Conserved quantities indicate fundamental physical properties of systems, and are therefore eager... more Conserved quantities indicate fundamental physical properties of systems, and are therefore eagerly sought after in science. Conservation of energy and conservation of angular momentum, for example, are two fundamental principles that offer profound insights into the nature of the world we live in. Cellular automata, as models of physical systems, can exhibit conserved functions of relevance to the system under study. Number conservation is a simple example, but far more sophisticated ones can be discovered with appropriate algorithmic techniques. Cellular automata with identical conserved functions are, in some sense, closely related to one another. Thus, conserved functions can be used to classify cellular automata, and to identify connections between seemingly unrelated systems. There are known algorithms to find all conserved energy functions of a given order for a given cellular automaton. They are exponentially slow, but can be made faster by eliminating the trivial conserved ...
We present theorems that can be used for improved efficiency in the calculation of conservation f... more We present theorems that can be used for improved efficiency in the calculation of conservation functions for cellular automata. We report results obtained from implementations of algorithms based on these theorems that show conservation laws for 1-D cellular automata of higher order than any previously known. We introduce the notion of trivial and core conservation functions to distinguish truly new conservation functions from simple extensions of lower-order ones. We then present the complete list of conservation functions up to order 16 for the 256 elementary 1-d binary cellular automata. These include CAs that were not previously known to have nontrivial conservation functions.
This article presents an Ada interface to the Lego MindstormsTM RCX "bri... more This article presents an Ada interface to the Lego MindstormsTM RCX "brick", the core element of a commercial product that emerged from a collaboration between the Lego Corporation and MIT's Media Laboratory. Since its arrival on the market in 1998, it has considerable interest in the computing community: a variety of operating systems and language interfaces are available for it,
Conserved quantities indicate fundamental physical properties of systems, and are therefore eager... more Conserved quantities indicate fundamental physical properties of systems, and are therefore eagerly sought after in science. Conservation of energy and conservation of angular momentum, for example, are two fundamental principles that offer profound insights into the nature of the world we live in. Cellular automata, as models of physical systems, can exhibit conserved functions of relevance to the system under study. Number conservation is a simple example, but far more sophisticated ones can be discovered with appropriate algorithmic techniques. Cellular automata with identical conserved functions are, in some sense, closely related to one another. Thus, conserved functions can be used to classify cellular automata, and to identify connections between seemingly unrelated systems. There are known algorithms to find all conserved energy functions of a given order for a given cellular automaton. They are exponentially slow, but can be made faster by eliminating the trivial conserved ...
We present theorems that can be used for improved efficiency in the calculation of conservation f... more We present theorems that can be used for improved efficiency in the calculation of conservation functions for cellular automata. We report results obtained from implementations of algorithms based on these theorems that show conservation laws for 1-D cellular automata of higher order than any previously known. We introduce the notion of trivial and core conservation functions to distinguish truly new conservation functions from simple extensions of lower-order ones. We then present the complete list of conservation functions up to order 16 for the 256 elementary 1-d binary cellular automata. These include CAs that were not previously known to have nontrivial conservation functions.
This article presents an Ada interface to the Lego MindstormsTM RCX "bri... more This article presents an Ada interface to the Lego MindstormsTM RCX "brick", the core element of a commercial product that emerged from a collaboration between the Lego Corporation and MIT's Media Laboratory. Since its arrival on the market in 1998, it has considerable interest in the computing community: a variety of operating systems and language interfaces are available for it,
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Papers by Barry Fagin