We show that circuit lower bound proofs based on the method of random restrictions yield non-trivial
compression algorithms
for “easy” Boolean functions from the corresponding circuit classes. The ...compression problem is defined as follows: given the truth table of an
n
-variate Boolean function
f
computable by some
unknown small circuit
from a
known class
of circuits, find in deterministic time poly(2
n
) a circuit
C
(no restriction on the type of
C
) computing
f
so that the size of
C
is less than the trivial circuit size
2
n
/
n
. We get non-trivial compression for functions computable by AC
0
circuits, (de Morgan) formulas, and (read-once) branching programs of the size for which the lower bounds for the corresponding circuit class are known.
These compression algorithms rely on the structural characterizations of “easy” functions, which are useful both for proving circuit lower bounds and for designing “meta-algorithms” (such as Circuit-SAT). For (de Morgan) formulas, such structural characterization is provided by the “shrinkage under random restrictions” results by Subbotovskaya (Doklady Akademii Nauk SSSR 136(3):553–555,
1961
) and Håstad (SIAM J Comput 27:48–64,
1998
), strengthened to the “high-probability” version by Santhanam (Proceedings of the Fifty-First Annual IEEE Symposium on Foundations of Computer Science, pp 183–192,
2010
), Impagliazzo, Meka & Zuckerman (Proceedings of the Fifty-Third Annual IEEE Symposium on Foundations of Computer Science, pp 111–119,
2012b
), and Komargodski & Raz (Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, pp 171–180,
2013
). We give a new, simple proof of the “high-probability” version of the shrinkage result for (de Morgan) formulas, with improved parameters. We use this shrinkage result to get both compression and #SAT algorithms for (de Morgan) formulas of size about
n
2
. We also use this shrinkage result to get an alternative proof of the result by Komargodski & Raz (Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, pp 171–180,
2013
) of the average-case lower bound against small (de Morgan) formulas.
Finally, we show that the existence of any non-trivial compression algorithm for a circuit class
C
⊆
P
/
poly
would imply the circuit lower bound
NEXP
⊈
C
; a similar implication is independently proved also by Williams (Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, pp 21–30,
2013
). This complements the result by Williams (Proceedings of the Forty-Second Annual ACM Symposium on Theory of Computing, pp 231–240,
2010
) that any non-trivial Circuit-SAT algorithm for a circuit class
C
would imply a superpolynomial lower bound against
C
for a language in NEXP.
This study develops a sequential game between the incumbent and the intruder to examine how endowment effect decides natural property rights of a territory without third-party intervention.
•It is a ...sequential game that links endowment effect with natural property rights.•Natural property rights is jointly decided by endowment effect and relative contestability.•Abundant idle resources helps to secure natural property rights.•Third-party help is needed when the intruder significantly dominates in contestability.
The distinction World Heritage, granted by UNESCO, has become a quality hallmark of cultural tourism and nature for its international relevance. Since its establishment in 1978, have registered 1007 ...sites of cultural, natural or mixed type. In the case of Ibiza, after a first failed attempt in 1986, in 1998 a new project improved as indicated by the Committee was submitted. In 1999, he was enrolled the set called "Ibiza, Biodiversity and Culture", consisting of the protected property of the fortification city of Ibiza (Dalt Vila), the Phoenician-Punic necropolis of Puig des Molins, the Phoenician settlement of Sa Caleta and prairies of oceanic Posidonia located within the Natural Reserve of ses Salines, between Ibiza and Formentera. Since then there have been important actions, such as the restoration and musealization of the walls, and signaling properties inscribed and buffer zones. But some confusion, especially in communication, and a need for improvement in the design of attractive tourist products containing World Heritage elements are detected. The tourism promotion is very focused on Ibiza as World Heritage city, when it’s a mixed site formed by a part of the old town and items in other locations, both cultural (sa Caleta) as natural (prairies of Posidonia). The relative neglect of the natural part was remembered by UNESCO in reports of 2009, 2010 and 2011.
La distinción Patrimonio Mundial, concedida por la UNESCO, se ha convertido en un sello de calidad del turismo cultural y de naturaleza por su relevancia internacional. Desde su establecimiento en 1978, se han inscrito 1007 lugares de tipo cultural, natural o mixto. En el caso de Ibiza, tras un primer intento fallido en 1986, en 1998 se presentó un nuevo proyecto mejorado según las indicaciones del Comité. En 1999, fue inscrito el conjunto denominado “Ibiza, Biodiversidad y Cultura”, formado por los bienes protegidos de la ciudad amurallada de Ibiza (Dalt Vila), la necrópolis fenicio-púnica de Puig des Molins, el asentamiento fenicio de sa Caleta y las praderas de posidonia oceánica situadas dentro de la Reserva Natural de ses Salines, entre Ibiza y Formentera. Desde entonces se han realizado importantes acciones, como la restauración y musealización de las murallas, y la señalización de los bienes inscritos y de las zonas de protección. Pero se detectan algunas confusiones, principalmente en la comunicación, y una necesidad de mejora en el diseño de productos turísticos atractivos que contengan los elementos declarados Patrimonio Mundial. La promoción turística está muy centrada en Ibiza como ciudad Patrimonio Mundial, cuando se trata de un emplazamiento mixto formado por una parte de la ciudad antigua y elementos en otras localizaciones, tanto culturales (sa Caleta) como naturales (praderas de Posidonia). El relativo abandono de la parte natural fue recordado por la UNESCO en informes de 2009, 2010 y 2011.
We show that circuit lower bound proofs based on the method of random restrictions yield non-trivial compression algorithms for "easy" Boolean functions from the corresponding circuit classes. The ...compression problem is defined as follows: given the truth table of an n-variate Boolean function f computable by some unknown small circuit from a known class of circuits, find in deterministic time poly(2 n ) a circuit C (no restriction on the type of C) computing f so that the size of C is less than the trivial circuit size 2 n /n. We get nontrivial compression for functions computable by AC 0 circuits, (de Morgan) formulas, and (read-once) branching programs of the size for which the lower bounds for the corresponding circuit class are known. These compression algorithms rely on the structural characterizations of "easy" functions, which are useful both for proving circuit lower bounds and for designing "meta-algorithms" (such as Circuit-SAT). For (de Morgan) formulas, such structural characterization is provided by the "shrinkage under random restrictions" results 52, 21, strengthened to the "high-probability" version by 48, 26, 33. We give a new, simple proof of the "high-probability" version of the shrinkage result for (de Morgan) formulas, with improved parameters. We use this shrinkage result to get both compression and #SAT algorithms for (de Morgan) formulas of size about n 2 . We also use this shrinkage result to get an alternative proof of the recent result by Komargodski and Raz 33 of the average-case lower bound against small (de Morgan) formulas. Finally, we show that the existence of any non-trivial compression algorithm for a circuit class C ⊆ P/poly would imply the circuit lower bound NEXP ⊈ C. This complements Williams's result 55 that any non-trivial Circuit-SAT algorithm for a circuit class C would imply a superpolynomial lower bound against C for a language in NEXP1.
The first section presents three ways of conceiving dignity ontologically: as a natural property, as a nonnatural property, or as a conferred social status. It is then argued that, regardless of ...which ontology of dignity one adopts, if one wants to address practical issues of how our actions affect or accord with dignity, dignity must be discussed in terms of some set of natural properties. In the second section it is suggested that the natural properties corresponding to human dignity should be seen as our capacities to create meaningful lives for ourselves. In the remaining sections, three challenging conditions associated with aging are discussed – dependency, dementia, and dying – along with the obstacles and opportunities each presents for the creation and expression of meaning.
The French costline, fragile space, subject of conflicts in differents ways, above all for its use, needs protection and development, that is challenge. We need to achieve a balance between ...environmental protection and business activities related with water. So the protection must be against natural hazards and against hazards liked with human activities.
El litoral francés, objeto de numerosos conflictos en cuanto a su uso, es un territorio delicado cuyo desarrollo equilibrado constituye un reto. Se necesita conseguir un equilibrio entre la conservación del medioambiente y el desarrollo de actividades económicas relacionadas con el agua, es decir proteger le frente a dos tipos de peligros: los riesgos de origen humano y los riesgos naturales.
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