5,648 research outputs found
The Good Old Davis-Putnam Procedure Helps Counting Models
As was shown recently, many important AI problems require counting the number
of models of propositional formulas. The problem of counting models of such
formulas is, according to present knowledge, computationally intractable in a
worst case. Based on the Davis-Putnam procedure, we present an algorithm, CDP,
that computes the exact number of models of a propositional CNF or DNF formula
F. Let m and n be the number of clauses and variables of F, respectively, and
let p denote the probability that a literal l of F occurs in a clause C of F,
then the average running time of CDP is shown to be O(nm^d), where
d=-1/log(1-p). The practical performance of CDP has been estimated in a series
of experiments on a wide variety of CNF formulas
Good Learning and Implicit Model Enumeration
MathSBML is an open-source, freely-downloadable Mathematica package that facilitates working with Systems Biology Markup Language (SBML) models. SBML is a toolneutral,computer-readable format for representing models of biochemical reaction networks, applicable to metabolic networks, cell-signaling pathways, genomic regulatory networks, and other modeling problems in systems biology that is widely supported by the systems biology community. SBML is based on XML, a standard medium for representing and transporting data that is widely supported on the internet as well as in computational biology and bioinformatics. Because SBML is tool-independent, it enables model transportability, reuse, publication and survival. In addition to MathSBML, a number of other tools that support SBML model examination and manipulation are provided on the sbml.org website, including libSBML, a C/C++ library for reading SBML models; an SBML Toolbox for MatLab; file conversion programs; an SBML model validator and visualizer; and SBML specifications and schemas. MathSBML enables SBML file import to and export from Mathematica as well as providing an API for model manipulation and simulation
Bit-Vector Model Counting using Statistical Estimation
Approximate model counting for bit-vector SMT formulas (generalizing \#SAT)
has many applications such as probabilistic inference and quantitative
information-flow security, but it is computationally difficult. Adding random
parity constraints (XOR streamlining) and then checking satisfiability is an
effective approximation technique, but it requires a prior hypothesis about the
model count to produce useful results. We propose an approach inspired by
statistical estimation to continually refine a probabilistic estimate of the
model count for a formula, so that each XOR-streamlined query yields as much
information as possible. We implement this approach, with an approximate
probability model, as a wrapper around an off-the-shelf SMT solver or SAT
solver. Experimental results show that the implementation is faster than the
most similar previous approaches which used simpler refinement strategies. The
technique also lets us model count formulas over floating-point constraints,
which we demonstrate with an application to a vulnerability in differential
privacy mechanisms
Bulletin of the Center for Children's Books 13 (07) 1960
published or submitted for publicatio
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