra and
geometry, the method of elimination of quantifiers, the semantics of formal
languages, modeltheoretic preservation theorems, and algebraic logic; various
connections of each with computer science are taken up
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Leveling transparency via situated intermediary learning objectives (SILOs)
When designers set out to create a mathematics learning activity, they have a fair sense of its objectives: students will understand a concept and master relevant procedural skills. In reform-oriented activities, students first engage in concrete situations, wherein they achieve situated, intermediary learning objectives (SILOs), and only then they rearticulate their solutions formally. We define SILOs as heuristics learners devise to accommodate contingencies in an evolving problem space, e.g., monitoring and repairing manipulable structures so that they model with fidelity a source situation. Students achieve SILOs through problem-solving with media, instructors orient toward SILOs via discursive solicitation, and designers articulate SILOs via analyzing implementation data. We describe the emergence of three SILOs in developing the activity Giant Steps for Algebra. Whereas the notion of SILOs emerged spontaneously as a framework to organize a system of practice, i.e. our collaborative design, it aligns with phenomenological theory of knowledge as instrumented action
The foundational legacy of ASL
Abstract. We recall the kernel algebraic specification language ASL and outline its main features in the context of the state of research on algebraic specification at the time it was conceived in the early 1980s. We discuss the most significant new ideas in ASL and the influence they had on subsequent developments in the field and on our own work in particular.
A Survey of Languages for Specifying Dynamics: A Knowledge Engineering Perspective
A number of formal specification languages for knowledge-based systems has been developed. Characteristics for knowledge-based systems are a complex knowledge base and an inference engine which uses this knowledge to solve a given problem. Specification languages for knowledge-based systems have to cover both aspects. They have to provide the means to specify a complex and large amount of knowledge and they have to provide the means to specify the dynamic reasoning behavior of a knowledge-based system. We focus on the second aspect. For this purpose, we survey existing approaches for specifying dynamic behavior in related areas of research. In fact, we have taken approaches for the specification of information systems (Language for Conceptual Modeling and TROLL), approaches for the specification of database updates and logic programming (Transaction Logic and Dynamic Database Logic) and the generic specification framework of abstract state machine
Infusing technology and algebra grant proposal
Includes bibliographical references
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