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 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 introduces the concept of 'large' zeros in linear recurrence sequences and establishes that they either do not exist or are very sparse, which could lead to decidability of the Skolem Probl…

This paper proves that testing the equivalence of finite closure systems specified by implicational and intersection methods is coNP-complete.

This paper develops distributive laws for parallel composition in a rely/guarantee style theory for reasoning about concurrent programs.

The paper provides a unified algebraic framework to determine the formal language expressivity of recurrent neural language models, resolving conflicts in existing literature by linking expressivity t…

This paper establishes mathematical limits of AGI safety, proving structural unverifiability as the core barrier.

This paper establishes a finite combinatorial version of Gödel's incompleteness theorems in Boolean $K$-SAT, resolving assignment correlations and constructing structurally irreducible SAT/UNSAT pairs…

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…

This paper proves that the satisfiability problem of existential Presburger arithmetic extended with divisibility predicates (EPAD) is PP-hard.

This paper studies the decidability and complexity properties of unary three-way and two-way deterministic and nondeterministic two-dimensional automata.

This paper presents Calf, a dependent type theory for cost verification, which synthesizes the physicist's and banker's views on amortized analysis using potential functions and credit annotations.

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…