Necessary conditions for tractability of valued CSPs

The connection between constraint languages and clone theory has been a fruitful line of research on the complexity of constraint satisfaction problems. In a recent result, Cohen et al. [SICOMP'13] have characterised a Galois connection between valued constraint languages and so-called weighted clones. In this paper, we study the structure of weighted clones. We extend the results of Creed and Zivny from [CP'11/SICOMP'13] on types of weightings necessarily contained in every nontrivial weighted clone. This result has immediate computational complexity consequences as it provides necessary conditions for tractability of weighted clones and thus valued constraint languages. We demonstrate that some of the necessary conditions are also sufficient for tractability, while others are provably not.Comment: To appear in SIAM Journal on Discrete Mathematics (SIDMA

The ubiquity of conservative translations

We study the notion of conservative translation between logics introduced by Feitosa and D'Ottaviano. We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set of formulas can be conservatively translated into CPC. The translation is computable if the consequence relation is decidable. More generally, we show that one can take instead of CPC a broad class of logics (extensions of a certain fragment of full Lambek calculus FL) including most nonclassical logics studied in the literature, hence in a sense, (almost) any two reasonable deductive systems can be conservatively translated into each other. We also provide some counterexamples, in particular the paraconsistent logic LP is not universal.Comment: 15 pages; to appear in Review of Symbolic Logi

A survey of clones on infinite sets

A clone on a set X is a set of finitary operations on X which contains all projections and which is moreover closed under functional composition. Ordering all clones on X by inclusion, one obtains a complete algebraic lattice, called the clone lattice. We summarize what we know about the clone lattice on an infinite base set X and formulate what we consider the most important open problems.Comment: 37 page

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

A Galois Connection for Weighted (Relational) Clones of Infinite Size

A Galois connection between clones and relational clones on a fixed finite domain is one of the cornerstones of the so-called algebraic approach to the computational complexity of non-uniform Constraint Satisfaction Problems (CSPs). Cohen et al. established a Galois connection between finitely-generated weighted clones and finitely-generated weighted relational clones [SICOMP'13], and asked whether this connection holds in general. We answer this question in the affirmative for weighted (relational) clones with real weights and show that the complexity of the corresponding valued CSPs is preserved

A Parallelizable Acceleration Framework for Packing Linear Programs

This paper presents an acceleration framework for packing linear programming problems where the amount of data available is limited, i.e., where the number of constraints m is small compared to the variable dimension n. The framework can be used as a black box to speed up linear programming solvers dramatically, by two orders of magnitude in our experiments. We present worst-case guarantees on the quality of the solution and the speedup provided by the algorithm, showing that the framework provides an approximately optimal solution while running the original solver on a much smaller problem. The framework can be used to accelerate exact solvers, approximate solvers, and parallel/distributed solvers. Further, it can be used for both linear programs and integer linear programs

The methionine salvage pathway in Bacillus subtilis

BACKGROUND: Polyamine synthesis produces methylthioadenosine, which has to be disposed of. The cell recycles it into methionine through methylthioribose (MTR). Very little was known about MTR recycling for methionine salvage in Bacillus subtilis. RESULTS: Using in silico genome analysis and transposon mutagenesis in B. subtilis we have experimentally uncovered the major steps of the dioxygen-dependent methionine salvage pathway, which, although similar to that found in Klebsiella pneumoniae, recruited for its implementation some entirely different proteins. The promoters of the genes have been identified by primer extension, and gene expression was analyzed by Northern blotting and lacZ reporter gene expression. Among the most remarkable discoveries in this pathway is the role of an analog of ribulose diphosphate carboxylase (Rubisco, the plant enzyme used in the Calvin cycle which recovers carbon dioxide from the atmosphere) as a major step in MTR recycling. CONCLUSIONS: A complete methionine salvage pathway exists in B. subtilis. This pathway is chemically similar to that in K. pneumoniae, but recruited different proteins to this purpose. In particular, a paralogue or Rubisco, MtnW, is used at one of the steps in the pathway. A major observation is that in the absence of MtnW, MTR becomes extremely toxic to the cell, opening an unexpected target for new antimicrobial drugs. In addition to methionine salvage, this pathway protects B. subtilis against dioxygen produced by its natural biotope, the surface of leaves (phylloplane)