41 research outputs found
Probabilistic Logic Programming with Beta-Distributed Random Variables
We enable aProbLog---a probabilistic logical programming approach---to reason
in presence of uncertain probabilities represented as Beta-distributed random
variables. We achieve the same performance of state-of-the-art algorithms for
highly specified and engineered domains, while simultaneously we maintain the
flexibility offered by aProbLog in handling complex relational domains. Our
motivation is that faithfully capturing the distribution of probabilities is
necessary to compute an expected utility for effective decision making under
uncertainty: unfortunately, these probability distributions can be highly
uncertain due to sparse data. To understand and accurately manipulate such
probability distributions we need a well-defined theoretical framework that is
provided by the Beta distribution, which specifies a distribution of
probabilities representing all the possible values of a probability when the
exact value is unknown.Comment: Accepted for presentation at AAAI 201
Model Counting for Formulas of Bounded Clique-Width
We show that #SAT is polynomial-time tractable for classes of CNF formulas
whose incidence graphs have bounded symmetric clique-width (or bounded
clique-width, or bounded rank-width). This result strictly generalizes
polynomial-time tractability results for classes of formulas with signed
incidence graphs of bounded clique-width and classes of formulas with incidence
graphs of bounded modular treewidth, which were the most general results of
this kind known so far.Comment: Extended version of a paper published at ISAAC 201
Quantum Weighted Model Counting
In Weighted Model Counting (WMC) we assign weights to Boolean literals and we
want to compute the sum of the weights of the models of a Boolean function
where the weight of a model is the product of the weights of its literals. WMC
was shown to be particularly effective for performing inference in graphical
models, with a complexity of where is the number of variables and
is the treewidth. In this paper, we propose a quantum algorithm for
performing WMC, Quantum WMC (QWMC), that modifies the quantum model counting
algorithm to take into account the weights. In turn, the model counting
algorithm uses the algorithms of quantum search, phase estimation and Fourier
transform. In the black box model of computation, where we can only query an
oracle for evaluating the Boolean function given an assignment, QWMC solves the
problem approximately with a complexity of oracle
calls while classically the best complexity is , thus achieving a
quadratic speedup