All-SAT Using Minimal Blocking Clauses

Author(s):  
Yinlei Yu ◽  
Pramod Subramanyan ◽  
Nestan Tsiskaridze ◽  
Sharad Malik
Keyword(s):  
2007 ◽  
Vol 19 (3) ◽  
pp. 99-111
Author(s):  
L.Yasin Nada Yassen Kasm Yahya ◽  
Abdul Khalik

2011 ◽  
Vol 19 (4) ◽  
pp. 313-316 ◽  
Author(s):  
Antonio Cossidente ◽  
Oliver H. King

2003 ◽  
Vol 11 (3) ◽  
pp. 162-169 ◽  
Author(s):  
J. Barát ◽  
S. Innamorati

10.37236/5717 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Jan De Beule ◽  
Tamás Héger ◽  
Tamás Szőnyi ◽  
Geertrui Van de Voorde

In this paper, by using properties of Baer subplanes, we describe the construction of a minimal blocking set in the Hall plane of order $q^2$ of size $q^2+2q+2$ admitting $1-$, $2-$, $3-$, $4-$, $(q+1)-$ and $(q+2)-$secants. As a corollary, we obtain the existence of a minimal blocking set of a non-Desarguesian affine plane of order $q^2$ of size at most $4q^2/3+5q/3$, which is considerably smaller than $2q^2-1$, the Jamison bound for the size of a minimal blocking set in an affine Desarguesian plane of order $q^2$.We also consider particular André planes of order $q$, where $q$ is a power of the prime $p$, and give a construction of a small minimal blocking set which admits a secant line not meeting the blocking set in $1$ mod $p$ points. Furthermore, we elaborate on the connection of this problem with the study of value sets of certain polynomials and with the construction of small double blocking sets in Desarguesian projective planes; in both topics we provide some new results.


2007 ◽  
Vol 44 (4) ◽  
pp. 852-864 ◽  
Author(s):  
Josep Freixas

Owen's multilinear extension (MLE) of a game is a very important tool in game theory and particularly in the field of simple games. Among other applications it serves to efficiently compute several solution concepts. In this paper we provide bounds for the MLE. Apart from its self-contained theoretical interest, the bounds offer the means in voting system studies of approximating the probability that a proposal is approved in a particular simple game having a complex component arrangement. The practical interest of the bounds is that they can be useful for simple games having a tedious MLE to evaluate exactly, but whose minimal winning coalitions and minimal blocking coalitions can be determined by inspection. Such simple games are quite numerous.


10.37236/446 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
G. Van De Voorde

A small minimal $k$-blocking set $B$ in $\mathrm{PG}(n,q)$, $q=p^t$, $p$ prime, is a set of less than $3(q^k+1)/2$ points in $\mathrm{PG}(n,q)$, such that every $(n-k)$-dimensional space contains at least one point of $B$ and such that no proper subset of $B$ satisfies this property. The linearity conjecture states that all small minimal $k$-blocking sets in $\mathrm{PG}(n,q)$ are linear over a subfield $\mathbb{F}_{p^e}$ of $\mathbb{F}_q$. Apart from a few cases, this conjecture is still open. In this paper, we show that to prove the linearity conjecture for $k$-blocking sets in $\mathrm{PG}(n,p^t)$, with exponent $e$ and $p^e\geq 7$, it is sufficient to prove it for one value of $n$ that is at least $2k$. Furthermore, we show that the linearity of small minimal blocking sets in $\mathrm{PG}(2,q)$ implies the linearity of small minimal $k$-blocking sets in $\mathrm{PG}(n,p^t)$, with exponent $e$, with $p^e\geq t/e+11$.


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