The paper proves equivalence between big-step and small-step derivations for Horn clauses and transforms Horn clauses into equivalent sets of clauses based on the given derivation strategy.

This paper introduces witness complexity, a measure for the minimum running time of a string's near-shortest description on a universal Turing machine.

This paper introduces an activation hierarchy and proves a Predictor-Impossibility Theorem, showing that no effective predictor family can determine all stage languages. It also establishes a slice th…

The paper provides the first machine-checked universal proof, using ring theory, that value-independence implies identical marginal distributions for arithmetic masking, thereby extending the verifica…

The paper introduces lazy Streett supermartingales and their lexicographic extension to certify almost-sure satisfaction of omega-regular properties with polynomial templates under a broad class of sa…

This book provides a compact, derivation-oriented mathematical primer that connects major families of generative AI models, showing their underlying structural relationships.

This paper proves the conjecture that Local SGD outperforms Mini-batch SGD under bounded second-order heterogeneity for general convex objectives, improving the convergence guarantee and lower bounds.

The paper presents black box algorithms for constructing standard generators and performing membership testing in Suzuki groups, with no false positives.

This paper presents a new nondeterministic finite automaton (NFA) for recognizing repetition-free words over a given alphabet, improving on the previous construction.

The paper investigates the relationship between optimal proof systems and recursive jump operators, showing that while the existence of a jump operator rules out optimality, the converse is provably h…

This paper identifies a technical oversight in Mossel and Peres (2005) theorem on designing Bernoulli factories for multivariable functions and provides a counterexample.

The paper introduces Strong Stochastic Flow Maps (SSFMs), a novel framework that directly learns the strong solution map of additive-noise Stochastic Differential Equations (SDEs), enabling few-step s…

This paper introduces InvWeaver, a neuro-symbolic framework for synthesizing loop invariants in programs with multiple interacting loops.

This paper determines that verifying global parameter identifiability for linear ODE models is an NP-hard problem, establishing a computational complexity boundary for the field.

The paper analyzes the structured CVP distance on the log-unit lattice of cyclotomic fields, significantly reducing the conjectured CDPR factor for the ML-KEM cryptosystem from exponential to sub-poly…