On the Exact Algorithmic Extraction of Finite Tesselations Through Prime Extraction of Minimal Representative Forms

The identification of repeating patterns in discrete grids is rudimentary within symbolic reasoning, algorithm synthesis and structural optimization across diverse computational domains. Although statistical approaches targeting noisy data can approximately recognize patterns, symbolic analysis utilizing deterministic extraction of periodic structures is underdeveloped. This paper aims to fill this gap by employing a hierarchical algorithm that discovers exact tessellations in finite planar grids, addressing the problem where multiple independent patterns may coexist within a hierarchical structure. The proposed method utilizes composite discovery (dual inspection and breadth-first pruning) for identifying rectangular regions with internal repetition, normalization to a minimal representative form, and prime extraction (selective duplication and hierarchical memoization) to account for irregular dimensions and to achieve efficient computation time. We evaluate scalability on grid sizes from 2x2 to 32x32, showing overlap detection on simple repeating tiles exhibits processing time under 1ms, while complex patterns which require exhaustive search and systematic exploration shows exponential growth. This algorithm provides deterministic behavior for exact, axis-aligned, rectangular tessellations, addressing a critical gap in symbolic grid analysis techniques, applicable to puzzle solving reasoning tasks and identification of exact repeating structures in discrete symbolic domains.

Dynamic Reconfiguration of Robotic Swarms: Coordination and Control for Precise Shape Formation

Coordination of movement and configuration in robotic swarms is a challenging endeavor. Deciding when and where each individual robot must move is a computationally complex problem. The challenge is further exacerbated by difficulties inherent to physical systems, such as measurement error and control dynamics. Thus, how to best determine the optimal path for each robot, when moving from one configuration to another, and how to best perform such determination and effect corresponding motion remains an open problem. In this paper, we show an algorithm for such coordination of robotic swarms. Our methods allow seamless transition from one configuration to another, leveraging geometric formulations that are mapped to the physical domain through appropriate control, localization, and mapping techniques. This paves the way for novel applications of robotic swarms by enabling more sophisticated distributed behaviors.

Cyber Physical Games

We describe a formulation of multi-agents operating within a Cyber-Physical System, resulting in collaborative or adversarial games. We show that the non-determinism inherent in the communication medium between agents and the underlying physical environment gives rise to environment evolution that is a probabilistic function of agents' strategies. We name these emergent properties Cyber Physical Games and study its properties. We present an algorithmic model that determines the most likely system evolution, approximating Cyber Physical Games through Probabilistic Finite State Automata, and evaluate it on collaborative and adversarial versions of the Iterated Boolean Game, comparing theoretical results with simulated ones. Results support the validity of the proposed model, and suggest several required research directions to continue evolving our understanding of Cyber Physical System, as well as how to best design agents that must operate within such environments.

On a Functional Definition of Intelligence

Without an agreed-upon definition of intelligence, asking "is this system intelligent?"" is an untestable question. This lack of consensus hinders research, and public perception, on Artificial Intelligence (AI), particularly since the rise of generative- and large-language models. Most work on precisely capturing what we mean by "intelligence" has come from the fields of philosophy, psychology, and cognitive science. Because these perspectives are intrinsically linked to intelligence as it is demonstrated by natural creatures, we argue such fields cannot, and will not, provide a sufficiently rigorous definition that can be applied to artificial means. Thus, we present an argument for a purely functional, black-box definition of intelligence, distinct from how that intelligence is actually achieved; focusing on the "what", rather than the "how". To achieve this, we first distinguish other related concepts (sentience, sensation, agency, etc.) from the notion of intelligence, particularly identifying how these concepts pertain to artificial intelligent systems. As a result, we achieve a formal definition of intelligence that is conceptually testable from only external observation, that suggests intelligence is a continuous variable. We conclude by identifying challenges that still remain towards quantifiable measurement. This work provides a useful perspective for both the development of AI, and for public perception of the capabilities and risks of AI.