113 research outputs found
Unsolvability Cores in Classification Problems
Classification problems have been introduced by M. Ziegler as a
generalization of promise problems. In this paper we are concerned with
solvability and unsolvability questions with respect to a given set or language
family, especially with cores of unsolvability. We generalize the results about
unsolvability cores in promise problems to classification problems. Our main
results are a characterization of unsolvability cores via cohesiveness and
existence theorems for such cores in unsolvable classification problems. In
contrast to promise problems we have to strengthen the conditions to assert the
existence of such cores. In general unsolvable classification problems with
more than two components exist, which possess no cores, even if the set family
under consideration satisfies the assumptions which are necessary to prove the
existence of cores in unsolvable promise problems. But, if one of the
components is fixed we can use the results on unsolvability cores in promise
problems, to assert the existence of such cores in general. In this case we
speak of conditional classification problems and conditional cores. The
existence of conditional cores can be related to complexity cores. Using this
connection we can prove for language families, that conditional cores with
recursive components exist, provided that this family admits an uniform
solution for the word problem
Algebraic Properties of Valued Constraint Satisfaction Problem
The paper presents an algebraic framework for optimization problems
expressible as Valued Constraint Satisfaction Problems. Our results generalize
the algebraic framework for the decision version (CSPs) provided by Bulatov et
al. [SICOMP 2005]. We introduce the notions of weighted algebras and varieties
and use the Galois connection due to Cohen et al. [SICOMP 2013] to link VCSP
languages to weighted algebras. We show that the difficulty of VCSP depends
only on the weighted variety generated by the associated weighted algebra.
Paralleling the results for CSPs we exhibit a reduction to cores and rigid
cores which allows us to focus on idempotent weighted varieties. Further, we
propose an analogue of the Algebraic CSP Dichotomy Conjecture; prove the
hardness direction and verify that it agrees with known results for VCSPs on
two-element sets [Cohen et al. 2006], finite-valued VCSPs [Thapper and Zivny
2013] and conservative VCSPs [Kolmogorov and Zivny 2013].Comment: arXiv admin note: text overlap with arXiv:1207.6692 by other author
Optimal Planning Modulo Theories
Planning for real-world applications requires algorithms and tools with the ability to handle the complexity such scenarios entail. However, meeting the needs of such applications poses substantial challenges, both representational and algorithmic. On the one hand, expressive languages are needed to build faithful models. On the other hand, efficient solving techniques that can support these languages need to be devised. A response to this challenge is underway, and the past few years witnessed a community effort towards more expressive languages, including decidable fragments of first-order theories. In this work we focus on planning with arithmetic theories and propose Optimal Planning Modulo Theories, a framework that attempts to provide efficient means of dealing with such problems. Leveraging generic Optimization Modulo Theories (OMT) solvers, we first present domain-specific encodings for optimal planning in complex logistic domains. We then present a more general, domain- independent formulation that allows to extend OMT planning to a broader class of well-studied numeric problems in planning. To the best of our knowledge, this is the first time OMT procedures are employed in domain-independent planning
Calculation and Classification as Dimensions of Social Interaction
Cassirer interpreted the transition from medieval to modern theoretical thinking as an epistemological revolution which saw the concept of function to replace that of substance as a guide to knowledge. This article suggests that, in the practical world, classification into classes, types or genres is correlated to the concept of substance, while the concept of function is present in any practical calculation in the form of algorithmic procedures. The way in which algorithmic calculation and classification interact with each other has resulted in the preservation, expansion or loss of social interaction, understood as reciprocity between actors. The action of calculation and classification can then be used as epistemological coordinates to analyze social interaction. Such systematization results in a set of schemes presented in this paper along with ethnological studies supporting the theoretical model
Resource Bounded Immunity and Simplicity
Revisiting the thirty years-old notions of resource-bounded immunity and
simplicity, we investigate the structural characteristics of various immunity
notions: strong immunity, almost immunity, and hyperimmunity as well as their
corresponding simplicity notions. We also study limited immunity and
simplicity, called k-immunity and feasible k-immunity, and their simplicity
notions. Finally, we propose the k-immune hypothesis as a working hypothesis
that guarantees the existence of simple sets in NP.Comment: This is a complete version of the conference paper that appeared in
the Proceedings of the 3rd IFIP International Conference on Theoretical
Computer Science, Kluwer Academic Publishers, pp.81-95, Toulouse, France,
August 23-26, 200
3-manifolds efficiently bound 4-manifolds
It is known since 1954 that every 3-manifold bounds a 4-manifold. Thus, for
instance, every 3-manifold has a surgery diagram. There are several proofs of
this fact, including constructive proofs, but there has been little attention
to the complexity of the 4-manifold produced. Given a 3-manifold M of
complexity n, we show how to construct a 4-manifold bounded by M of complexity
O(n^2). Here we measure ``complexity'' of a piecewise-linear manifold by the
minimum number of n-simplices in a triangulation. It is an open question
whether this quadratic bound can be replaced by a linear bound.
The proof goes through the notion of "shadow complexity" of a 3-manifold M. A
shadow of M is a well-behaved 2-dimensional spine of a 4-manifold bounded by M.
We prove that, for a manifold M satisfying the Geometrization Conjecture with
Gromov norm G and shadow complexity S, c_1 G <= S <= c_2 G^2 for suitable
constants c_1, c_2. In particular, the manifolds with shadow complexity 0 are
the graph manifolds.Comment: 39 pages, 21 figures; added proof for spin case as wel
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