Minimal Size of Counters for (Real-Time) Multicounter Automata

2021 ◽  
Vol 181 (2-3) ◽  
pp. 99-127
Author(s):  
Viliam Geffert ◽  
Zuzana Bednárová
Keyword(s):  
Finite Number ◽  
Real Time ◽  
The Other ◽  
Binary Representation ◽  
Minimal Size ◽  
Nondeterministic Automaton ◽  
Other Hand ◽  
Weak Space ◽  
Fixed Constant

We show that, for automata using a finite number of counters, the minimal space that is required for accepting a nonregular language is (log n)ɛ. This is required for weak space bounds on the size of their counters, for real-time and one-way, and for nondeterministic and alternating versions of these automata. The same holds for two-way automata, independent of whether they work with strong or weak space bounds, and of whether they are deterministic, nondeterministic, or alternating. (Here ɛ denotes an arbitrarily small—but fixed—constant; the “space” refers to the values stored in the counters, rather than to the lengths of their binary representation.) On the other hand, we show that the minimal space required for accepting a nonregular language is nɛ for multicounter automata with strong space bounds, both for real-time and one-way versions, independent of whether they are deterministic, nondeterministic, or alternating, and also for real-time and one-way deterministic multicounter automata with weak space bounds. All these bounds are optimal both for unary and general nonregular languages. However, for automata equipped with only one counter, it was known that one-way nondeterministic automata cannot recognize any unary nonregular languages at all, even if the size of the counter is not restricted, while, with weak space bound log n, we present a real-time nondeterministic automaton recognizing a binary nonregular language here.

The No-Three-In-Line Problem

1968 ◽  
Vol 11 (4) ◽  
pp. 527-531 ◽  
Author(s):  
Richard K. Guy ◽  
Patrick A. Kelly
Keyword(s):  
Finite Number ◽  
The Other ◽  
Probabilistic Argument ◽  
Number Of Solutions ◽  
Other Hand ◽  
Image Position

Let Sn be the set of n2 points with integer coordinates n (x, y), 1 ≤ x, y <n. Let fn be the maximum cardinal of a subset T of Sn such that no three points of T are collinear. Clearly fn < 2n.For 2 ≤ n ≤ 10 it is known ([2], [3] for n = 8, [ 1] for n = 10, also [4], [6]) that fn = 2n, and that this bound is attained in 1, 1, 4, 5, 11, 22, 57, 51 and 156 distinct configurations for these nine values of n. On the other hand, P. Erdös [7] has pointed out that if n is prime, fn ≥ n, since the n points (x, x2) reduced modulo n have no three collinear. We give a probabilistic argument to support the conjecture that there is only a finite number of solutions to the no-three-in-line problem. More specifically, we conjecture that

Construction of Motion Model of Motion Simulation System of Airport Fire Engine Simulator

2013 ◽  
Vol 765-767 ◽  
pp. 634-638
Author(s):  
Li Shan Jia ◽  
Li Wen Wang
Keyword(s):  
Real Time ◽  
Simulation System ◽  
The Other ◽  
Motion Simulation ◽  
Motion Model ◽  
Quality Requirement ◽  
Virtual Training ◽  
Other Hand ◽  
Fire Engine ◽  
Setting Parameters

To the high real-time quality requirement of motion simulation system of airport fire engine simulator, a simulation system with simplified motion model was promoted. The simplified motion model simplifies motion model of vehicle based on application requirement of virtual training of vehicle driving. On one hand, the simplification can reduce calculation amount of simulation, on the other hand, the simplification can make it easier to get parameters of model. Motion simulation system based on simplified motion model of airport fire engine was constructed and experiment was taken. Experiment showed that the motion simulation system has high calculation speed and good fidelity through setting parameters properly.

scholarly journals Performance Evaluation of AOMDV and AODV in City Scenario With Changeable Traffic Density in VANETS BLSTM With Attention Mechanism

2021 ◽  
Author(s):  
S. Devi
Keyword(s):  
Performance Evaluation ◽  
Real Time ◽  
Routing Protocols ◽  
Emergency Situation ◽  
Attention Mechanism ◽  
The Other ◽  
Traffic Density ◽  
Other Hand ◽  
Simulation Results

Abstract The survey indicates that VANETs use two vital routing protocols namely AODV and AOMDV. AODV is implemented by providing a single dedicated path between source and receiver and it doesn’t search for the alternate path in the case of an emergency situation. On the other hand, AOMDV is implemented by providing an intermediate participant node to reach the receiver i.e., it provides multipath and unlike AODV, it searches for the alternate path in the case of an emergency situation. Due to this capability, AOMDV finds its application in broad areas of research. In this paper, both the protocols are established and their performances are analyzed in terms of PDR, PLR, E2E, and Throughput. The simulation results are obtained using NS2.34. Using these results, the appropriate protocols can be implemented in real-time for various city environments with changeable traffic density and topography in the established network.

String Generation by Cellular Automata

2021 ◽  
Vol 30 (2) ◽  
pp. 111-132
Author(s):  
Martin Kutrib ◽  
◽  
Andreas Malcher ◽  
Keyword(s):  
Cellular Automata ◽  
Real Time ◽  
Structural Properties ◽  
The Other ◽  
Time Constraints ◽  
Closure Properties ◽  
Other Hand ◽  
The One

In contrast to many investigations of cellular automata with regard to their ability to accept inputs under certain time constraints, in this paper we are studying cellular automata with regard to their ability to generate strings in real time. Structural properties such as speedup results and closure properties are investigated. On the one hand, constructions for the closure under intersection, reversal and length-preserving homomorphism are presented, whereas on the other hand the nonclosure under union, complementation and arbitrary homomorphism are obtained. Finally, decidability questions such as emptiness, finiteness, equivalence, inclusion, regularity and context-freeness are addressed.

scholarly journals The Core of Voting Games: A Partition Approach

2015 ◽  
Vol 17 (03) ◽  
pp. 1550001
Author(s):  
Aymeric Lardon
Keyword(s):  
Finite Number ◽  
Coalition Formation ◽  
The Other ◽  
Veto Power ◽  
The Core ◽  
Voting Games ◽  
Other Hand ◽  
The One

The purpose of this paper is to analyze a class of voting games in a partition approach. We consider a society in which coalitions can be formed and where a finite number of voters have to choose among a set of alternatives. A coalition is winning if it can veto any proposed alternative. In our model, the veto power of a coalition is dependent on the coalition formation of the outsiders. We show that whether or not the core is non-empty depends crucially on the expectations of each coalition regarding outsiders' behavior when it wishes to veto an alternative. On the one hand, if each coalition has pessimistic expectations, then the core is non-empty if and only if the dimension of the set of alternatives is equal to one. On the other hand, if each coalition has optimistic expectations, the non-emptiness of the core is not ensured.

Automata with cyclic move operations for picture languages

2018 ◽  
Vol 52 (2-3-4) ◽  
pp. 235-251
Author(s):  
Friedrich Otto ◽  
František Mráz
Keyword(s):  
Finite Number ◽  
Expressive Power ◽  
Single Step ◽  
The Other ◽  
Cyclic Extension ◽  
Two Dimensional ◽  
Other Hand ◽  
Picture Languages ◽  
Restarting Automaton

Here, we study the cyclic extensions of Sgraffito automata and of deterministic two-dimensional two-way ordered restarting automata for picture languages. Such a cyclically extended automaton can move in a single step from the last column (or row) of a picture to the first column (or row). For Sgraffito automata, we show that this cyclic extension does not increase the expressive power of the model, while for deterministic two-dimensional two-way restarting automata, the expressive power is strictly increased by allowing cyclic moves. In fact, for the latter automata, we take the number of allowed cyclic moves in any column or row as a parameter, and we show that already with a single cyclic move per column (or row) the deterministic two-dimensional extended two-way restarting automaton can be simulated. On the other hand, we show that two cyclic moves per column or row already give the same expressive power as any finite number of cyclic moves.

Science with the Australia Telescope (Invited Paper)

1987 ◽  
Vol 7 (2) ◽  
pp. 220-226 ◽  
Author(s):  
B. J. Robinson
Keyword(s):  
Phase Space ◽  
Real Time ◽  
The Other ◽  
The Real ◽  
New Science ◽  
Long Baseline ◽  
Other Hand ◽  
Selection Of ◽  
Compact Array

AbstractThe research now under way with the real-time 275 km Parkes-Tidbinbila interferometer is used as a guide to the initial science to be undertaken with the 319 km Australia Telescope (AT) Long Baseline Array. On the other hand, it is risky to guess at the new science likely to be attempted with the 6 km AT Compact Array at Culgoora; instead the potential that has been built into this array is discussed and a selection of basic questions in astrophysics is posed as a guide to significant science that might yield to new observers on a fresh instrument under the southern skies. In conclusion two questions are probed: Can discoveries be made by users of national facilities? Does the AT cross into new domains in the phase space of observations?

Note on a theorem of R. Baer

1949 ◽  
Vol 45 (3) ◽  
pp. 321-327 ◽  
Author(s):  
G. Higman
Keyword(s):  
Finite Number ◽  
Present Note ◽  
The Other ◽  
Fixed Integer ◽  
Other Hand

It is trivial that a group all of whose elements except the identity have order two is Abelian; and F. Levi and B. L. van der Waerden(1) have shown that a group all of whose elements except the identity have order three has class less than or equal to three. On the other hand, R. Baer(3) has shown that if the fact that all the elements of a group have orders dividing n implies a limitation on the class of the group, then n is a prime. The object of the present note is to extend this result by showing that if M is a fixed integer there are at most a finite number of prime powers n other than primes, such that the fact that all the elements of a group have orders dividing n implies a limitation on the class of its Mth derived group.

On the idea of frequency

1925 ◽  
Vol 22 (5) ◽  
pp. 726-727 ◽  
Author(s):  
W. Burnside
Keyword(s):  
Finite Number ◽  
The Other ◽  
Finite Collection ◽  
Other Hand ◽  
Statistical Table

A statistical table is in effect a classification of a finite number, N, of objects in respect of a finite number of different classes, A, B, C, … It is assumed that unambiguous rules have been laid down by which it is possible to determine whether any particular one of the objects does or does not belong to any particular one of the classes. The application of these rules to a particular object does not depend on the fact that that object is one of a finite number of N objects, so that the process of classification may be started on a non-finite collection of objects. When the collection of objects is non-finite the process can never end. On the other hand when the collection is finite the process must end; and when completed it will determine how many of the objects belong to any particular class. If in this way it is found that N1 (≤ N) of the objects belong to class A, the proper fraction N1/N is spoken of as the frequency of class A in the collection. In particular cases it may be zero or unity. In general it is a rational proper fraction. For its determination in complicated cases it may be convenient to suppose the collection to be arranged in some special way, but its value is absolutely independent of any such particular arrangement.

scholarly journals Control a 2-Axis Servomechanism by Gesture Recognition Using a Generic WebCam

10.5772/5803 ◽  
2005 ◽  
Vol 2 (1) ◽  
pp. 5 ◽  
Author(s):  
J. M. R. S. Tavares ◽  
R. Ferreira ◽  
F. Freitas
Keyword(s):  
Real Time ◽  
Gesture Recognition ◽  
Learning Phase ◽  
The Other ◽  
Control Sets ◽  
Other Hand ◽  
Control Image

This paper presents two approaches used to control a 2-axis servomechanism by gesture recognition. For both approaches, the adopted control philosophy was: In the system's learning phase, the control images are acquired by a generic webcam and associated to the desired orders. On the other hand, in the working phase, each control image is acquired, by the same webcam and, by comparison with the stored orders images, the desired order is recognized and processed by the servomechanism in quasi real time. In this paper, the used servomechanism and both implemented approaches are described, and are indicated some advantages and weakness of each one. Two examples of images control sets are also presented, and some conclusions and future works are addressed.

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