scholarly journals Strategic Reasoning with a Bounded Number of Resources: the Quest for Tractability

2021 ◽  
pp. 103557
Author(s):  
Francesco Belardinelli ◽  
Stéphane Demri
Keyword(s):  
Strategic Reasoning ◽  
Bounded Number

scholarly journals Clustered 3-colouring graphs of bounded degree

2021 ◽  
pp. 1-13
Author(s):  
Vida Dujmović ◽  
Louis Esperet ◽  
Pat Morin ◽  
Bartosz Walczak ◽  
David R. Wood
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Bounded Degree ◽  
Bounded Number ◽  
Proper Vertex ◽  
Vertex Colouring

Abstract A (not necessarily proper) vertex colouring of a graph has clustering c if every monochromatic component has at most c vertices. We prove that planar graphs with maximum degree $\Delta$ are 3-colourable with clustering $O(\Delta^2)$ . The previous best bound was $O(\Delta^{37})$ . This result for planar graphs generalises to graphs that can be drawn on a surface of bounded Euler genus with a bounded number of crossings per edge. We then prove that graphs with maximum degree $\Delta$ that exclude a fixed minor are 3-colourable with clustering $O(\Delta^5)$ . The best previous bound for this result was exponential in $\Delta$ .

The Equational Specification of Finite Minimal Unoids Using only Unary Hidden Functions

1982 ◽  
Vol 5 (2) ◽  
pp. 143-170
Author(s):  
Jan A. Bergstra ◽  
John-Jules Ch. Meyer
Keyword(s):  
Data Type ◽  
Bounded Number ◽  
Special Case ◽  
Finite Data

In [5] it has been proved that by using hidden functions the number of equations needed to specify a finite data type is bounded by numbers depending only on the signature of that data type. In the special case of a finite minimal unoid, however, it seems to be relevant to ask whether or not a specification can also be made by a bounded number of equations using only unary hidden functions. In this paper we prove that this can be done.

Deterrence

1989 ◽  
Vol 15 (1) ◽  
pp. 67-74 ◽  
Author(s):  
Charles Reynolds
Keyword(s):  
Professional Status ◽  
Strategic Reasoning ◽  
Theory To Practice ◽  
Theoretical Status

These three books cover the gamut of argument about deterrence, ranging from its politics to its theoretical status and its morality. The authors, while diverse in their professional status, being government 'experts', lawyers, theologians, political scientists and philosophers, all have this in common: they seek to tell us what to do. They attempt to relate theory to practice either to justify instrumental means or goals or to prescribe them. In this sense they are all contributors to the field of strategic reasoning.

The role of hindsight in foresight: refining strategic reasoning

Futures ◽  
2004 ◽  
Vol 36 (2) ◽  
pp. 161-179 ◽  
Author(s):  
R.Bradley MacKay ◽  
Peter McKiernan
Keyword(s):  
Strategic Reasoning

scholarly journals Extrema of Low Eigenvalues of the Dirichlet–Neumann Laplacian on a Disk

2010 ◽  
Vol 62 (4) ◽  
pp. 808-826
Author(s):  
Eveline Legendre
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Neumann Boundary ◽  
Mixed Boundary Conditions ◽  
First Eigenvalue ◽  
Bounded Number ◽  
Eigenvalues Of The Laplacian ◽  
Neumann Laplacian ◽  
Dirichlet And Neumann Conditions ◽  
Second Eigenvalue

AbstractWe study extrema of the first and the second mixed eigenvalues of the Laplacian on the disk among some families of Dirichlet–Neumann boundary conditions. We show that the minimizer of the second eigenvalue among all mixed boundary conditions lies in a compact 1-parameter family for which an explicit description is given. Moreover, we prove that among all partitions of the boundary with bounded number of parts on which Dirichlet and Neumann conditions are imposed alternately, the first eigenvalue is maximized by the uniformly distributed partition.

scholarly journals Distribution of Variables in Lambda-Terms with Restrictions on De Bruijn Indices and De Bruijn Levels

10.37236/8579 ◽  
2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Bernhard Gittenberger ◽  
Isabella Larcher
Keyword(s):  
The Other ◽  
Bounded Number ◽  
Mean And Variance ◽  
De Bruijn ◽  
De Bruijn Indices ◽  
Strange Phenomenon ◽  
Normally Distributed

We consider two special subclasses of lambda-terms that are restricted by a bound on the number of abstractions between a variable and its binding lambda, the so-called De-Bruijn index, or by a bound on the nesting levels of abstractions, i.e., the number of De Bruijn levels, respectively. We show that the total number of variables is asymptotically normally distributed for both subclasses of lambda-terms with mean and variance asymptotically equal to $Cn$ and $\tilde{C}n$, respectively, where the constants $C$ and $\tilde{C}$ depend on the bound that has been imposed. For the class of lambda-terms with bounded De Bruijn index we derive closed formulas for the constant. For the other class of lambda-terms that we consider, namely lambda-terms with a bounded number of De Bruijn levels, we show quantitative and distributional results on the number of variables, as well as abstractions and applications, in the different De Bruijn levels and thereby exhibit a so-called "unary profile" that attains a very interesting shape.  Our results give a combinatorial explanation of an earlier discovered strange phenomenon exhibited by the counting sequence of this particular class of lambda-terms. 

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