scholarly journals On Sufficient and Necessary Conditions in Bounded CTL: A Forgetting Approach

2020 ◽  
Author(s):  
Renyan Feng ◽  
Erman Acar ◽  
Stefan Schlobach ◽  
Yisong Wang ◽  
Wanwei Liu
Keyword(s):  
Computational Complexity ◽  
System Design ◽  
Formal Verification ◽  
Information Content ◽  
Necessary Conditions ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Computation Tree ◽  
Sufficient And Necessary Conditions ◽  
Points Of View

Computation Tree Logic (CTL) is one of the central formalisms in formal verification. As a specification language, it is used to express a property that the system at hand is expected to satisfy. From both the verification and the system design points of view, some information content of such property might become irrelevant for the system due to various reasons, e.g., it might become obsolete by time, or perhaps infeasible due to practical difficulties. Then, the problem arises on how to subtract such piece of information without altering the relevant system behaviour or violating the existing specifications over a given signature. Moreover, in such a scenario, two crucial notions are informative: the strongest necessary condition (SNC) and the weakest sufficient condition (WSC) of a given property. To address such a scenario in a principled way, we introduce a forgetting-based approach in CTL and show that it can be used to compute SNC and WSC of a property under a given model and over a given signature. We study its theoretical properties and also show that our notion of forgetting satisfies existing essential postulates of knowledge forgetting. Furthermore, we analyse the computational complexity of some basic reasoning tasks for the fragment CTLAF in particular.

scholarly journals Syarat Perlu dan Cukup untuk Keterbatasan Potensial Riesz di Ruang Morrey Klasik

2013 ◽  
Vol 14 (3) ◽  
pp. 227
Author(s):  
Mohammad Imam Utoyo ◽  
Basuki Widodo ◽  
Toto Nusantara ◽  
Suhariningsih Suhariningsih
Keyword(s):  
Characteristic Function ◽  
Morrey Space ◽  
Necessary Conditions ◽  
Riesz Potential ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Research Results ◽  
Necessary And Sufficient

This script was aimed to determine the necessary conditions for boundedness of Riesz potential in the classical Morrey space. If these results are combined with previous research results will be obtained the necessary and sufficient condition for boundedness of Riesz potential. This necessary condition is obtained through the use of characteristic function as one member of the classical Morrey space.

scholarly journals Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Kai Wang ◽  
Zhidong Teng ◽  
Fengqin Zhang
Keyword(s):  
Function Method ◽  
Global Attractivity ◽  
Necessary Conditions ◽  
Nutrient Recycling ◽  
Liapunov Function ◽  
Sufficient Condition ◽  
Chemostat Model ◽  
Dynamic Behaviors ◽  
Analysis Technique ◽  
Sufficient And Necessary Conditions

The dynamic behaviors in a chemostat model with delayed nutrient recycling and periodically pulsed input are studied. By introducing new analysis technique, the sufficient and necessary conditions on the permanence and extinction of the microorganisms are obtained. Furthermore, by using the Liapunov function method, the sufficient condition on the global attractivity of the model is established. Finally, an example is given to demonstrate the effectiveness of the results in this paper.

scholarly journals Extreme points and rotundity of Orlicz-Sobolev spaces

2002 ◽  
Vol 32 (5) ◽  
pp. 293-299
Author(s):  
Shutao Chen ◽  
Changying Hu ◽  
Charles Xuejin Zhao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Sobolev Spaces ◽  
Necessary Conditions ◽  
Nonlinear Partial Differential Equations ◽  
Extreme Points ◽  
Necessary Condition ◽  
Partial Differential ◽  
Sufficient And Necessary Conditions ◽  
Sufficient And Necessary Condition

It is well known that Sobolev spaces have played essential roles in solving nonlinear partial differential equations. Orlicz-Sobolev spaces are generalized from Sobolev spaces. In this paper, we present sufficient and necessary conditions of extreme points of Orlicz-Sobolev spaces. A sufficient and necessary condition of rotundity of Orlicz-Sobolev spaces is obtained.

CHARACTERIZATION OF THE EXISTENCE OF GALLED-TREE NETWORKS

2006 ◽  
Vol 04 (06) ◽  
pp. 1309-1328 ◽  
Author(s):  
ARVIND GUPTA ◽  
JÁN MAŇUCH ◽  
XIAOHONG ZHAO ◽  
LADISLAV STACHO
Keyword(s):  
Necessary Conditions ◽  
Simple Algorithm ◽  
Complete Characterization ◽  
Necessary Condition ◽  
Tree Networks ◽  
Tree Network ◽  
Sufficient And Necessary Conditions

In this paper, we give a complete characterization of the existence of a galled-tree network in the form of simple sufficient and necessary conditions for both root-known and root-unknown cases. As a by-product we obtain a simple algorithm for constructing galled-tree networks. We also introduce a new necessary condition for the existence of a galled-tree network similar to bi-convexity.

ON THE OBSERVABILITY OF CONTINUOUS-TIME DYNAMIC FUZZY CONTROL SYSTEMS

2007 ◽  
Vol 15 (01) ◽  
pp. 75-91
Author(s):  
YUHU FENG ◽  
MIN CHEN ◽  
LIANGJIAN HU
Keyword(s):  
Fuzzy Control ◽  
Control Systems ◽  
Continuous Time ◽  
Necessary Conditions ◽  
Rule Base ◽  
Sufficient Condition ◽  
Initial Value ◽  
Time Dynamic ◽  
Sufficient And Necessary Conditions ◽  
Logic Description

This paper studies the observability of the initial value of continuous-time dynamic fuzzy control systems. The sufficient and necessary conditions for the initial value of fuzzy control system to be observable are given. A concept called strong observability is introduced and a sufficient condition for the initial value of system to be strongly observable is discussed. The fuzzy logic description of input-output relations using IF-THEN rule base is presented.

scholarly journals DISCRETENESS CRITERIA FOR MÖBIUS GROUPS ACTING ON II

2009 ◽  
Vol 80 (2) ◽  
pp. 275-290 ◽  
Author(s):  
LIU-LAN LI ◽  
XIAN-TAO WANG
Keyword(s):  
Fixed Point ◽  
Necessary Conditions ◽  
Careful Analysis ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Point Sets ◽  
Discreteness Criteria ◽  
Möbius Groups ◽  
Jørgensen’S Inequality ◽  
Fixed Point Sets

AbstractJørgensen’s famous inequality gives a necessary condition for a subgroup of PSL(2,ℂ) to be discrete. It is also true that if Jørgensen’s inequality holds for every nonelementary two-generator subgroup, the group is discrete. The sufficient condition has been generalized to many settings. In this paper, we continue the work of Wang, Li and Cao (‘Discreteness criteria for Möbius groups acting on $\overline {\mathbb {R}}^n$’, Israel J. Math.150 (2005), 357–368) and find three more (infinite) discreteness criteria for groups acting on $\overline {\mathbb {R}}^n$; we also correct a linguistic ambiguity of their Theorem 3.3 where one of the necessary conditions might be vacuously fulfilled. The results of this paper are obtained by using known results regarding two-generator subgroups and a careful analysis of the relation among the fixed point sets of various elements of the group.

scholarly journals Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1323
Author(s):  
Shyam Sundar Santra ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher
Keyword(s):  
Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mixed Delays ◽  
Neutral Differential Equations ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
The Future ◽  
Sufficient And Necessary Conditions

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

scholarly journals Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1035
Author(s):  
Cai-Mei Yan ◽  
Rekha Srivastava ◽  
Jin-Lin Liu
Keyword(s):  
Difference Operator ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Sufficient And Necessary Conditions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

scholarly journals Sufficient and necessary conditions for oscillation of linear fractional-order delay differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Qiong Meng ◽  
Zhen Jin ◽  
Guirong Liu
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Multiple Delays ◽  
All Solutions ◽  
Sufficient And Necessary Conditions ◽  
Delay Differential ◽  
T Tau ◽  
Sufficient And Necessary Condition

AbstractThis paper studies the linear fractional-order delay differential equation $$ {}^{C}D^{\alpha }_{-}x(t)-px(t-\tau )= 0, $$ D − α C x ( t ) − p x ( t − τ ) = 0 , where $0<\alpha =\frac{\text{odd integer}}{\text{odd integer}}<1$ 0 < α = odd integer odd integer < 1 , $p, \tau >0$ p , τ > 0 , ${}^{C}D_{-}^{\alpha }x(t)=-\Gamma ^{-1}(1-\alpha )\int _{t}^{\infty }(s-t)^{- \alpha }x'(s)\,ds$ D − α C x ( t ) = − Γ − 1 ( 1 − α ) ∫ t ∞ ( s − t ) − α x ′ ( s ) d s . We obtain the conclusion that $$ p^{1/\alpha } \tau >\alpha /e $$ p 1 / α τ > α / e is a sufficient and necessary condition of the oscillations for all solutions of Eq. (*). At the same time, some sufficient conditions are obtained for the oscillations of multiple delays linear fractional differential equation. Several examples are given to illustrate our theorems.

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