Neil Immerman. Upper and lower bounds for first order expressibility. Journal of computer and system sciences, vol. 25 (1982), pp. 76–98. - Neil Immerman. Relational queries computable in polynomial time. Information and control, vol. 68 (1986), pp. 86–104. - Neil Immerman. Languages that capture complexity classes. SIAM journal on computing, vol. 16 (1987), pp. 760–778.

1989 ◽  
Vol 54 (1) ◽  
pp. 287-288
Author(s):  
Samuel Buss
Keyword(s):  
Lower Bounds ◽  
Polynomial Time ◽  
Upper And Lower Bounds ◽  
Complexity Classes ◽  
Siam Journal ◽  
First Order ◽  
And Control ◽  
Time Information

scholarly journals An exact expression of positive periodic solution for a first-order singular equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yun Xin ◽  
Xiaoxiao Cui ◽  
Jie Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Lower Bounds ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Positive Periodic Solution ◽  
Exact Expression ◽  
Upper And Lower Bounds ◽  
Singular Equation ◽  
First Order

Abstract The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

scholarly journals Computational Approaches for Stochastic Shortest Path on Succinct MDPs

2018 ◽  
Author(s):  
Krishnendu Chatterjee ◽  
Hongfei Fu ◽  
Amir Goharshady ◽  
Nastaran Okati
Keyword(s):  
Lower Bounds ◽  
Polynomial Time ◽  
Shortest Path ◽  
Upper Bounds ◽  
Decision Processes ◽  
Upper And Lower Bounds ◽  
Computational Approaches ◽  
Stochastic Shortest Path ◽  
Markov Decision ◽  
Infinite State

We consider the stochastic shortest path (SSP) problem for succinct Markov decision processes (MDPs), where the MDP consists of a set of variables, and a set of nondeterministic rules that update the variables. First, we show that several examples from the AI literature can be modeled as succinct MDPs. Then we present computational approaches for upper and lower bounds for the SSP problem: (a) for computing upper bounds, our method is polynomial-time in the implicit description of the MDP; (b) for lower bounds, we present a polynomial-time (in the size of the implicit description) reduction to quadratic programming. Our approach is applicable even to infinite-state MDPs. Finally, we present experimental results to demonstrate the effectiveness of our approach on several classical examples from the AI literature.

scholarly journals A New Method to Study the Periodic Solutions of the Ordinary Differential Equations Using Functional Analysis

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 677 ◽  
Author(s):  
Kadry ◽  
Alferov ◽  
Ivanov ◽  
Korolev ◽  
Selitskaya
Keyword(s):  
Functional Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Lower Bounds ◽  
New Method ◽  
Upper And Lower Bounds ◽  
First Order ◽  
Periodic Problems ◽  
Existence And Stability

In this paper, a new theorems of the derived numbers method to estimate the number of periodic solutions of first-order ordinary differential equations are formulated and proved. Approaches to estimate the number of periodic solutions of ordinary differential equations are considered. Conditions that allow us to determine both upper and lower bounds for these solutions are found. The existence and stability of periodic problems are considered.

scholarly journals Interchangeability of Relevant Cycles in Graphs

10.37236/1494 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
Petra M. Gleiss ◽  
Josef Leydold ◽  
Peter F. Stadler
Keyword(s):  
Lower Bounds ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Upper And Lower Bounds ◽  
Cycle Basis ◽  
Cycle Bases

The set ${\cal R}$ of relevant cycles of a graph $G$ is the union of its minimum cycle bases. We introduce a partition of ${\cal R}$ such that each cycle in a class ${\cal W}$ can be expressed as a sum of other cycles in ${\cal W}$ and shorter cycles. It is shown that each minimum cycle basis contains the same number of representatives of a given class ${\cal W}$. This result is used to derive upper and lower bounds on the number of distinct minimum cycle bases. Finally, we give a polynomial-time algorithm to compute this partition.

Tailoring recursion for complexity

1995 ◽  
Vol 60 (3) ◽  
pp. 952-969 ◽  
Author(s):  
Erich Grädel ◽  
Yuri Gurevich
Keyword(s):  
Polynomial Time ◽  
Recursion Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Complexity Classes ◽  
First Order ◽  
Logarithmic Space ◽  
Functional Analog

AbstractWe design functional algebras that characterize various complexity classes of global functions. For this purpose, classical schemata from recursion theory are tailored for capturing complexity. In particular we present a functional analog of first-order logic and describe algebras of the functions computable in nondeterministic logarithmic space, deterministic and nondeterministic polynomial time, and for the functions computable by AC1 -circuits.

scholarly journals Bounds on Heavy-to-Heavy Weak Decay Form Factors

2001 ◽  
Vol 16 (supp01a) ◽  
pp. 416-418
Author(s):  
Cheng-Wei Chiang
Keyword(s):  
Heavy Quark ◽  
Lower Bounds ◽  
Sum Rules ◽  
Form Factors ◽  
Weak Decay ◽  
Upper And Lower Bounds ◽  
Effective Theory ◽  
Heavy Quark Effective Theory ◽  
First Order ◽  
Decay Form

We provide upper and lower bounds on the semileptonic weak decay form factors for B → D(*) and Λb → Λc decays by utilizing inclusive heavy quark effective theory sum rules. These bounds are calculated to second order in ΛQCD/mQ and first order in αs. The [Formula: see text] corrections to the bounds at zero recoil are also presented.

Asymptotic conditional probabilities: The non-unary case

1996 ◽  
Vol 61 (1) ◽  
pp. 250-276 ◽  
Author(s):  
Adam J. Grove ◽  
Joseph Y. Halpern ◽  
Daphne Koller
Keyword(s):  
Lower Bounds ◽  
Predicate Symbol ◽  
Upper And Lower Bounds ◽  
Degrees Of Belief ◽  
Conditional Probabilities ◽  
Unary Predicate ◽  
First Order

AbstractMotivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for first-order sentences. Given first-order sentences φ and θ, we consider the structures with domain {1, …, N} that satisfy θ, and compute the fraction of them in which φ is true. We then consider what happens to this fraction as N gets large. This extends the work on 0-1 laws that considers the limiting probability of first-order sentences, by considering asymptotic conditional probabilities. As shown by Liogon'kiĭ [24], if there is a non-unary predicate symbol in the vocabulary, asymptotic conditional probabilities do not always exist. We extend this result to show that asymptotic conditional probabilities do not always exist for any reasonable notion of limit. Liogon'kiĭ also showed that the problem of deciding whether the limit exists is undecidable. We analyze the complexity of three problems with respect to this limit: deciding whether it is well-defined, whether it exists, and whether it lies in some nontrivial interval. Matching upper and lower bounds are given for all three problems, showing them to be highly undecidable.

Equivalent Composite Laminated Beams With Various Elastic Constitutive Models

1999 ◽  
Author(s):  
Izhak Sheinman ◽  
Yeoshua Frostig
Keyword(s):  
Lower Bounds ◽  
Plane Stress ◽  
Constitutive Models ◽  
Upper And Lower Bounds ◽  
Two Dimensional ◽  
Laminated Beams ◽  
Cylindrical Bending ◽  
One Dimensional ◽  
First Order ◽  
Shear Deformable

Abstract Equivalent one-dimensional constitutive models of composite laminated beams with shear deformation are derived from the classical laminate two-dimensional using first-order shear deformable theory. The present cylindrical bending constitutive models can be used — with much greater accuracy than their well known plane-strain and plane-stress counterparts — as upper and lower bounds, to one of which the behavior tends depending on the width-to-length ratio; this aspect was investigated and results are presented.

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