arXiv:2603.13854v2 Announce Type: replace-cross Abstract: We introduce power term polynomial algebra, a representation language for Boolean formulae designed to bridge conjunctive normal form (CNF) and algebraic normal form (ANF). The language is motivated by the tiling mismatch between these representations: direct CNF ANF conversion may cause exponential blowup unless formulas are decomposed into smaller fragments, typically through auxiliary variables and side constraints. In contrast, our framework addresses this mismatch within the representation itself, compactly encoding structured fami
This paper represents continued academic exploration into fundamental computational logic, a foundational area for AI, indicating ongoing efforts to optimize underlying algorithms. The persistent challenge of efficiently converting between Boolean representations motivates this research.
Improved Boolean logic representations can lead to more efficient and scalable AI algorithms, especially in areas like verification, constraint solving, and potentially neural network architectures. This could accelerate progress in advanced AI systems.
The development of power term polynomial algebra could offer a more compact and efficient method for logical operations, potentially overcoming current limitations in formula conversion and complexity. This would primarily impact fundamental AI research and algorithm design.
- · AI algorithm developers
- · Formal verification sector
- · Academic AI researchers
- · Inefficient logical solvers
- · Current state-of-the-art Boolean representation methods
More efficient tools for Boolean formula manipulation become available to researchers.
This could lead to breakthroughs in logical inference and automated reasoning within AI systems.
These advancements might enable the creation of more robust and verifiable complex AI agents and systems.
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Read at arXiv cs.AI