This paper traces the historical development of the square-and-multiply algorithm, arguing that while its conceptual foundation dates back to ancient Indian prosody, its formal articulation as a gener…

The paper demonstrates the potential of using LLMs within verifier-guided evolutionary coding agents to develop and improve algorithms, specifically applied to contraction order optimization in tensor…

The paper introduces Grid Programs, a novel, Turing-complete model of computation where programs are two-dimensional arrangements of instructions, fundamentally departing from linear code structures.

This paper introduces a method to automatically determine the optimal learning period ($ au$) for the Random Gradient hyper-heuristic, enabling it to optimally solve Pseudo-Boolean Problems without ma…

The paper empirically and theoretically demonstrates that incorporating Lamarckian and Baldwinian mechanisms into evolutionary algorithms significantly outperforms standard Darwinian evolution, especi…

The paper addresses limitations in the Linear Ordering Problem (LOP) by introducing a novel benchmark suite derived from current economic data and an algorithmic scheme to generate diverse, high-quali…

This paper derives multivariate generating functions to refine the enumeration of Fibonacci polyominoes.

This paper presents methods for ranking and unranking permutations avoiding a pattern of length three in lexicographic or colexicographic order.

The paper introduces CHECKMATE, a novel framework that uses code evolution to automatically generate and optimize algorithms for complex combinatorial problems, outperforming state-of-the-art solvers.

This paper presents an algorithm to generate snake-like polyominoes within a given rectangle and provides exact formulas for the maximal area of such polyominoes for certain dimensions.

The paper introduces and explores Truly Linear FPT (TLFPT), a complexity class defined by $O(n) + f(k)$, demonstrating that it is a strict subset of standard Linear FPT and providing new algorithms fo…

The paper introduces Iteris, an agentic research system, demonstrating its capability to generate numerical evidence, constructions, and proof drafts for open problems in computational mathematics, re…

The paper analyzes a fragment of Higher-Order Datalog, showing that restricting recursion to a linear form shifts its expressive power from time complexity to space complexity, specifically capturing…

The paper proposes constant depth threshold circuits for efficiently detecting epistasis by calculating the relative frequencies of all dataset combinations using specialized hardware architectures.

The paper provides a constructive, intuitionistically valid proof of Rice's Theorem and the Halting Problem undecidability by reducing the problem to the undecidability of Hilbert's Tenth Problem (MRD…

The paper proposes FOAM, an adaptive damping method that stabilizes the Shampoo optimization algorithm by dynamically controlling damping and eigendecomposition frequency, thereby reducing staleness-i…

The paper develops a general framework for dynamic consistent submodular maximization, achieving constant-factor approximations with sublinear consistency for both cardinality and rank-$k$ matroid con…

The paper introduces Hyperparam, a set of lightweight JavaScript libraries designed to enable direct, model-aware querying of unstructured data (like agent traces) within client-side AI applications.

The paper proposes using an auxiliary reconstruction task, specifically one that captures intra-state feature dependencies, to improve the quality of state representations learned by the encoder in ne…

AI-PROPELLER introduces a novel interprocedural code layout optimization system that uses an agentic evolutionary workflow to achieve significant, measurable performance gains in large-scale, real-wor…