This paper analyzes the computational complexity of evaluating recurrent functions, showing that the complexity depends heavily on how the input offsets are encoded and the structure of the recurrence…

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 generalized Wall-Sun-Sun primes, $WSS(d)$, and uses them to study the weight distributions of specific cyclic codes defined over $ ext{F}_p$ and $ ext{Z}_{p^2}$.

This paper develops a new threshold secret sharing scheme for cellular automata (CA) that enables anonymous reconstruction of the secret CA rules, improving upon previous characterizations using Mutua…

The paper systematically explores a vast design space of cryptographic Boolean networks by formalizing six structural constraints, finding that optimal designs result from sparse, mutually compatible…

This paper proves several properties about Extended Frege proof systems and circuit equivalence.

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

The paper proposes a novel set of combined cellular automaton (CA)-based pseudo-random number generators (PRNGs) that overcome the weak equidistribution issues of existing CA-based PRNGs, achieving ma…

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 characterizes the graph structure, including cycle and path lengths, of Chebyshev permutation polynomials over the ring $\mathbb{Z}_{2^{k_1}3^{k_2}}$, demonstrating strong regularities desp…

This paper completely characterizes cyclic equalizability for two words over any finite alphabet by proving that the words must share the same Parikh vector.

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

The paper introduces a method to efficiently detect 'essential' constraints in Boolean MinCSPs, significantly reducing the search space for solving these problems and providing a dichotomy theorem for…

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…

The paper introduces a novel, efficient mechanism based on permute-and-flip for applying differential privacy to symbolic state trajectories, significantly reducing the computational overhead compared…

The paper investigates the ability of evolutionary computation to discover monotone Boolean functions with high nonlinearity, demonstrating that genetic programming is a highly effective encoding for…

This paper provides a focused, preparatory introduction to sheaves and topoi, establishing the necessary structural background to understand the advanced sheaf-theoretic framework used in cryptographi…

This paper establishes an unconditional barrier for AC0-natural proofs, showing that they cannot prove lower bounds greater than $2^{n^{7/(d-5)}}$ against depth-$d$ circuits.

The paper establishes a unified framework for timed opacity by introducing a universal observation model and defining evolution-based timed opacity, proving its relationship to existing opacity defini…