Distilling programs for verification

In this paper, we show how our program transformation algorithm called distillation can not only be used for the optimisation of programs, but can also be used to facilitate program verification. Using the distillation algorithm, programs are transformed into a specialised form in which functions are tail recursive, and very few intermediate structures are created. We then show how properties of this specialised form of program can be easily verified by the application of inductive proof rules. We therefore argue that the distillation algorithm is an ideal candidate for inclusion within compilers as it facilitates the two goals of program optimization and verification

Mixing Bandt-Pompe and Lempel-Ziv approaches: another way to analyze the complexity of continuous-states sequences

In this paper, we propose to mix the approach underlying Bandt-Pompe permutation entropy with Lempel-Ziv complexity, to design what we call Lempel-Ziv permutation complexity. The principle consists of two steps: (i) transformation of a continuous-state series that is intrinsically multivariate or arises from embedding into a sequence of permutation vectors, where the components are the positions of the components of the initial vector when re-arranged; (ii) performing the Lempel-Ziv complexity for this series of `symbols', as part of a discrete finite-size alphabet. On the one hand, the permutation entropy of Bandt-Pompe aims at the study of the entropy of such a sequence; i.e., the entropy of patterns in a sequence (e.g., local increases or decreases). On the other hand, the Lempel-Ziv complexity of a discrete-state sequence aims at the study of the temporal organization of the symbols (i.e., the rate of compressibility of the sequence). Thus, the Lempel-Ziv permutation complexity aims to take advantage of both of these methods. The potential from such a combined approach - of a permutation procedure and a complexity analysis - is evaluated through the illustration of some simulated data and some real data. In both cases, we compare the individual approaches and the combined approach.Comment: 30 pages, 4 figure

Comparative efficacy of different botanicals and chemical insecticides for controlling rice stem borer

An experiment was carried out in the field laboratory, Department of Entomology, Bangladesh Agricultural University to find out the efficacy of different botanicals and chemical insecticides against rice stem borer during the period from July to December 2013. The treatments included Neem oil, Mahogany oil, combination of Neem and Mahogany oil, Bishkatali leaf extract, Lantana leaf extract, combination of Bishkatali and Lantana leaf extract, Convoy 25EC, Biesterthoate 40EC, Biesteren 5G and Diatone 10G. The efficacies of treatments were evaluated based on the percent dead heart and white head resulted by rice stem borer infestation at vegetative and reproductive stages, respectively. The efficacies of treatments were varied significantly against the rice stem borers. Among the selected botanicals, Neem + Mahogany oil followed by Bishkatali leaf extract performed best and Bishkatali + Lantana followed by Lantana leaf extract and leaf extract were least effective to reduce dead heart as well as white head at different counting. Similarly, combination of Neem and Mahogany oil gave the maximum yield among the selected botanicals. Diatone 10G showed the best performance to reduce percent dead and white head among the selected chemical insecticides and gave maximum yield among different chemical insecticides. On the other hand, Convoy 25EC was the least effective to control dead heart and white head infestation with yield. Therefore, Neem + Mahogony oil and Diatone 10G were the best to control rice stem borer and to increase the yield of rice grain

Normal Forms and Reduction for Theories of Binary Relations

We consider equational theories of binary relations, in a language expressing composition, converse, and lattice operations. We treat the equations valid in the standard model of sets and also defne a hierachy of equational axiomatizations stratifying the standard theory. By working directly with a presentation of relation-expressions as graphs we are able to de ne a notion of reduction which is conuent and strongly normalizing, in sharp contrast to traditional treatments based on rst-order terms. As consequences we obtain unique normal forms, decidability of the decision problem for equality for each theory, indeed an non-deterministic polynomial-time upper bound for the complexity of the decision problems