Related papers: On the linear complexity for multidimensional sequ…
This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original finite space, and constitutes an upper bound for the…
We give a bound, linear in the complexity of the surface, on the asymptotic dimension of the curve complex as well as the capacity dimension of the ending lamination space.
A multicomplex, also known as a twisted chain complex, has an associated spectral sequence via a filtration of its total complex. We give explicit formulas for all the differentials in this spectral sequence.
We define and calculate versions of complexity for free fermionic quantum field theories in 1+1 and 3+1 dimensions, adopting Nielsen's geodesic perspective in the space of circuits. We do this both by discretizing and identifying…
We compute the equivariant fundamental class of the orbit closure of a linear series on the projective line. We also describe the boundary of the orbit closure and how the orbits specialise in one parameter families.
In this paper we introduce a general framework for defining the depth of a sequence with respect to a class of observers. We show that our general framework captures all depth notions introduced in complexity theory so far. We review most…
This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly…
Maximum-length sequences (m-sequences for short) over finite fields are generated by linear feedback shift registers with primitive characteristic polynomials. These sequences have nice mathematical structures and good randomness properties…
We compute the degree complexity of a family of birational mappings of the plane with high order singularities.
If an infinite non-periodic word is uniformly recurrent or is of bounded repetition, then the limit of its periodicity complexity is infinity. Moreover, there are uniformly recurrent words with the periodicity complexity arbitrarily high at…
Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…
We investigate the $k$-error linear complexity over $\mathbb{F}_p$ of binary sequences of length $2p$ with optimal three-level autocorrelation. These balanced sequences are constructed by cyclotomic classes of order four using a method…
Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to…
For a given hyperelliptic curve $C$ over a finite field with Jacobian $J_C$, we consider the hyperelliptic analogue of the congruential generator defined by $W_n=W_{n-1}+D$ for $n\geq 1$ and $D,W_0\in J_C$. We show that curves of genus 2…
In this paper, we define an ordering relation for a set of complex numbers, and research the properties and theorems of the ordering, solve some simple complex inequalities with the ordering.
We describe the "generic" part of the character ring of general linear groups over a finite field in terms of quiver representations.
In this research article, we consider the uniqueness sequences for multidimensional vector-valued Laplace transform. We establish the fundamental relationships between uniqueness sequences for one-dimensional Laplace transform and…
In this article, we study the palindromic length sequences of the ruler sequence and of the period-doubling sequence. We give a precise formula of the palindromic length sequence of the first one and find a lower bound of the limit superior…
We use algebraic geometry to study matrix rigidity, and more generally, the complexity of computing a matrix-vector product, continuing a study initiated by Kumar, et. al. We (i) exhibit many non-obvious equations testing for (border)…