400 research outputs found
Achieving New Upper Bounds for the Hypergraph Duality Problem through Logic
The hypergraph duality problem DUAL is defined as follows: given two simple
hypergraphs and , decide whether
consists precisely of all minimal transversals of (in which case
we say that is the dual of ). This problem is
equivalent to deciding whether two given non-redundant monotone DNFs are dual.
It is known that non-DUAL, the complementary problem to DUAL, is in
, where
denotes the complexity class of all problems that after a nondeterministic
guess of bits can be decided (checked) within complexity class
. It was conjectured that non-DUAL is in . In this paper we prove this conjecture and actually
place the non-DUAL problem into the complexity class which is a subclass of . We here refer to the logtime-uniform version of
, which corresponds to , i.e., first order
logic augmented by counting quantifiers. We achieve the latter bound in two
steps. First, based on existing problem decomposition methods, we develop a new
nondeterministic algorithm for non-DUAL that requires to guess
bits. We then proceed by a logical analysis of this algorithm, allowing us to
formulate its deterministic part in . From this result, by
the well known inclusion , it follows
that DUAL belongs also to . Finally, by exploiting
the principles on which the proposed nondeterministic algorithm is based, we
devise a deterministic algorithm that, given two hypergraphs and
, computes in quadratic logspace a transversal of
missing in .Comment: Restructured the presentation in order to be the extended version of
a paper that will shortly appear in SIAM Journal on Computin
Counterexample Guided Abstraction Refinement Algorithm for Propositional Circumscription
Circumscription is a representative example of a nonmonotonic reasoning
inference technique. Circumscription has often been studied for first order
theories, but its propositional version has also been the subject of extensive
research, having been shown equivalent to extended closed world assumption
(ECWA). Moreover, entailment in propositional circumscription is a well-known
example of a decision problem in the second level of the polynomial hierarchy.
This paper proposes a new Boolean Satisfiability (SAT)-based algorithm for
entailment in propositional circumscription that explores the relationship of
propositional circumscription to minimal models. The new algorithm is inspired
by ideas commonly used in SAT-based model checking, namely counterexample
guided abstraction refinement. In addition, the new algorithm is refined to
compute the theory closure for generalized close world assumption (GCWA).
Experimental results show that the new algorithm can solve problem instances
that other solutions are unable to solve
The DLV System for Knowledge Representation and Reasoning
This paper presents the DLV system, which is widely considered the
state-of-the-art implementation of disjunctive logic programming, and addresses
several aspects. As for problem solving, we provide a formal definition of its
kernel language, function-free disjunctive logic programs (also known as
disjunctive datalog), extended by weak constraints, which are a powerful tool
to express optimization problems. We then illustrate the usage of DLV as a tool
for knowledge representation and reasoning, describing a new declarative
programming methodology which allows one to encode complex problems (up to
-complete problems) in a declarative fashion. On the foundational
side, we provide a detailed analysis of the computational complexity of the
language of DLV, and by deriving new complexity results we chart a complete
picture of the complexity of this language and important fragments thereof.
Furthermore, we illustrate the general architecture of the DLV system which
has been influenced by these results. As for applications, we overview
application front-ends which have been developed on top of DLV to solve
specific knowledge representation tasks, and we briefly describe the main
international projects investigating the potential of the system for industrial
exploitation. Finally, we report about thorough experimentation and
benchmarking, which has been carried out to assess the efficiency of the
system. The experimental results confirm the solidity of DLV and highlight its
potential for emerging application areas like knowledge management and
information integration.Comment: 56 pages, 9 figures, 6 table
Compilability of Abduction
Abduction is one of the most important forms of reasoning; it has been
successfully applied to several practical problems such as diagnosis. In this
paper we investigate whether the computational complexity of abduction can be
reduced by an appropriate use of preprocessing. This is motivated by the fact
that part of the data of the problem (namely, the set of all possible
assumptions and the theory relating assumptions and manifestations) are often
known before the rest of the problem. In this paper, we show some complexity
results about abduction when compilation is allowed
Causality and the semantics of provenance
Provenance, or information about the sources, derivation, custody or history
of data, has been studied recently in a number of contexts, including
databases, scientific workflows and the Semantic Web. Many provenance
mechanisms have been developed, motivated by informal notions such as
influence, dependence, explanation and causality. However, there has been
little study of whether these mechanisms formally satisfy appropriate policies
or even how to formalize relevant motivating concepts such as causality. We
contend that mathematical models of these concepts are needed to justify and
compare provenance techniques. In this paper we review a theory of causality
based on structural models that has been developed in artificial intelligence,
and describe work in progress on a causal semantics for provenance graphs.Comment: Workshop submissio
Raman scattering evidence for a cascade-like evolution of the charge-density-wave collective amplitude mode
The two-dimensional rare-earth tri-tellurides undergo a unidirectional
charge-density-wave (CDW) transition at high temperature and, for the heaviest
members of the series, a bidirectional one at low temperature. Raman scattering
experiments as a function of temperature on DyTe and on LaTe at 6 GPa
provide a clear-cut evidence for the emergence of the respective collective CDW
amplitude excitations. In the unidirectional CDW phase, we surprisingly
discover that the amplitude mode develops as a succession of two mean-field,
BCS-like transitions in different temperature ranges
A balancing act: Evidence for a strong subdominant d-wave pairing channel in
We present an analysis of the Raman spectra of optimally doped based on LDA band structure calculations and the
subsequent estimation of effective Raman vertices. Experimentally a narrow,
emergent mode appears in the () Raman spectra only below
, well into the superconducting state and at an energy below twice the
energy gap on the electron Fermi surface sheets. The Raman spectra can be
reproduced quantitatively with estimates for the magnitude and momentum space
structure of the s pairing gap on different Fermi surface sheets, as
well as the identification of the emergent sharp feature as a
Bardasis-Schrieffer exciton, formed as a Cooper pair bound state in a
subdominant channel. The binding energy of the exciton relative
to the gap edge shows that the coupling strength in this subdominant
channel is as strong as 60% of that in the dominant
channel. This result suggests that may be the dominant pairing
symmetry in Fe-based sperconductors which lack central hole bands.Comment: 10 pages, 6 Figure
The Complexity of Computing Minimal Unidirectional Covering Sets
Given a binary dominance relation on a set of alternatives, a common thread
in the social sciences is to identify subsets of alternatives that satisfy
certain notions of stability. Examples can be found in areas as diverse as
voting theory, game theory, and argumentation theory. Brandt and Fischer [BF08]
proved that it is NP-hard to decide whether an alternative is contained in some
inclusion-minimal upward or downward covering set. For both problems, we raise
this lower bound to the Theta_{2}^{p} level of the polynomial hierarchy and
provide a Sigma_{2}^{p} upper bound. Relatedly, we show that a variety of other
natural problems regarding minimal or minimum-size covering sets are hard or
complete for either of NP, coNP, and Theta_{2}^{p}. An important consequence of
our results is that neither minimal upward nor minimal downward covering sets
(even when guaranteed to exist) can be computed in polynomial time unless P=NP.
This sharply contrasts with Brandt and Fischer's result that minimal
bidirectional covering sets (i.e., sets that are both minimal upward and
minimal downward covering sets) are polynomial-time computable.Comment: 27 pages, 7 figure
A Goal-based Framework for Contextual Requirements Modeling and Analysis
Requirements Engineering (RE) research often ignores, or presumes a uniform nature of the context in which the system operates. This assumption is no longer valid in emerging computing paradigms, such as ambient, pervasive and ubiquitous computing, where it is essential to monitor and adapt to an inherently varying context. Besides influencing the software, context may influence stakeholders' goals and their choices to meet them. In this paper, we propose a goal-oriented RE modeling and reasoning framework for systems operating in varying contexts. We introduce contextual goal models to relate goals and contexts; context analysis to refine contexts and identify ways to verify them; reasoning techniques to derive requirements reflecting the context and users priorities at runtime; and finally, design time reasoning techniques to derive requirements for a system to be developed at minimum cost and valid in all considered contexts. We illustrate and evaluate our approach through a case study about a museum-guide mobile information system
Alternative route to charge density wave formation in multiband systems
Charge and spin density waves, periodic modulations of the electron and
magnetization densities, respectively, are among the most abundant and
non-trivial low-temperature ordered phases in condensed matter. The ordering
direction is widely believed to result from the Fermi surface topology.
However, several recent studies indicate that this common view needs to be
supplemented. Here, we show how an enhanced electron-lattice interaction can
contribute to or even determine the selection of the ordering vector in the
model charge density wave system ErTe3. Our joint experimental and theoretical
study allows us to establish a relation between the selection rules of the
electronic light scattering spectra and the enhanced electron-phonon coupling
in the vicinity of band degeneracy points. This alternative proposal for charge
density wave formation may be of general relevance for driving phase
transitions into other broken-symmetry ground states, particularly in multiband
systems such as the iron based superconductors
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