Partial clones containing all Boolean monotone self-dual partial functions

International audienceThe study of partial clones on 2 := {0, 1} was initiated by R. V. Freivald. In his fundamental paper published in 1966, Freivald showed, among otherthings, that the set of all monotone partial functions and the set of all self-dual partial functions are both maximal partial clones on 2. Several papers dealing with intersections of maximal partial clones on 2 have appeared after Freivald work. It is known that there are infinitely many partial clones that contain the set of all monotone self-dual partial functions on 2, and the problem of describing them all was posed by some authors. In this paper we show that the set of partial clones that contain all monotone self-dual partial functions is of continuum cardinality on 2

Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis

Obtaining lower bounds for NP-hard problems has for a long time been an active area of research. Recent algebraic techniques introduced by Jonsson et al. (SODA 2013) show that the time complexity of the parameterized SAT($\cdot$) problem correlates to the lattice of strong partial clones. With this ordering they isolated a relation $R$ such that SAT($R$) can be solved at least as fast as any other NP-hard SAT($\cdot$) problem. In this paper we extend this method and show that such languages also exist for the max ones problem (MaxOnes($\Gamma$)) and the Boolean valued constraint satisfaction problem over finite-valued constraint languages (VCSP($\Delta$)). With the help of these languages we relate MaxOnes and VCSP to the exponential time hypothesis in several different ways.Comment: This is an extended version of Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis, appearing in Proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science MFCS 2014 Budapest, August 25-29, 201

Weak Bases of Boolean Co-Clones

Universal algebra and clone theory have proven to be a useful tool in the study of constraint satisfaction problems since the complexity, up to logspace reductions, is determined by the set of polymorphisms of the constraint language. For classifications where primitive positive definitions are unsuitable, such as size-preserving reductions, weaker closure operations may be necessary. In this article we consider strong partial clones which can be seen as a more fine-grained framework than Post's lattice where each clone splits into an interval of strong partial clones. We investigate these intervals and give simple relational descriptions, weak bases, of the largest elements. The weak bases have a highly regular form and are in many cases easily relatable to the smallest members in the intervals, which suggests that the lattice of strong partial clones is considerably simpler than the full lattice of partial clones

Galois correspondence for counting quantifiers

We introduce a new type of closure operator on the set of relations, max-implementation, and its weaker analog max-quantification. Then we show that approximation preserving reductions between counting constraint satisfaction problems (#CSPs) are preserved by these two types of closure operators. Together with some previous results this means that the approximation complexity of counting CSPs is determined by partial clones of relations that additionally closed under these new types of closure operators. Galois correspondence of various kind have proved to be quite helpful in the study of the complexity of the CSP. While we were unable to identify a Galois correspondence for partial clones closed under max-implementation and max-quantification, we obtain such results for slightly different type of closure operators, k-existential quantification. This type of quantifiers are known as counting quantifiers in model theory, and often used to enhance first order logic languages. We characterize partial clones of relations closed under k-existential quantification as sets of relations invariant under a set of partial functions that satisfy the condition of k-subset surjectivity. Finally, we give a description of Boolean max-co-clones, that is, sets of relations on {0,1} closed under max-implementations.Comment: 28 pages, 2 figure

SourcererCC: Scaling Code Clone Detection to Big Code

Despite a decade of active research, there is a marked lack in clone detectors that scale to very large repositories of source code, in particular for detecting near-miss clones where significant editing activities may take place in the cloned code. We present SourcererCC, a token-based clone detector that targets three clone types, and exploits an index to achieve scalability to large inter-project repositories using a standard workstation. SourcererCC uses an optimized inverted-index to quickly query the potential clones of a given code block. Filtering heuristics based on token ordering are used to significantly reduce the size of the index, the number of code-block comparisons needed to detect the clones, as well as the number of required token-comparisons needed to judge a potential clone. We evaluate the scalability, execution time, recall and precision of SourcererCC, and compare it to four publicly available and state-of-the-art tools. To measure recall, we use two recent benchmarks, (1) a large benchmark of real clones, BigCloneBench, and (2) a Mutation/Injection-based framework of thousands of fine-grained artificial clones. We find SourcererCC has both high recall and precision, and is able to scale to a large inter-project repository (250MLOC) using a standard workstation.Comment: Accepted for publication at ICSE'16 (preprint, unrevised

Hyperspectral classification of Cyperus esculentus clones and morphologically similar weeds

Cyperus esculentus (yellow nutsedge) is one of the world's worst weeds as it can cause great damage to crops and crop production. To eradicate C. esculentus, early detection is key-a challenging task as it is often confused with other Cyperaceae and displays wide genetic variability. In this study, the objective was to classify C. esculentus clones and morphologically similar weeds. Hyperspectral reflectance between 500 and 800 nm was tested as a measure to discriminate between (I) C. esculentus and morphologically similar Cyperaceae weeds, and between (II) different clonal populations of C. esculentus using three classification models: random forest (RF), regularized logistic regression (RLR) and partial least squares-discriminant analysis (PLS-DA). RLR performed better than RF and PLS-DA, and was able to adequately classify the samples. The possibility of creating an affordable multispectral sensing tool, for precise in-field recognition of C. esculentus plants based on fewer spectral bands, was tested. Results of this study were compared against simulated results from a commercially available multispectral camera with four spectral bands. The model created with customized bands performed almost equally well as the original PLS-DA or RLR model, and much better than the model describing multispectral image data from a commercially available camera. These results open up the opportunity to develop a dedicated robust tool for C. esculentus recognition based on four spectral bands and an appropriate classification model

Reversibility of continuous-variable quantum cloning

We analyze a reversibility of optimal Gaussian $1\to 2$ quantum cloning of a coherent state using only local operations on the clones and classical communication between them and propose a feasible experimental test of this feature. Performing Bell-type homodyne measurement on one clone and anti-clone, an arbitrary unknown input state (not only a coherent state) can be restored in the other clone by applying appropriate local unitary displacement operation. We generalize this concept to a partial LOCC reversal of the cloning and we show that this procedure converts the symmetric cloner to an asymmetric cloner. Further, we discuss a distributed LOCC reversal in optimal $1\to M$ Gaussian cloning of coherent states which transforms it to optimal $1\to M'$ cloning for $M'<M$. Assuming the quantum cloning as a possible eavesdropping attack on quantum communication link, the reversibility can be utilized to improve the security of the link even after the attack.Comment: 7 pages, 5 figure

Improved Screening of cDNAs Generated by mRNA Differential Display Enables the Selection of True Positives and the Isolation of Weakly Expressed Messages

The high percentage of false positives generated by differential display (as high as 85%) has previously limited the potential of the method. This report describes an efficient methodology that enables false positives to be discarded prior to cloning, via reverse Northern analysis. This first step of the screening also allows the detection of putative lowabundance differential clones. Following cloning, a second reverseNorthern combined with partial DNA sequencing and RT-PCR detection allows isolation of all differential cDNAs including very lowabundance clones. Use of the sequential screening procedure described here led to the isolation of novel tomato genes responding to the plant hormone ethylene while minimising labor and materials input