Random number generation refers to many applications such as simulation, numerical analysis, cryptography etc. Field Programmable Gate Array (FPGA) are reconfigurable hardware systems, which allow rapid prototyping. This research work is the first comprehensive survey on how random number generators are implemented on Field Programmable Gate Arrays (FPGAs). A rich and upto-date list of generators specifically mapped to FPGA are presented with deep technical details on their definitions and implementations. A classification of these generators is presented, which encompasses linear and nonlinear (chaotic) pseudo and truly random number generators. A statistical comparison through standard batteries of tests, as well as implementation comparison based on speed and area performances, are finally presented.

Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a continuous function, whose discrete-time iterations are chaotic if and only if the iteration graph of the Boolean network is strongly connected. Then, sufficient conditions for this strong connectivity are expressed on the interaction graph of this network, leading to a constructive method of chaotic function computation. The whole approach is evaluated in the chaos-based pseudo-random number generation context.

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Hardware pseudorandom number generators are continuously improved to satisfy both physical and ubiquitous computing security system challenges. The main contribution of this work is to propose two post-processing modules in hardware, to improve the randomness of linear PRNGs while succeeding in passing the TestU01 statistical battery of tests. They are based on chaotic iterations and are denoted by CIPRNG-MC and CIPRNG-XOR. They have various interesting properties, encompassing the ability to improve the statistical profile of the generators on which they iterate. Such post-processing have been implemented on FPGA and ASIC without inferring any blocs (RAM or DSP). A comparison in terms of area, throughput, and statistical tests, is performed. The hardware pseudorandom number generation can reach a throughput/latency ratio equal to 8.5 Gbps for Zynq-FPGA and 10.9 Gbps for ASIC, being thus the fastest FPGA generators based on chaos that can pass TestU01. In particular, it is established that CIPRNG-XOR is 2.5 times faster and 5 times more efficient that almost all linear PRNGs who pass TestU01.

Abstract-Due to the recent evolution of sequencing techniques, the number of available genomes is rising steadily, leading to the possibility to make large scale genomic comparison between sets of close species. An interesting question to answer is: what is the common functionality genes of a collection of species, or conversely, to determine what is specific to a given species when compared to other ones belonging in the same genus, family, etc. Investigating such problem means to find both core and pan genomes of a collection of species, i.e., genes in common to all the species vs. the set of all genes in all species under consideration. However, obtaining trustworthy core and pan genomes is not an easy task, leading to a large amount of computation, and requiring a rigorous methodology. Surprisingly, as far as we know, this methodology in finding core and pan genomes has not really been deeply investigated. This research work tries to fill this gap by focusing only on chloroplastic genomes, whose reasonable sizes allow a deep study. To achieve this goal, a collection of 99 chloroplasts are considered in this article. Two methodologies have been investigated, respectively based on sequence similarities and genes names taken from annotation tools. The obtained results will finally be evaluated in terms of biological relevance.

Abstract. The amount of completely sequenced chloroplast genomes increases rapidly every day, leading to the possibility to build large scale phylogenetic trees of plant species. Considering a subset of close plant species defined according to their chloroplasts, the phylogenetic tree that can be inferred by their core genes is not necessarily well supported, due to the possible occurrence of "problematic" genes (i.e., homoplasy, incomplete lineage sorting, horizontal gene transfers, etc.) which may blur phylogenetic signal. However, a trustworthy phylogenetic tree can still be obtained if the number of problematic genes is low, the problem being to determine the largest subset of core genes that produces the best supported tree. To discard problematic genes and due to the overwhelming number of possible combinations, we propose an hybrid approach that embeds both genetic algorithms and statistical tests. Given a set of organisms, the result is a pipeline of many stages for the production of well supported phylogenetic trees. The proposal has been applied to different cases of plant families, leading to encouraging results for these families.

We present a technique to prove invariants of model-based specifications in a fragment of set theory. Proof obligations containing set theory constructs are translated to first-order logic with equality augmented with (an extension of) the theory of arrays with extensionality. The idea underlying the translation is that sets are represented by their characteristic function which, in turn, is encoded by an array of Booleans indexed on the elements of the set. A theorem proving procedure automating the verification of the proof obligations obtained by the translation is described. Furthermore, we discuss how a sub-formula can be extracted from a failed proof attempt and used by a model finder to build a counter-example. To be concrete, we use a B specification of a simple process scheduler on which we illustrate our technique.