481 research outputs found
Exploiting Structure in Backtracking Algorithms for Propositional and Probabilistic Reasoning
Boolean propositional satisfiability (SAT) and probabilistic reasoning represent
two core problems in AI. Backtracking based algorithms have been applied in both
problems. In this thesis, I investigate structure-based techniques for solving real world
SAT and Bayesian networks, such as software testing and medical diagnosis instances.
When solving a SAT instance using backtracking search, a sequence of decisions
must be made as to which variable to branch on or instantiate next. Real world problems
are often amenable to a divide-and-conquer strategy where the original instance
is decomposed into independent sub-problems. Existing decomposition techniques
are based on pre-processing the static structure of the original problem. I propose
a dynamic decomposition method based on hypergraph separators. Integrating this
dynamic separator decomposition into the variable ordering of a modern SAT solver
leads to speedups on large real world SAT problems.
Encoding a Bayesian network into a CNF formula and then performing weighted
model counting is an effective method for exact probabilistic inference. I present two
encodings for improving this approach with noisy-OR and noisy-MAX relations. In
our experiments, our new encodings are more space efficient and can speed up the
previous best approaches over two orders of magnitude.
The ability to solve similar problems incrementally is critical for many probabilistic
reasoning problems. My aim is to exploit the similarity of these instances by
forwarding structural knowledge learned during the analysis of one instance to the
next instance in the sequence. I propose dynamic model counting and extend the dynamic
decomposition and caching technique to multiple runs on a series of problems
with similar structure. This allows us to perform Bayesian inference incrementally as
the evidence, parameter, and structure of the network change. Experimental results
show that my approach yields significant improvements over previous model counting
approaches on multiple challenging Bayesian network instances
Structure and Complexity in Planning with Unary Operators
Unary operator domains -- i.e., domains in which operators have a single
effect -- arise naturally in many control problems. In its most general form,
the problem of STRIPS planning in unary operator domains is known to be as hard
as the general STRIPS planning problem -- both are PSPACE-complete. However,
unary operator domains induce a natural structure, called the domain's causal
graph. This graph relates between the preconditions and effect of each domain
operator. Causal graphs were exploited by Williams and Nayak in order to
analyze plan generation for one of the controllers in NASA's Deep-Space One
spacecraft. There, they utilized the fact that when this graph is acyclic, a
serialization ordering over any subgoal can be obtained quickly. In this paper
we conduct a comprehensive study of the relationship between the structure of a
domain's causal graph and the complexity of planning in this domain. On the
positive side, we show that a non-trivial polynomial time plan generation
algorithm exists for domains whose causal graph induces a polytree with a
constant bound on its node indegree. On the negative side, we show that even
plan existence is hard when the graph is a directed-path singly connected DAG.
More generally, we show that the number of paths in the causal graph is closely
related to the complexity of planning in the associated domain. Finally we
relate our results to the question of complexity of planning with serializable
subgoals
09461 Abstracts Collection -- Algorithms and Applications for Next Generation SAT Solvers
From 8th to 13th November 2009, the Dagstuhl Seminar 09461 "Algorithms and Applications for Next Generation SAT Solvers" was held in Schloss Dagstuhl--Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts, slides or full papers are provided, if available
CP-nets: A Tool for Representing and Reasoning withConditional Ceteris Paribus Preference Statements
Information about user preferences plays a key role in automated decision
making. In many domains it is desirable to assess such preferences in a
qualitative rather than quantitative way. In this paper, we propose a
qualitative graphical representation of preferences that reflects conditional
dependence and independence of preference statements under a ceteris paribus
(all else being equal) interpretation. Such a representation is often compact
and arguably quite natural in many circumstances. We provide a formal semantics
for this model, and describe how the structure of the network can be exploited
in several inference tasks, such as determining whether one outcome dominates
(is preferred to) another, ordering a set outcomes according to the preference
relation, and constructing the best outcome subject to available evidence
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