Title: Kiskentamowin Apachichikan: A New Paradigm in Computational Models Author: Michael Waynne Lawrenchuk Email: ORCID iD: 0000-0003-0403-5721
Research Statement: Exploration of Kiskentamowin Apachichikan — A Novel Multidimensional Computational Model
Introduction
Traditional computational models, such as Turing machines, have set the foundation for our understanding of computation and complexity theory. While powerful and universal, these one-dimensional models offer a limited view of the computational landscape. Kiskentamowin Apachichikan, a Cree term for "knowledge tool," introduces a groundbreaking shift from the conventional one-dimensional tape to an infinitely expansive, multi-directional grid. This research project aims to define, explore, and understand this innovative computational model, thereby challenging established paradigms and expanding the scope of computational theory.
Objectives
To formally define the Kiskentamowin Apachichikan model, including its grid, cells, states, head, symbols, transitions, and operational rules. To establish axioms that serve as the foundational principles of Kiskentamowin Apachichikan, including initialization, determinism, and halting conditions. To evaluate the computational power of Kiskentamowin Apachichikan in comparison to traditional Turing machines. To investigate novel features like grid compression to a singular point or specific patterns and shapes. To explore practical applications where Kiskentamowin Apachichikan may offer unique advantages, such as in pattern recognition or multi-dimensional problem-solving. Methodology Formalization: Develop a rigorous mathematical framework to define all elements of the Kiskentamowin Apachichikan model. Simulation and Implementation: Utilize software tools to simulate the model's operations and test its functional capabilities. Analytical Comparison: Use existing computational theories to evaluate the computational power of Kiskentamowin Apachichikan against that of traditional Turing machines. Case Studies: Employ a series of problems solvable through the Kiskentamowin Apachichikan model to demonstrate its practical utility.
Expected Contributions Introduction of Kiskentamowin Apachichikan as a groundbreaking computational model that extends the principles of Turing machines into multidimensional realms. Insights into the computational advantages and limitations of employing a multi-directional grid over a one-dimensional tape. Conceptual exploration of 'grid compression' and its theoretical and practical implications. Conclusion
Kiskentamowin Apachichikan invites a novel and enriched dialogue on computational theory by integrating multidimensional complexities. It opens the door to alternative forms of knowledge representation, acknowledging the diverse avenues through which understanding can be attained. Through this research, we aim to establish Kiskentamowin Apachichikan as a formidable contribution to the field of computational theory, offering new insights into the very nature of computation and problem-solving.