45,125 research outputs found
Achieving New Upper Bounds for the Hypergraph Duality Problem through Logic
The hypergraph duality problem DUAL is defined as follows: given two simple
hypergraphs and , decide whether
consists precisely of all minimal transversals of (in which case
we say that is the dual of ). This problem is
equivalent to deciding whether two given non-redundant monotone DNFs are dual.
It is known that non-DUAL, the complementary problem to DUAL, is in
, where
denotes the complexity class of all problems that after a nondeterministic
guess of bits can be decided (checked) within complexity class
. It was conjectured that non-DUAL is in . In this paper we prove this conjecture and actually
place the non-DUAL problem into the complexity class which is a subclass of . We here refer to the logtime-uniform version of
, which corresponds to , i.e., first order
logic augmented by counting quantifiers. We achieve the latter bound in two
steps. First, based on existing problem decomposition methods, we develop a new
nondeterministic algorithm for non-DUAL that requires to guess
bits. We then proceed by a logical analysis of this algorithm, allowing us to
formulate its deterministic part in . From this result, by
the well known inclusion , it follows
that DUAL belongs also to . Finally, by exploiting
the principles on which the proposed nondeterministic algorithm is based, we
devise a deterministic algorithm that, given two hypergraphs and
, computes in quadratic logspace a transversal of
missing in .Comment: Restructured the presentation in order to be the extended version of
a paper that will shortly appear in SIAM Journal on Computin
Social Preferences, Skill Segregation and Wage Dynamics
We study the earning structure and the equilibrium asignment of workers to firms in a model in which workers have social preferences, and skills are perfectly substitutable in production. Firms offer long-term contracts, and we allow for frictions in the labour market in the form of mobility costs. The model delivers specific predictions about the nature of worker flows, about the characteristic of workplace skill segregation, and about wage dispersion both within and cross firms. We shows that long-term contracts in the resence of social preferences associate within-firm wage dispersion with novel "internal labour market" features such as gradual promotions, productivity-unrelated wage increases, and downward wage flexibility. These three dynamic features lead to productivity-unrelated wage volatily within firms.Publicad
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