Development Of Complexity Theory Research Articles

Cognition, Complexity, and Teacher Education

Drawing on recent developments in complexity theory, ecology, and hermeneutics, Brent Davis and Dennis Sumara present an "enactivist" model of cognition and contrast it to popular notions of what it means to learn and think that pervade formal education. They illustrate their model by drawing from their experiences during a year-long study in a small, inner-city elementary school. According to this model, cognition does not occur in individual minds or brains, but in the possibility for shared action. An enactivist theory of cognition, the authors suggest, requires teachers and teacher educators to reconceive the practice of teaching by blurring the lines between knower and known, teacher and student, school and community.

Complexity reduction in a telephone switching system

This paper reviews some of the recent developments in complexity theory as applied to telephone-switching. Some of these techniques are suitable for practical implementation in India.

Logic and programming languages

Logic has been long interested in whether answers to certain questions are computable in principle, since the outcome puts bounds on the possibilities of formalization. More recently, precise comparisons in the efficiency of decision methods have become available through the developments in complexity theory. These, however, are applications to logic, and a big question is whether methods of logic have significance in the other direction for the more applied parts of computability theory. Programming languages offer an obvious opportunity as their syntactic formalization is well advanced; however, the semantical theory can hardly be said to be complete. Though we have many examples, we have still to give wide-ranging mathematical answers to these queries: What is a machine? What is a computable process? How (or how well) does a machine simulate a process? Programs naturally enter in giving descriptions of processes. The definition of the precise meaning of a program then requires us to explain what are the objects of computation (in a way, the statics of the problem) and how they are to be transformed (the dynamics). So far the theories of automata and of nets, though most interesting for dynamics, have formalized only a portion of the field, and there has been perhaps too much concentration on the finite-state and algebraic aspects. It would seem that the understanding of higher-level program features involves us with infinite objects and forces us to pass through several levels of explanation to go from the conceptual ideas to the final simulation on a real machine. These levels can be made mathematically exact if we can find the right abstractions to represent the necessary structures. The experience of many independent workers with the method of data types as lattices (or partial orderings) under an information content ordering, and with their continuous mappings, has demonstrated the flexibility of this approach in providing definitions and proofs, which are clean and without undue dependence on implementations. Nevertheless much remains to be done in showing how abstract conceptualizations can (or cannot) be actualized before we can say we have a unified theory.