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Shrinking games and local formulas

H.Jerome Keisler, Wafik Boulos Lotfallah
2004 Annals of Pure and Applied Logic  
We use Ehrenfeucht-Fra ssà e type games with a "shrinking horizon" to get a spectrum of normal form theorems of the Gaifman type, depending on the rate of shrinking.  ...  Gaifman's normal form theorem showed that every ÿrst-order sentence of quantiÿer rank n is equivalent to a Boolean combination of "scattered local sentences", where the local neighborhoods have radius  ...  We now establish the connection between shrinking formulas and the shrinking game. Proof. This is proved by induction on n.  ... 
doi:10.1016/j.apal.2004.01.004 fatcat:bse6muvh6vdlpluvvf6fqmqxii

Shrinking games and local formulas*1

H KEISLER
2004 Annals of Pure and Applied Logic  
We use Ehrenfeucht-Fra ssà e type games with a "shrinking horizon" to get a spectrum of normal form theorems of the Gaifman type, depending on the rate of shrinking.  ...  Gaifman's normal form theorem showed that every ÿrst-order sentence of quantiÿer rank n is equivalent to a Boolean combination of "scattered local sentences", where the local neighborhoods have radius  ...  We now establish the connection between shrinking formulas and the shrinking game. Proof. This is proved by induction on n.  ... 
doi:10.1016/s0168-0072(04)00002-8 fatcat:ddzl6xajyneevczewps2slxdry

Algorithm for overcoming the curse of dimensionality for certain non-convex Hamilton–Jacobi equations, projections and differential games

Yat Tin Chow, Jérôme Darbon, Stanley Osher, Wotao Yin
2018 Annals of Mathematical Sciences and Applications  
Our approach is expected to have wide applications in continuous dynamic games, control theory problems, and elsewhere. Mathematics Subject Classification (MSC2000):  ...  We extend previous work in [6] and apply the Hopf formula to solve HJ PDE involving non-convex Hamiltonians. We propose an ADMM approach for finding the minimizer associated with the Hopf formula.  ...  Since the shrink operators shrink p (x, α)(x) and shrink q (x, α)(x) are related to each other by (4.2) and (4.3), we can switch to the shrink operator that is easier to evaluate.  ... 
doi:10.4310/amsa.2018.v3.n2.a1 fatcat:dbs4vqozsjgitkkn7kai4vahom

Author Index

2004 Annals of Pure and Applied Logic  
, W.B., Shrinking games and local formulas (1-3) 215-225 Lotfallah, W.B., see Keisler, H.J. 1-3) 227-276 Wells, B., Erratum to ''Applying, extending, and specializing pseudorecursiveness'' [Ann.  ...  -101 Di Nola, A. and Grigolia, R., On monadic MV-algebras (1-3) 125-139 Feng, Q. and Jensen, R., Supercomplete extenders and type , S. and Nerode, A., Effective completeness theorems for modal logic (1  ... 
doi:10.1016/s0168-0072(04)00076-4 fatcat:q4btetraercjbe5mdfbszk6pbm

Research on the Positioning of Moving Nodes in Wireless Sensor Network Based on Vector Machine

Hongjuan Li
2016 International Journal of Hybrid Information Technology  
Based on the research to the mobile node positioning, this paper proposes position estimation method based on support vector machine (SVM) and game theory.  ...  From the mobile node localization effect, ranging error, anchor node distribution density and non-line-of-sight coefficient, simulation results illustrate that the algorithm of this paper can effectively  ...  But in order to avoid the maximum or minimum values in the game theory, k e shall be divided into two parts and be processed, then Formula (9) is as follows: 1 1 1 2 ( ) ( ) k k k k k k k k k k k k k k  ... 
doi:10.14257/ijhit.2016.9.5.18 fatcat:2wzs4qbiybbnjca3dfjnt3ccyy

Counting Bounded Tree Depth Homomorphisms [article]

Martin Grohe
2020 arXiv   pre-print
We prove that graphs G, G' satisfy the same sentences of first-order logic with counting of quantifier rank at most k if and only if they are homomorphism-indistinguishable over the class of all graphs  ...  In the k-round game, the play ends after k-rounds, and Duplicator wins the play if v k → v ′ k := (v i → v ′ i | 1 ≤ i ≤ k + ℓ) is a local isomorphism from G to G ′ , that is, for all i, j ∈ [ℓ + k] the  ...  It can be seen simultaneously as a locality theorem and as a quantifier elimination theorem.  ... 
arXiv:2003.08164v1 fatcat:xr3tgpnvmbd55dzq6bj7goqwcm

AI Science and Engineering

Longbing Cao
2022 IEEE Intelligent Systems  
This issue launches four new columns of IS this year: Editor's Perspective, AI Expert, AI Future, and AI Focus. AI Expert is edited by Fei-Yue Wang, and AI Future is edited by Michael Wooldridge.  ...  I then propose several AI formulas in terms of AI systems, goals and tasks, functions, and processes.  ...  the Tower of Hanoi problems in AI, game, and robotics.  ... 
doi:10.1109/mis.2022.3158785 fatcat:f6kc2oi4lngsnpk36m7g3hi62y

Uniform Substitution for Differential Game Logic [chapter]

André Platzer
2018 Lecture Notes in Computer Science  
After generalizing them to differential game logic and allowing for the substitution of hybrid games for game symbols, uniform substitutions make it possible to only use axioms instead of axiom schemata  ...  This paper presents a uniform substitution calculus for differential game logic (dGL). Church's uniform substitutions substitute a term or formula for a function or predicate symbol everywhere.  ...  Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  ... 
doi:10.1007/978-3-319-94205-6_15 fatcat:thomkfigonedtgnpxl4vuxuvra

Research on operational model of PUBG

Yong Ding, J. Heled, A. Yuan
2018 MATEC Web of Conferences  
situations the relationship between various factors and the result of game problem solving and plotting table.  ...  and the individual scores and rankings, distribution to determine the winners of the prize gaming contest.  ...  Acknowledgement The research was carried out by the science and technology project of Hubei Provincial Transport Department "the and exploration and practice of Chinese traditional Taoist philosophy cultural  ... 
doi:10.1051/matecconf/201817303062 fatcat:ga6l2pwpx5a23hzezrmmtqt7ca

Uniform Substitution at One Fell Swoop [chapter]

André Platzer
2019 Lecture Notes in Computer Science  
Uniform substitution of function, predicate, program or game symbols is the core operation in parsimonious provers for hybrid systems and hybrid games.  ...  The setting in this paper is that of differential hybrid games, in which discrete, continuous, and adversarial dynamics interact in differential game logic dGL.  ...  I thank Frank Pfenning for useful discussions and the anonymous reviewers for their helpful feedback.  ... 
doi:10.1007/978-3-030-29436-6_25 fatcat:2oqubcaiwfaqfns6ydaler2lt4

Global Migration Can Lead to Stronger Spatial Selection than Local Migration

Feng Fu, Martin A. Nowak
2012 Journal of statistical physics  
But it is largely unknown whether global or local migration leads to stronger spatial selection and would therefore favor to a larger extent the evolution of cooperation.  ...  We derive general results for weak selection and large population size. Our key parameters are: the number of islands, the migration rate and the mutation rate.  ...  R01GM078986), the Bill and Melinda Gates Foundation (Grand Challenges grant 37874), the National Institute on Aging (P01-AG031093) and the John Templeton Foundation.  ... 
doi:10.1007/s10955-012-0631-6 pmid:23853390 pmcid:PMC3706309 fatcat:oaxsbpz3kvha7dzrpgygiy2pjy

Anisotropic invasion and its consequences in two-strategy evolutionary games on a square lattice

György Szabó, Levente Varga, Mátyás Szabó
2016 Physical review. E  
In this parameter region faceted islands of both strategies shrink and the system evolves from a random initial state into the homogeneous state that first percolated.  ...  Monte Carlo simulations are performed for systems where the pair interactions are composed of a unit strength coordination game when varying the strengths of the self-dependent and cross-dependent components  ...  Subsequently, both types of domains shrink and vanish.  ... 
doi:10.1103/physreve.94.052314 pmid:27967092 fatcat:pkgu27nhcvhd5ashgzbrbwnjoi

A splitting method for overcoming the curse of dimensionality in Hamilton–Jacobi equations arising from nonlinear optimal control and differential games with applications to trajectory generation

Alex Tong Lin, Yat Tin Chow, Stanley J. Osher
2018 Communications in Mathematical Sciences  
Chambolle-Pock) to nonlinear optimal control and differential games problems, based on techniques from the derivation of the new Hopf and Lax formulas, which allow us to compute solutions at specified  ...  More recent observations were made in generalizing the Hopf and Lax formulas to state-and-time-dependent cases.  ...  Kirchner and Gary Hewer for their enlightening discussions and suggested edits during this work.  ... 
doi:10.4310/cms.2018.v16.n7.a9 fatcat:houhhjyd6rci5nengfzism62ii

Interpolating triangular meshes by Loop subdivision scheme

ChongYang Deng, GuoZhao Wang
2010 Science China Information Sciences  
Using the limit point formula of the Loop subdivision scheme, we propose a very simple and efficient method for constructing interpolation surface of triangular meshes by Loop subdivision scheme.  ...  The excellent properties of the method are: (1) Locality: the perturbation of a given vertex only influences the surface shape near this vertex. (2) Efficiency: the locations of new points can be computed  ...  Some movie productions and game engines, such as 3DMax, Maya, Renderman and Softimage, have the function of modeling surface by subdivision schemes [1] .  ... 
doi:10.1007/s11432-010-4049-y fatcat:oykpwxnvonf3becx6uvo2hfyqi

Uniform Substitution in One Fell Swoop [article]

André Platzer
2019 arXiv   pre-print
Uniform substitution of function, predicate, program or game symbols is the core operation in parsimonious provers for hybrid systems and hybrid games.  ...  The setting in this paper is that of differential hybrid games, in which discrete, continuous, and adversarial dynamics interact in differential game logic dGL.  ...  The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution  ... 
arXiv:1902.07230v2 fatcat:64aog4zzjzbetbkpdhfnvtgzdy
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