SIMULATIONS BY TIME-BOUNDED COUNTER MACHINES

2011 ◽  
Vol 22 (02) ◽  
pp. 395-409 ◽  
Author(s):  
HOLGER PETERSEN
Keyword(s):  
Lower Bound ◽  
Real Time ◽  
Polynomial Time ◽  
Time Complexity ◽  
Linear Time ◽  
Fixed Number ◽  
Exponential Time ◽  
New Family ◽  
Counter Machines ◽  
Time Bounds

We investigate the efficiency of simulations of storages by several counters. A simulation of a pushdown store is described which is optimal in the sense that reducing the number of counters of a simulator leads to an increase in time complexity. The lower bound also establishes a tight counter hierarchy in exponential time. Then we turn to simulations of a set of counters by a different number of counters. We improve and generalize a known simulation in polynomial time. Greibach has shown that adding s + 1 counters increases the power of machines working in time ns. Using a new family of languages we show here a tight hierarchy result for machines with the same polynomial time-bound. We also prove hierarchies for machines with a fixed number of counters and with growing polynomial time-bounds. For machines with one counter and an additional "store zero" instruction we establish the equivalence of real-time and linear time. If at least two counters are available, the classes of languages accepted in real-time and linear time can be separated.

Further Study on Reverse 1-Center Problem on Trees

2020 ◽  
Vol 37 (06) ◽  
pp. 2050034
Author(s):  
Ali Reza Sepasian ◽  
Javad Tayyebi
Keyword(s):  
Dynamic Programming ◽  
Time Complexity ◽  
Numerical Experiments ◽  
Linear Time ◽  
Minimum Cost ◽  
Fixed Number ◽  
The Other ◽  
Center Problem ◽  
Objective Value ◽  
Linear Cost

This paper studies two types of reverse 1-center problems under uniform linear cost function where edge lengths are allowed to reduce. In the first type, the aim is that the objective value is bounded by a prescribed fixed value [Formula: see text] at minimum cost. The aim of the other is to improve the objective value as much as possible within a given budget. An algorithm based on dynamic programming is proposed to solve the first problem in linear time. Then, this algorithm is applied as a subroutine to design an algorithm to solve the second type of the problem in [Formula: see text] time in which [Formula: see text] is a fixed number dependent on the problem parameters. Under the similarity assumption, this algorithm has a better complexity than the Nguyen algorithm (2013) with quadratic-time complexity. Some numerical experiments are conducted to validate this fact in practice.

scholarly journals Global Greedy Dependency Parsing

2020 ◽  
Vol 34 (05) ◽  
pp. 8319-8326
Author(s):  
Zuchao Li ◽  
Hai Zhao ◽  
Kevin Parnow
Keyword(s):  
Feature Extraction ◽  
Polynomial Time ◽  
Time Complexity ◽  
Linear Time ◽  
Parse Tree ◽  
Dependency Parsing ◽  
Graph Models ◽  
Parse Trees ◽  
Left And Right ◽  
Syntactic Dependency

Most syntactic dependency parsing models may fall into one of two categories: transition- and graph-based models. The former models enjoy high inference efficiency with linear time complexity, but they rely on the stacking or re-ranking of partially-built parse trees to build a complete parse tree and are stuck with slower training for the necessity of dynamic oracle training. The latter, graph-based models, may boast better performance but are unfortunately marred by polynomial time inference. In this paper, we propose a novel parsing order objective, resulting in a novel dependency parsing model capable of both global (in sentence scope) feature extraction as in graph models and linear time inference as in transitional models. The proposed global greedy parser only uses two arc-building actions, left and right arcs, for projective parsing. When equipped with two extra non-projective arc-building actions, the proposed parser may also smoothly support non-projective parsing. Using multiple benchmark treebanks, including the Penn Treebank (PTB), the CoNLL-X treebanks, and the Universal Dependency Treebanks, we evaluate our parser and demonstrate that the proposed novel parser achieves good performance with faster training and decoding.

scholarly journals Fast and Reliable Mouse Picking Using Graphics Hardware

2009 ◽  
Vol 2009 ◽  
pp. 1-7 ◽  
Author(s):  
Hanli Zhao ◽  
Xiaogang Jin ◽  
Jianbing Shen ◽  
Shufang Lu
Keyword(s):  
Real Time ◽  
Time Complexity ◽  
High Performance ◽  
Linear Time ◽  
Graphics Hardware ◽  
3D Graphics ◽  
Novel Approach ◽  
Geometry Shader ◽  
Intersection Test ◽  
Fast Responses

Mouse picking is the most commonly used intuitive operation to interact with 3D scenes in a variety of 3D graphics applications. High performance for such operation is necessary in order to provide users with fast responses. This paper proposes a fast and reliable mouse picking algorithm using graphics hardware for 3D triangular scenes. Our approach uses a multi-layer rendering algorithm to perform the picking operation in linear time complexity. The objectspace based ray-triangle intersection test is implemented in a highly parallelized geometry shader. After applying the hardware-supported occlusion queries, only a small number of objects (or sub-objects) are rendered in subsequent layers, which accelerates the picking efficiency. Experimental results demonstrate the high performance of our novel approach. Due to its simplicity, our algorithm can be easily integrated into existing real-time rendering systems.

REDUCING SIMPLE GRAMMARS: EXPONENTIAL AGAINST HIGHLY-POLYNOMIAL TIME IN PRACTICE

2007 ◽  
Vol 18 (04) ◽  
pp. 715-725
Author(s):  
CÉDRIC BASTIEN ◽  
JUREK CZYZOWICZ ◽  
WOJCIECH FRACZAK ◽  
WOJCIECH RYTTER
Keyword(s):  
Polynomial Time ◽  
Experimental Analysis ◽  
Time Complexity ◽  
Packet Classification ◽  
State Machines ◽  
Worst Case ◽  
Exponential Time ◽  
Push Down

Simple grammar reduction is an important component in the implementation of Concatenation State Machines (a hardware version of stateless push-down automata designed for wire-speed network packet classification). We present a comparison and experimental analysis of the best-known algorithms for grammar reduction. There are two approaches to this problem: one processing compressed strings without decompression and another one which processes strings explicitly. It turns out that the second approach is more efficient in the considered practical scenario despite having worst-case exponential time complexity (while the first one is polynomial). The study has been conducted in the context of network packet classification, where simple grammars are used for representing the classification policies.

scholarly journals Language classes associated with automata over matrix groups

2018 ◽  
Vol 52 (2-3-4) ◽  
pp. 253-268
Author(s):  
Özlem Salehi ◽  
Flavio D’Alessandro ◽  
A.C. Cem Say
Keyword(s):  
Time Complexity ◽  
Linear Time ◽  
Finite Automata ◽  
Matrix Group ◽  
Integer Matrix ◽  
Matrix Groups ◽  
Language Classes ◽  
Discrete Heisenberg Group ◽  
Special Matrix ◽  
Time Bounds

We investigate the language classes recognized by group automata over matrix groups. For the case of 2 × 2 matrices, we prove that the corresponding group automata for rational matrix groups are more powerful than the corresponding group automata for integer matrix groups. Finite automata over some special matrix groups, such as the discrete Heisenberg group and the Baumslag-Solitar group are also examined. We also introduce the notion of time complexity for group automata and demonstrate some separations among related classes. The case of linear-time bounds is examined in detail throughout our repertory of matrix group automata.

scholarly journals A hardware based technique to reduce the timing complexity of number factoring problem

2021 ◽  
Author(s):  
Pirouz Pourdowlat
Keyword(s):  
Polynomial Time ◽  
Time Complexity ◽  
Digital Circuits ◽  
Computational Time ◽  
Quantum Computers ◽  
Exponential Rate ◽  
Silicon Area ◽  
Exponential Time ◽  
Clock Speed ◽  
Conventional Systems

Most digital circuits which have been developed to implement algorithms, can benefit from an increase in clock speed, but do not completely map the problem to all available silicon resources. We have introduced a hardware based scheme capable of effectively using technology, specifically the increase in silicon area, to improve the computational time of complicated applications. In this thesis, we applied this scheme to solve the factoring problem, which requires exponential time (with respect to the number of bits in n) in conventional computers and could be only solved in polynomial time with quantum computers. The scheme successfully mapped the problem to most of the silicon area of Altera Stratix FPGA. The results show that the scheme is capable of reducing the time complexity to a polynomial rate with respect to the number of bits of the number n. The results also show an exponential rate of use for silicon with respect to the number of bits of n. Our analysis shows that the new scheme is scalable with technology speed and available space, could be applied to other applications to solve the performance limitations of conventional systems.

Complement, Complexity, and Symmetric Representation

2015 ◽  
Vol 26 (05) ◽  
pp. 557-581 ◽  
Author(s):  
Thomas E. O'Neil
Keyword(s):  
Time Complexity ◽  
Linear Time ◽  
Vertex Cover ◽  
Independent Set ◽  
Symmetric Representation ◽  
Exponential Time ◽  
Complexity Of Algorithms ◽  
Space Efficiency ◽  
Complete Problems ◽  
Dense Sets

A representation for a set is defined to be symmetric if the space required for the representation of the set is the same as the space required for representation of the set's complement. The use of symmetric representation is shown to be important when studying the time complexity of algorithms. A symmetric data structure called a flip list is defined, and it is employed for the Clique, Independent Set, and Vertex Cover problems in a case study. The classic reductions among these problems require the complement of either a graph's edge set or a subset of its vertices. Flip lists can be complemented in constant time with no increase in space. When a flip list is used to represent the edge set of a graph, Clique, Independent Set, and Vertex Cover are shown to have identical (and strongly exponential) time complexity when the classical complexity parameter of input length is used. On the other hand, when a flip list is used to represent a set of numbers as input for the Partition problem, an algorithm can be built that retains strongly sub-exponential time complexity. This provides new evidence with respect to which NP- complete problems should be classified as sub-exponential. Symmetric representation has the advantage of space efficiency, at most linear-time and space complement operations, and symmetry in representing sparse and dense sets. These features can have a significant impact on complexity studies.

scholarly journals A Linear Time Complexity of Breadth-First Search UsingPSystem with Membrane Division

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Einallah Salehi ◽  
Siti Mariyam Shamsuddin ◽  
Kourosh Nemati
Keyword(s):  
Time Complexity ◽  
Membrane Computing ◽  
Linear Time ◽  
Real Life ◽  
Brute Force ◽  
Breadth First Search ◽  
Exponential Time ◽  
Complete Problems ◽  
Division Rule ◽  
Blind Search

One of the known methods for solving the problems with exponential time complexity such as NP-complete problems is using the brute force algorithms. Recently, a new parallel computational framework called Membrane Computing is introduced which can be applied in brute force algorithms. The usual way to find a solution for the problems with exponential time complexity with Membrane Computing techniques is byPSystem with active membrane using division rule. It makes an exponential workspace and solves the problems with exponential complexity in a polynomial (even linear) time. On the other hand, searching is currently one of the most used methods for finding solution for problems in real life, that the blind search algorithms are accurate, but their time complexity is exponential such as breadth-first search (BFS) algorithm. In this paper, we proposed a new approach for implementation of BFS by usingPsystem with division rule technique for first time. The theorem shows time complexity of BSF in this framework on randomly binary trees reduced fromO(2d)toO(d).

scholarly journals Krull dimension and regularity of binomial edge ideals of block graphs

2019 ◽  
Vol 19 (07) ◽  
pp. 2050133 ◽  
Author(s):  
Carla Mascia ◽  
Giancarlo Rinaldo
Keyword(s):  
Lower Bound ◽  
Linear Time ◽  
Betti Numbers ◽  
Krull Dimension ◽  
Edge Ideals ◽  
New Family ◽  
Block Graphs ◽  
Linear Time Algorithms

We give a lower bound for the Castelnuovo-Mumford regularity of binomial edge ideals of block graphs by computing the two distinguished extremal Betti numbers of a new family of block graphs, called flower graphs. Moreover, we present linear time algorithms to compute the Castelnuovo–Mumford regularity and the Krull dimension of binomial edge ideals of block graphs.

Improved quantum dilation and erosion operations

2016 ◽  
Vol 14 (07) ◽  
pp. 1650036 ◽  
Author(s):  
Suzhen Yuan ◽  
Xia Mao ◽  
Lijiang Chen ◽  
Xiaofa Wang
Keyword(s):  
Polynomial Time ◽  
Time Complexity ◽  
Complexity Analysis ◽  
Quantum Image ◽  
Exponential Time ◽  
Previous Version ◽  
Quantum Operations ◽  
Neighborhood Information ◽  
Image Set ◽  
Quantum Parallelism

To reduce the time complexity of quantum morphology operations, two kinds of improved quantum dilation and erosion operations are proposed. Quantum parallelism is well used in the design of these operations. Consequently, the time complexity is greatly reduced compared with the previous quantum dilation and erosion operations. The neighborhood information of each pixel is needed in the process of designing quantum dilation and erosion operations. In order to get the neighborhood information, quantum position shifting transformation is utilized, which can make the neighborhood information store in a quantum image set. In this image set, the neighborhood information of pixel at location ([Formula: see text], [Formula: see text]) is stored at the same location ([Formula: see text], [Formula: see text]) of other images in the image set. All the pixels will be processed simultaneously, which is the performance of quantum parallelism. The time complexity analysis shows that these quantum operations have polynomial-time complexity which is much lower than the exponential-time complexity of the previous version.

Sign in / Sign up

Export Citation Format

Share Document