相关论文: Lower bounds and complete problems in nondetermini…
In 1975, Ladner showed that under the hypothesis that P is not equal to NP, there exists a language which is neither in P, nor NP-complete. This result was latter generalized by Schoning and several authors to various polynomial-time…
The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
We determine the complexity of counting models of bounded size of specifications expressed in Linear-time Temporal Logic. Counting word models is #P-complete, if the bound is given in unary, and as hard as counting accepting runs of…
This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…
The parameterized complexity of a problem is considered "settled" once it has been shown to lie in FPT or to be complete for a class in the W-hierarchy or a similar parameterized hierarchy. Several natural parameterized problems have,…
The concept of space-bounded computability has become significantly important in handling vast data sets on memory-limited computing devices. To replenish the existing short list of NL-complete problems whose instance sizes are dictated by…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
This paper presents a new semantic method for proving lower bounds in computational complexity. We use it to prove that maxflow, a PTIME complete problem, is not computable in polylogarithmic time on parallel random access machines (PRAMs)…
There is a subset of computational problems that are computable in polynomial time for which an existing algorithm may not complete due to a lack of high performance technology on a mission field. We define a subclass of deterministic…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…
The quantum statistics mechanism is very powerful for investigating the equilibrium states and the phase transitions in complex spin disorder systems. The spin disorder systems act as an interdisciplinary platform for solving the optimum…
We consider a wireless network with a set of transmitter-receiver pairs, or links, that share a common channel, and address the problem of emptying finite traffic volume from the transmitters in minimum time. This, so called, minimum-time…
We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and…
In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on…
Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and…
The polylogarithmic time hierarchy structures sub-linear time complexity. In recent work it was shown that all classes $\tilde{\Sigma}_{m}^{\mathit{plog}}$ or $\tilde{\Pi}_{m}^{\mathit{plog}}$ ($m \in \mathbb{N}$) in this hierarchy can be…