1,126 research outputs found
Average Degree in the Interval Graph of a Random Boolean Function
We consider an n-ary random Boolean function f such that for and study its geometric model, the so called interval graph. The interval graph of a Boolean function was introduced by Sapozhenko and has been used in construction of schemes realizing Boolean functions. Using this model, we estimate the number of maximal intervals intersecting a given maximal interval of a random Boolean function and prove that the asymptotic bound on the logarithm of the number is , where ?(n) ? 0 as
Using data-driven rules to predict mortality in severe community acquired pneumonia
Prediction of patient-centered outcomes in hospitals is useful for performance benchmarking, resource allocation, and guidance regarding active treatment and withdrawal of care. Yet, their use by clinicians is limited by the complexity of available tools and amount of data required. We propose to use Disjunctive Normal Forms as a novel approach to predict hospital and 90-day mortality from instance-based patient data, comprising demographic, genetic, and physiologic information in a large cohort of patients admitted with severe community acquired pneumonia. We develop two algorithms to efficiently learn Disjunctive Normal Forms, which yield easy-to-interpret rules that explicitly map data to the outcome of interest. Disjunctive Normal Forms achieve higher prediction performance quality compared to a set of state-of-the-art machine learning models, and unveils insights unavailable with standard methods. Disjunctive Normal Forms constitute an intuitive set of prediction rules that could be easily implemented to predict outcomes and guide criteria-based clinical decision making and clinical trial execution, and thus of greater practical usefulness than currently available prediction tools. The Java implementation of the tool JavaDNF will be publicly available. © 2014 Wu et al
The Connectivity of Boolean Satisfiability: Dichotomies for Formulas and Circuits
For Boolean satisfiability problems, the structure of the solution space is
characterized by the solution graph, where the vertices are the solutions, and
two solutions are connected iff they differ in exactly one variable. In 2006,
Gopalan et al. studied connectivity properties of the solution graph and
related complexity issues for CSPs, motivated mainly by research on
satisfiability algorithms and the satisfiability threshold. They proved
dichotomies for the diameter of connected components and for the complexity of
the st-connectivity question, and conjectured a trichotomy for the connectivity
question. Recently, we were able to establish the trichotomy [arXiv:1312.4524].
Here, we consider connectivity issues of satisfiability problems defined by
Boolean circuits and propositional formulas that use gates, resp. connectives,
from a fixed set of Boolean functions. We obtain dichotomies for the diameter
and the two connectivity problems: on one side, the diameter is linear in the
number of variables, and both problems are in P, while on the other side, the
diameter can be exponential, and the problems are PSPACE-complete. For
partially quantified formulas, we show an analogous dichotomy.Comment: 20 pages, several improvement
Polynomial-time algorithms for generation of prime implicants
AbstractA notion of a neighborhood cube of a term of a Boolean function represented in the canonical disjunctive normal form is introduced. A relation between neighborhood cubes and prime implicants of a Boolean function is established. Various aspects of the problem of prime implicants generation are identified and neighborhood cube-based algorithms for their solution are developed. The correctness of algorithms is proven and their time complexity is analyzed. It is shown that all presented algorithms are polynomial in the number of minterms occurring in the canonical disjunctive normal form representation of a Boolean function. A summary of the known approaches to the solution of the problem of the generation of prime implicants is also included
Testing systems of identical components
We consider the problem of testing sequentially the components of a multi-component reliability system in order to figure out the state of the system via costly tests. In particular, systems with identical components are considered. The notion of lexicographically large binary decision trees is introduced and a heuristic algorithm based on that notion is proposed. The performance of the heuristic algorithm is demonstrated by computational results, for various classes of functions. In particular, in all 200 random cases where the underlying function is a threshold function, the proposed heuristic produces optimal solutions
Answer Set Planning Under Action Costs
Recently, planning based on answer set programming has been proposed as an
approach towards realizing declarative planning systems. In this paper, we
present the language Kc, which extends the declarative planning language K by
action costs. Kc provides the notion of admissible and optimal plans, which are
plans whose overall action costs are within a given limit resp. minimum over
all plans (i.e., cheapest plans). As we demonstrate, this novel language allows
for expressing some nontrivial planning tasks in a declarative way.
Furthermore, it can be utilized for representing planning problems under other
optimality criteria, such as computing ``shortest'' plans (with the least
number of steps), and refinement combinations of cheapest and fastest plans. We
study complexity aspects of the language Kc and provide a transformation to
logic programs, such that planning problems are solved via answer set
programming. Furthermore, we report experimental results on selected problems.
Our experience is encouraging that answer set planning may be a valuable
approach to expressive planning systems in which intricate planning problems
can be naturally specified and solved
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