This paper proves a new lower bound of $ ildeΩ(n^2)$ for read-once parity branching programs on boolean functions, improving upon the previous bound of $ ildeΩ(n^{1.5})$.

The polynomial-time low-degree conjecture, which predicts that low-degree indistinguishability, a uniform null distribution, permutation invariance, and independent resampling imply polynomial-time ha…

This paper connects a generalized notion of tensor rank with multiplicative complexity, enabling control of arithmetic complexity in any constant degree of multilinearity and applications to fine-grai…

The paper studies properties of parity based bit-counting complexity classes B|0|⊕P and B|1|⊕P, proves inclusions and closures, and shows they contain PH and are contained in CH.

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

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…

The paper refutes Steurer's conjecture regarding the existence of large constant-separated sets within families of unit-norm vectors with low average correlation, using high-dimensional expanders to s…

This paper proves DP-completeness of Exact-3-DNP and Exact-4-DNP by reducing 3SAT to these problems.

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…

This paper extends quantum lattice reduction techniques (CDPR) from ideal to module lattices over cyclotomic rings, achieving a constant module reduction factor and providing a rigorous, bounded-preci…

The paper develops an explicit multi-linear polynomial form for binary polynomial optimization problems after eliminating a subset of variables, allowing for characterization of new special classes wi…

This paper shows #P-completeness for several graph counting problems using a new technique.

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…