Information Processing Letters最新文献

Recently, a class of quaternary sequences with period pq, where p and q are two distinct odd primes introduced by Zhang et al. were proved to possess high linear complexity and 4-adic complexity. In this paper, we determine the autocorrelation distribution of this class of quaternary sequence. Our results indicate that the studied quaternary sequence are weak with respect to the correlation property.

The qCCS model proposed by Feng et al. provides a powerful framework to describe and reason about quantum communication systems that could be entangled with the environment. However, they only studied weak bisimulation semantics. In this paper we propose a new branching bisimilarity for qCCS and show that it is a congruence. The new bisimilarity is based on the concept of ϵ-tree and preserves the branching structure of concurrent processes where both quantum and classical components are allowed. Furthermore, we present a polynomial time equivalence checking algorithm for the ground version of our branching bisimilarity.

In this paper we consider two vertex deletion problems. In the Block Vertex Deletion problem, the input is a graph G and an integer k, and the goal is to decide whether there is a set of at most k vertices whose removal from G result in a block graph (a graph in which every biconnected component is a clique). In the Pathwidth One Vertex Deletion problem, the input is a graph G and an integer k, and the goal is to decide whether there is a set of at most k vertices whose removal from G result in a graph with pathwidth at most one. We give a kernel for Block Vertex Deletion with $O\left(k^3\right)$ vertices and a kernel for Pathwidth One Vertex Deletion with $O\left(k^2\right)$ vertices. Our results improve the previous $O\left(k^4\right)$-vertex kernel for Block Vertex Deletion (Agrawal et al., 2016 [1]) and the $O\left(k^3\right)$-vertex kernel for Pathwidth One Vertex Deletion (Cygan et al., 2012 [3]).

In the Longest $(s,t)$-Detour problem, we look for an $(s,t)$-path that is at least k vertices longer than a shortest one. We study the parameterized complexity of Longest $(s,t)$-Detour when parameterized by k: this falls into the research paradigm of ‘parameterization above guarantee’. Whereas the problem is known to be fixed-parameter tractable (FPT) on undirected graphs, the status of Longest $(s,t)$-Detour on directed graphs remains highly unclear: it is not even known to be solvable in polynomial time for $k=1$. Recently, Fomin et al. made progress in this direction by showing that the problem is FPT on every class of directed graphs where the 3-Disjoint Paths problem is solvable in polynomial time. We improve upon their result by weakening this assumption: we show that only a polynomial-time algorithm for 2-Disjoint Paths is required.

The seminal work of Charikar et al. [1] called Count-Sketch suggests a sketching algorithm for real-valued vectors that has been used in frequency estimation for data streams and pairwise inner product estimation for real-valued vectors etc. One of the major advantages of Count-Sketch over other similar sketching algorithms, such as random projection, is that its running time, as well as the sparsity of sketch, depends on the sparsity of the input. Therefore, sparse datasets enjoy space-efficient (sparse sketches) and faster running time. However, on dense datasets, these advantages of Count-Sketch might be negligible over other baselines. In this work, we address this challenge by suggesting a simple and effective approach that outputs (asymptotically) a sparser sketch than that obtained via Count-Sketch, and as a by-product, we also achieve a faster running time. Simultaneously, the quality of our estimate is closely approximate to that of Count-Sketch. For frequency estimation and pairwise inner product estimation problems, our proposal Sparse-Count-Sketch provides unbiased estimates. These estimations, however, have slightly higher variances than their respective estimates obtained via Count-Sketch. To address this issue, we present improved estimators for these problems based on maximum likelihood estimation (MLE) that offer smaller variances even w.r.t. Count-Sketch. We suggest a rigorous theoretical analysis of our proposal for frequency estimation for data streams and pairwise inner product estimation for real-valued vectors.

Given a universe $U=R\cup B$ of a finite set of red elements R, and a finite set of blue elements B and a family $F$ of subsets of $U$, the Red Blue Set Cover problem is to find a subset $F^{\prime }$ of $F$ that covers all blue elements of B and minimum number of red elements from R.

We prove that the Red Blue Set Cover problem is NP-hard even when R and B respectively are sets of red and blue points in ${\mathrm{IR}}^2$ and the sets in $F$ are defined by axis−parallel lines i.e., every set is a maximal set of points with the same x or y coordinate.

We then study the parameterized complexity of a generalization of this problem, where $U$ is a set of points in ${\mathrm{IR}}^d$ and $F$ is a collection of set of axis−parallel hyperplanes in ${\mathrm{IR}}^d$ under different parameterizations, where d is a constant. For every parameter, we show that the problem is fixed-parameter tractable and also show the existence of a polynomial kernel. We further consider the Red Blue Set Cover problem for some special types of rectangles in ${\mathrm{IR}}^2$.

With the development of Lie theory, Lie groups have profound significance in many branches of mathematics and physics. In Lie theory, matrix exponential plays a crucial role between Lie groups and Lie algebras. Meanwhile, as finite analogues of Lie groups, finite groups of Lie type also have wide application scenarios in mathematics and physics owning to their unique mathematical structures. In this context, it is meaningful to explore the potential applications of finite groups of Lie type in cryptography. In this paper, we firstly built the relationship between matrix exponential and discrete logarithmic problem (DLP) in finite groups of Lie type. Afterwards, we proved that the complexity of solving non-abelian factorization (NAF) problem is polynomial with the rank n of the finite group of Lie type. Furthermore, combining with the Algebraic Span, we proposed an efficient algorithm for solving group factorization problem (GFP) in finite groups of Lie type. Therefore, it's still an open problem to devise secure cryptosystems based on Lie theory.

Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs in regular resolution while admitting polynomial-size proofs in resolution. Thus, with respect to the usual notion of simulation, regular resolution is separated from resolution. An alternative, and weaker, notion for comparing proof systems is that of an “effective simulation,” which allows the translation of the formula along with the proof when moving between proof systems. We prove that regular resolution is equivalent to resolution under effective simulations. As a corollary, we recover in a black-box fashion a recent result on the hardness of automating regular resolution.

We propose a framework for speeding up maximum flow computation by using predictions. A prediction is a flow, i.e., an assignment of non-negative flow values to edges, which satisfies the flow conservation property, but does not necessarily respect the edge capacities of the actual instance (since these were unknown at the time of learning). We present an algorithm that, given an m-edge flow network and a predicted flow, computes a maximum flow in $O\left(m\eta \right)$ time, where η is the ${\ell }_1$ error of the prediction, i.e., the sum over the edges of the absolute difference between the predicted and optimal flow values. Moreover, we prove that, given an oracle access to a distribution over flow networks, it is possible to efficiently PAC-learn a prediction minimizing the expected ${\ell }_1$ error over that distribution. Our results fit into the recent line of research on learning-augmented algorithms, which aims to improve over worst-case bounds of classical algorithms by using predictions, e.g., machine-learned from previous similar instances. So far, the main focus in this area was on improving competitive ratios for online problems. Following Dinitz et al. (2021) [6], our results are among the firsts to improve the running time of an offline problem.

We show that every prenex universal syntactic first-order safety property can be compiled into a universal invariant of a first-order transition system using quantifier-free substitutions only. We apply this insight to prove that every such safety property is decidable for first-order transition systems with stratified guarded updates only.