4,783 research outputs found
The role of working memory and contextual constraints in children's processing of relative clauses
An auditory sentence comprehension task investigated the extent to which the integration of contextual and structural cues was mediated by verbal memory span with 32 English-speaking 6- to 8-year old children. Spoken relative clause sentences were accompanied by visual context pictures which fully (depicting the actions described within the relative clause) or partially (depicting several referents) met the pragmatic assumptions of relativisation. Comprehension of the main and relative clauses of centre-embedded and right-branching structures was compared for each context. Pragmatically-appropriate contexts exerted a positive effect on relative clause comprehension, but children with higher memory spans demonstrated a further benefit for main clauses. Comprehension for centre-embedded main clauses was found to be very poor, independently of either context or memory span. The results suggest that children have access to adult-like linguistic processing mechanisms, and that sensitivity to extra-linguistic cues is evident in young children and develops as cognitive capacity increases
Hardness measures and resolution lower bounds
Various "hardness" measures have been studied for resolution, providing
theoretical insight into the proof complexity of resolution and its fragments,
as well as explanations for the hardness of instances in SAT solving. In this
report we aim at a unified view of a number of hardness measures, including
different measures of width, space and size of resolution proofs. We also
extend these measures to all clause-sets (possibly satisfiable).Comment: 43 pages, preliminary version (yet the application part is only
sketched, with proofs missing
On SAT representations of XOR constraints
We study the representation of systems S of linear equations over the
two-element field (aka xor- or parity-constraints) via conjunctive normal forms
F (boolean clause-sets). First we consider the problem of finding an
"arc-consistent" representation ("AC"), meaning that unit-clause propagation
will fix all forced assignments for all possible instantiations of the
xor-variables. Our main negative result is that there is no polysize
AC-representation in general. On the positive side we show that finding such an
AC-representation is fixed-parameter tractable (fpt) in the number of
equations. Then we turn to a stronger criterion of representation, namely
propagation completeness ("PC") --- while AC only covers the variables of S,
now all the variables in F (the variables in S plus auxiliary variables) are
considered for PC. We show that the standard translation actually yields a PC
representation for one equation, but fails so for two equations (in fact
arbitrarily badly). We show that with a more intelligent translation we can
also easily compute a translation to PC for two equations. We conjecture that
computing a representation in PC is fpt in the number of equations.Comment: 39 pages; 2nd v. improved handling of acyclic systems, free-standing
proof of the transformation from AC-representations to monotone circuits,
improved wording and literature review; 3rd v. updated literature,
strengthened treatment of monotonisation, improved discussions; 4th v. update
of literature, discussions and formulations, more details and examples;
conference v. to appear LATA 201
Towards Understanding and Harnessing the Potential of Clause Learning
Efficient implementations of DPLL with the addition of clause learning are
the fastest complete Boolean satisfiability solvers and can handle many
significant real-world problems, such as verification, planning and design.
Despite its importance, little is known of the ultimate strengths and
limitations of the technique. This paper presents the first precise
characterization of clause learning as a proof system (CL), and begins the task
of understanding its power by relating it to the well-studied resolution proof
system. In particular, we show that with a new learning scheme, CL can provide
exponentially shorter proofs than many proper refinements of general resolution
(RES) satisfying a natural property. These include regular and Davis-Putnam
resolution, which are already known to be much stronger than ordinary DPLL. We
also show that a slight variant of CL with unlimited restarts is as powerful as
RES itself. Translating these analytical results to practice, however, presents
a challenge because of the nondeterministic nature of clause learning
algorithms. We propose a novel way of exploiting the underlying problem
structure, in the form of a high level problem description such as a graph or
PDDL specification, to guide clause learning algorithms toward faster
solutions. We show that this leads to exponential speed-ups on grid and
randomized pebbling problems, as well as substantial improvements on certain
ordering formulas
Solving the Resource Constrained Project Scheduling Problem with Generalized Precedences by Lazy Clause Generation
The technical report presents a generic exact solution approach for
minimizing the project duration of the resource-constrained project scheduling
problem with generalized precedences (Rcpsp/max). The approach uses lazy clause
generation, i.e., a hybrid of finite domain and Boolean satisfiability solving,
in order to apply nogood learning and conflict-driven search on the solution
generation. Our experiments show the benefit of lazy clause generation for
finding an optimal solutions and proving its optimality in comparison to other
state-of-the-art exact and non-exact methods. The method is highly robust: it
matched or bettered the best known results on all of the 2340 instances we
examined except 3, according to the currently available data on the PSPLib. Of
the 631 open instances in this set it closed 573 and improved the bounds of 51
of the remaining 58 instances.Comment: 37 pages, 3 figures, 16 table
Efficient data structures for backtrack search SAT solvers
The implementation of efficient Propositional Satisfiability (SAT) solvers entails the utilization of highly efficient data structures, as illustrated by most of the recent state-of-the-art SAT solvers. However, it is in general hard to compare existing data structures, since different solvers are often characterized by fairly different algorithmic organizations and techniques, and by different search strategies and heuristics. This paper aims the evaluation of data structures for backtrack search SAT solvers, under a common unbiased SAT framework. In addition, advantages and drawbacks of each existing data structure are identified. Finally, new data structures are proposed, that are competitive with the most efficient data structures currently available, and that may be preferable for the next generation SAT solvers
Bayesian Logic Programs
Bayesian networks provide an elegant formalism for representing and reasoning
about uncertainty using probability theory. Theyare a probabilistic extension
of propositional logic and, hence, inherit some of the limitations of
propositional logic, such as the difficulties to represent objects and
relations. We introduce a generalization of Bayesian networks, called Bayesian
logic programs, to overcome these limitations. In order to represent objects
and relations it combines Bayesian networks with definite clause logic by
establishing a one-to-one mapping between ground atoms and random variables. We
show that Bayesian logic programs combine the advantages of both definite
clause logic and Bayesian networks. This includes the separation of
quantitative and qualitative aspects of the model. Furthermore, Bayesian logic
programs generalize both Bayesian networks as well as logic programs. So, many
ideas developedComment: 52 page
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