5,385 research outputs found
Oblivious Bounds on the Probability of Boolean Functions
This paper develops upper and lower bounds for the probability of Boolean
functions by treating multiple occurrences of variables as independent and
assigning them new individual probabilities. We call this approach dissociation
and give an exact characterization of optimal oblivious bounds, i.e. when the
new probabilities are chosen independent of the probabilities of all other
variables. Our motivation comes from the weighted model counting problem (or,
equivalently, the problem of computing the probability of a Boolean function),
which is #P-hard in general. By performing several dissociations, one can
transform a Boolean formula whose probability is difficult to compute, into one
whose probability is easy to compute, and which is guaranteed to provide an
upper or lower bound on the probability of the original formula by choosing
appropriate probabilities for the dissociated variables. Our new bounds shed
light on the connection between previous relaxation-based and model-based
approximations and unify them as concrete choices in a larger design space. We
also show how our theory allows a standard relational database management
system (DBMS) to both upper and lower bound hard probabilistic queries in
guaranteed polynomial time.Comment: 34 pages, 14 figures, supersedes: http://arxiv.org/abs/1105.281
Tight polynomial worst-case bounds for loop programs
In 2008, Ben-Amram, Jones and Kristiansen showed that for a simple programming language - representing non-deterministic imperative programs with bounded loops, and arithmetics limited to addition and multiplication - it is possible to decide precisely whether a program has certain growth-rate properties, in particular whether a computed value, or the program's running time, has a polynomial growth rate. A natural and intriguing problem was to move from answering the decision problem to giving a quantitative result, namely, a tight polynomial upper bound. This paper shows how to obtain asymptotically-tight, multivariate, disjunctive polynomial bounds for this class of programs. This is a complete solution: whenever a polynomial bound exists it will be found. A pleasant surprise is that the algorithm is quite simple; but it relies on some subtle reasoning. An important ingredient in the proof is the forest factorization theorem, a strong structural result on homomorphisms into a finite monoid
Construction of aggregation operators with noble reinforcement
This paper examines disjunctive aggregation operators used in various recommender systems. A specific requirement in these systems is the property of noble reinforcement: allowing a collection of high-valued arguments to reinforce each other while avoiding reinforcement of low-valued arguments. We present a new construction of Lipschitz-continuous aggregation operators with noble reinforcement property and its refinements. <br /
Symmetric Disjunctive List-Decoding Codes
A binary code is said to be a disjunctive list-decoding -code (LD
-code), , , if the code is identified by the incidence
matrix of a family of finite sets in which the union (or disjunctive sum) of
any sets can cover not more than other sets of the family. In this
paper, we consider a similar class of binary codes which are based on a {\em
symmetric disjunctive sum} (SDS) of binary symbols. By definition, the
symmetric disjunctive sum (SDS) takes values from the ternary alphabet , where the symbol~ denotes "erasure". Namely: SDS is equal to ()
if all its binary symbols are equal to (), otherwise SDS is equal
to~. List decoding codes for symmetric disjunctive sum are said to be {\em
symmetric disjunctive list-decoding -codes} (SLD -codes). In the
given paper, we remind some applications of SLD -codes which motivate the
concept of symmetric disjunctive sum. We refine the known relations between
parameters of LD -codes and SLD -codes. For the ensemble of binary
constant-weight codes we develop a random coding method to obtain lower bounds
on the rate of these codes. Our lower bounds improve the known random coding
bounds obtained up to now using the ensemble with independent symbols of
codewords.Comment: 18 pages, 1 figure, 1 table, conference pape
Reliability of systems with dependent components based on lattice polynomial description
Reliability of a system is considered where the components' random lifetimes
may be dependent. The structure of the system is described by an associated
"lattice polynomial" function. Based on that descriptor, general framework
formulas are developed and used to obtain direct results for the cases where a)
the lifetimes are "Bayes-dependent", that is, their interdependence is due to
external factors (in particular, where the factor is the "preliminary phase"
duration) and b) where the lifetimes' dependence is implied by upper or lower
bounds on lifetimes of components in some subsets of the system. (The bounds
may be imposed externally based, say, on the connections environment.) Several
special cases are investigated in detail
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