25,180 research outputs found
Generalized Totalizer Encoding for Pseudo-Boolean Constraints
Pseudo-Boolean constraints, also known as 0-1 Integer Linear Constraints, are
used to model many real-world problems. A common approach to solve these
constraints is to encode them into a SAT formula. The runtime of the SAT solver
on such formula is sensitive to the manner in which the given pseudo-Boolean
constraints are encoded. In this paper, we propose generalized Totalizer
encoding (GTE), which is an arc-consistency preserving extension of the
Totalizer encoding to pseudo-Boolean constraints. Unlike some other encodings,
the number of auxiliary variables required for GTE does not depend on the
magnitudes of the coefficients. Instead, it depends on the number of distinct
combinations of these coefficients. We show the superiority of GTE with respect
to other encodings when large pseudo-Boolean constraints have low number of
distinct coefficients. Our experimental results also show that GTE remains
competitive even when the pseudo-Boolean constraints do not have this
characteristic.Comment: 10 pages, 2 figures, 2 tables. To be published in 21st International
Conference on Principles and Practice of Constraint Programming 201
Rational Deployment of CSP Heuristics
Heuristics are crucial tools in decreasing search effort in varied fields of
AI. In order to be effective, a heuristic must be efficient to compute, as well
as provide useful information to the search algorithm. However, some well-known
heuristics which do well in reducing backtracking are so heavy that the gain of
deploying them in a search algorithm might be outweighed by their overhead.
We propose a rational metareasoning approach to decide when to deploy
heuristics, using CSP backtracking search as a case study. In particular, a
value of information approach is taken to adaptive deployment of solution-count
estimation heuristics for value ordering. Empirical results show that indeed
the proposed mechanism successfully balances the tradeoff between decreasing
backtracking and heuristic computational overhead, resulting in a significant
overall search time reduction.Comment: 7 pages, 2 figures, to appear in IJCAI-2011, http://www.ijcai.org
Logic Programming as Constructivism
The features of logic programming that
seem unconventional from the viewpoint of classical logic
can be explained in terms of constructivistic logic. We
motivate and propose a constructivistic proof theory of
non-Horn logic programming. Then, we apply this formalization
for establishing results of practical interest.
First, we show that 'stratification can be motivated in a
simple and intuitive way. Relying on similar motivations,
we introduce the larger classes of 'loosely stratified' and
'constructively consistent' programs. Second, we give a
formal basis for introducing quantifiers into queries and
logic programs by defining 'constructively domain
independent* formulas. Third, we extend the Generalized
Magic Sets procedure to loosely stratified and constructively
consistent programs, by relying on a 'conditional
fixpoini procedure
Guarantees and Limits of Preprocessing in Constraint Satisfaction and Reasoning
We present a first theoretical analysis of the power of polynomial-time
preprocessing for important combinatorial problems from various areas in AI. We
consider problems from Constraint Satisfaction, Global Constraints,
Satisfiability, Nonmonotonic and Bayesian Reasoning under structural
restrictions. All these problems involve two tasks: (i) identifying the
structure in the input as required by the restriction, and (ii) using the
identified structure to solve the reasoning task efficiently. We show that for
most of the considered problems, task (i) admits a polynomial-time
preprocessing to a problem kernel whose size is polynomial in a structural
problem parameter of the input, in contrast to task (ii) which does not admit
such a reduction to a problem kernel of polynomial size, subject to a
complexity theoretic assumption. As a notable exception we show that the
consistency problem for the AtMost-NValue constraint admits a polynomial kernel
consisting of a quadratic number of variables and domain values. Our results
provide a firm worst-case guarantees and theoretical boundaries for the
performance of polynomial-time preprocessing algorithms for the considered
problems.Comment: arXiv admin note: substantial text overlap with arXiv:1104.2541,
arXiv:1104.556
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