On Constraint Satisfaction Problems below P

Symmetric Datalog, a fragment of the logic programming language Datalog, is conjectured to capture all constraint satisfaction problems (CSP) in L. Therefore developing tools that help us understand whether or not a CSP can be defined in symmetric Datalog is an important task. It is widely known that a CSP is definable in Datalog and linear Datalog iff that CSP has bounded treewidth and bounded pathwidth duality, respectively. In the case of symmetric Datalog, Bulatov, Krokhin and Larose ask for such a duality [2008]. We provide two such dualities, and give applications. In particular, we give a short and simple new proof of the result of Dalmau and Larose that "Maltsev + Datalog -> symmetric Datalog" [2008]. In the second part of the paper, we provide some evidence for the conjecture of Dalmau [2002] that every CSP in NL is definable in linear Datalog. Our results also show that a wide class of CSPs ---CSPs which do not have bounded pathwidth duality (e.g. the P-complete Horn-3Sat problem)--- cannot be defined by any polynomial size family of monotone read-once nondeterministic branching programs. We consider the following restrictions of the previous models: read-once linDat(suc) (1-linDat(suc)), and monotone readonce nondeterministic branching programs (mnBP1). Although restricted, these models can still define NL-complete problems such as directed st-Connectivity, and also nontrivial problems in NL which are not definable in linear Datalog. We show that any CSP definable by a 1-linDat(suc) program or by a poly-size family of mnBP1s can also be defined by a linear Datalog program. It also follows that a wide class of CSPs ---CSPs which do not have bounded pathwidth duality (e.g. the P-complete Horn-3Sat problem)--- cannot be defined by any 1-linDat(suc) program or by any poly-size family of mnBP1s

On Maltsev Digraphs

This is an Open Access article, first published by E-CJ on 25 February 2015.We study digraphs preserved by a Maltsev operation: Maltsev digraphs. We show that these digraphs retract either onto a directed path or to the disjoint union of directed cycles, showing in this way that the constraint satisfaction problem for Maltsev digraphs is in logspace, L. We then generalize results from Kazda (2011) to show that a Maltsev digraph is preserved not only by a majority operation, but by a class of other operations (e.g., minority, Pixley) and obtain a O(|VG|4)-time algorithm to recognize Maltsev digraphs. We also prove analogous results for digraphs preserved by conservative Maltsev operations which we use to establish that the list homomorphism problem for Maltsev digraphs is in L. We then give a polynomial time characterisation of Maltsev digraphs admitting a conservative 2-semilattice operation. Finally, we give a simple inductive construction of directed acyclic digraphs preserved by a Maltsev operation, and relate them with series parallel digraphs.Peer reviewedFinal Published versio

The complexity of the list homomorphism problem for graphs

We completely classify the computational complexity of the list H-colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph H the problem is either NP-complete, NL-complete, L-complete or is first-order definable; descriptive complexity equivalents are given as well via Datalog and its fragments. Our algebraic characterisations match important conjectures in the study of constraint satisfaction problems.Comment: 12 pages, STACS 201

A Compositional Neural-network Solution to Prime-number Testing

A long-standing difficulty for connectionism has been to implement compositionality, the idea of building a knowledge representation out of components such that the meaning arises from the meanings of the individual components and how they are combined. Here we show how a neural-learning algorithm, knowledge-based cascade-correlation (KBCC), creates a compositional representation of the prime-number concept and uses this representation to decide whether its input n is a prime number or not. KBCC conformed to a basic prime-number testing algorithm by recruiting source networks representing division by prime numbers in order from smallest to largest prime divisor up to √n. KBCC learned how to test prime numbers faster and generalized better to untrained numbers than did similar knowledge-free neural learners. The results demonstrate that neural networks can learn to perform in a compositional manner and underscore the importance of basing learning on existing knowledge

Unexpected attraction of polarotactic water-leaving insects to matt black car surfaces: mattness of paintwork cannot eliminate the polarized light pollution of black cars.

The horizontally polarizing surface parts of shiny black cars (the reflection-polarization characteristics of which are similar to those of water surfaces) attract water-leaving polarotactic insects. Thus, shiny black cars are typical sources of polarized light pollution endangering water-leaving insects. A new fashion fad is to make car-bodies matt black or grey. Since rough (matt) surfaces depolarize the reflected light, one of the ways of reducing polarized light pollution is to make matt the concerned surface. Consequently, matt black/grey cars may not induce polarized light pollution, which would be an advantageous feature for environmental protection. To test this idea, we performed field experiments with horizontal shiny and matt black car-body surfaces laid on the ground. Using imaging polarimetry, in multiple-choice field experiments we investigated the attractiveness of these test surfaces to various water-leaving polarotactic insects and obtained the following results: (i) The attractiveness of black car-bodies to polarotactic insects depends in complex manner on the surface roughness (shiny, matt) and species (mayflies, dolichopodids, tabanids). (ii) Non-expectedly, the matt dark grey car finish is much more attractive to mayflies (being endangered and protected in many countries) than matt black finish. (iii) The polarized light pollution of shiny black cars usually cannot be reduced with the use of matt painting. On the basis of these, our two novel findings are that (a) matt car-paints are highly polarization reflecting, and (b) these matt paints are not suitable to repel polarotactic insects. Hence, the recent technology used to make matt the car-bodies cannot eliminate or even can enhance the attractiveness of black/grey cars to water-leaving insects. Thus, changing shiny black car painting to matt one is a disadvantageous fashion fad concerning the reduction of polarized light pollution of black vehicles

Statistical comparisons (Kruskal Wallis and Mann-Whitney U test) between the numbers of dolichopodids landed on the shiny black, matt black and matt grey horizontal test surfaces in experiment 1 (Fig. 4, Table S1).

<p>Statistical comparisons (Kruskal Wallis and Mann-Whitney U test) between the numbers of dolichopodids landed on the shiny black, matt black and matt grey horizontal test surfaces in experiment 1 (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103339#pone-0103339-g004" target="_blank">Fig. 4</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103339#pone.0103339.s006" target="_blank">Table S1</a>).</p

Total numbers of mayflies landed on the shiny black, matt black and matt grey horizontal test surfaces in experiment 1.

<p>The inset is a photograph of a mayfly landed on the shiny black test surface. The number of repetition is 6 (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103339#s4" target="_blank">Materials and methods</a>, and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103339#s3" target="_blank">Discussion</a>).</p

Total numbers of dolichopodids landed on the shiny black, matt black and matt grey horizontal test surfaces in experiment 1.

<p>The inset is a photograph of a dolichopodid fly landed on the matt black test surface. The number of repetition is 6 (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103339#s4" target="_blank">Materials and methods</a>, and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103339#s3" target="_blank">Discussion</a>).</p