Language and Proofs for Higher-Order SMT (Work in Progress)

Satisfiability modulo theories (SMT) solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full first-order logic modulo theories. Nevertheless, higher-order logic within SMT is still little explored. One main goal of the Matryoshka project, which started in March 2017, is to extend the reasoning capabilities of SMT solvers and other automatic provers beyond first-order logic. In this preliminary report, we report on an extension of the SMT-LIB language, the standard input format of SMT solvers, to handle higher-order constructs. We also discuss how to augment the proof format of the SMT solver veriT to accommodate these new constructs and the solving techniques they require.Comment: In Proceedings PxTP 2017, arXiv:1712.0089

Evolution of substrate-specific gene expression and RNA editing in brown rot wood-decaying fungi.

Fungi that decay wood have characteristic associations with certain tree species, but the mechanistic bases for these associations are poorly understood. We studied substrate-specific gene expression and RNA editing in six species of wood-decaying fungi from the 'Antrodia clade' (Polyporales, Agaricomycetes) on three different wood substrates (pine, spruce, and aspen) in submerged cultures. We identified dozens to hundreds of substrate-biased genes (i.e., genes that are significantly upregulated in one substrate relative to the other two substrates) in each species, and these biased genes are correlated with their host ranges. Evolution of substrate-biased genes is associated with gene family expansion, gain and loss of genes, and variation in cis- and trans- regulatory elements, rather than changes in protein coding sequences. We also demonstrated widespread RNA editing events in the Antrodia clade, which differ from those observed in the Ascomycota in their distribution, substitution types, and the genomic environment. Moreover, we found that substrates could affect editing positions and frequency, including editing events occurring in mRNA transcribed from wood-decay-related genes. This work shows the extent to which gene expression and RNA editing differ among species and substrates, and provides clues into mechanisms by which wood-decaying fungi may adapt to different hosts

Between the Golden Age and the Gilded Age : A History of the Southern Thames Street Neighborhood

The Southern Thames St. Neighborhood is located on the west side of Newport, Rhode Island, and occupies the southern half of its harbor. This neighborhood is an outstanding example of 19th-century immigrant neighborhood built according to local, vernecular traditions. This area was home to a substantial portion of Newport\u27s Irish immigrant population, a working class group who arrived in Newport between 1820 and 1920

Electrically induced drop detachment and ejection

A deformed droplet may leap from a solid substrate, impelled to detach through the conversion of surface energy into kinetic energy that arises as it relaxes to a sphere. Electrowetting provides a means of preparing a droplet on a substrate for lift-off. When a voltage is applied between a water droplet and a dielectric-coated electrode, the wettability of the substrate increases in a controlled way, leading to the spreading of the droplet. Once the voltage is released, the droplet recoils, due to a sudden excess in surface energy, and droplet detachment may follow. The process of drop detachment and lift-off, prevalent in both biology and micro-engineering, has to date been considered primarily in terms of qualitative scaling arguments for idealized superhydrophobic substrates. We here consider the eletrically-induced ejection of droplets from substrates of finite wettability and analyze the process quantitatively. We compare experiments to numerical simulations and analyze how the energy conversion efficiency is affected by the applied voltage and the intrinsic contact angle of the droplet on the substrate. Our results indicate that the finite wettability of the substrate significantly affects the detachment dynamics, and so provide new rationale for the previously reported large critical radius for drop ejection from micro-textured substrates

Machine Learning for Instance Selection in SMT Solving

International audienceSMT solvers are among the most suited tools for quantifier-free first-order problems, and their support for quantified formulas has been improving in recent years. To instantiate quantifiers, they rely on heuristic techniques that generate thousands of instances, most of them useless. We propose to apply state-of-the-art machine learning techniques as classifiers for instances on top of the instantiation process. We show that such techniques can indeed decrease the number of generated useless instances. We envision that this could lead to more efficient SMT solving for quantified problems. Satisfiability-modulo-theories (SMT) solvers are among the best backends for verification tools and "hammers" in proof assistants. When proof obligations contain quantified formulas, SMT solvers rely on instantiation, replacing quantified subformulas by sets of ground instances. Three main techniques have been designed: enumerative [11], trigger-based [4], and conflict-based [12] instantiation. Among these, only conflict-based instantiation computes instances that are guaranteed to be relevant, but it is incomplete and is normally used in combination with other techniques. Enumerative and trigger-based techniques are highly heuristic and generate a large number of instances, most of them useless. As a result, the search space of the solver explodes. Reducing the number of instances could improve the solver's efficiency and success rate within a given time limit. We propose to use a state-of-the-art machine learning algorithm as a predictor over the generated set of instances to filter out irrelevant instances, and thus decrease the number of instances given to the ground solver. The predictor is invoked after each instantiation round to rate the potential usefulness of each generated instance. Several strategies are then used to build a subset of potentially relevant instances that are immediately added to the ground solver. Adding the other instances is postponed. We conducted our experiment in veriT [2], an SMT solver that implements all three in-stantiation techniques described above. We chose as predictor the XGBoost gradient boosting toolkit [3] with the binary classification objective. This configuration had already been used successfully in the context of theorem proving [6, 10]. Choosing a suitable set of features is crucial for effective machine learning. The features determine how precise the representation of the problem is. Previous works already investigate features for theorem proving [1, 5, 6, 8-10]. Our features are more specifically inspired by ENIGMA [6] and RLCoP [7]. They are basically term symbols and term walks with symbol sequences projected to features using Vowpal Wabbit hashing. Term variables and Skolem constants are translated analogously to constants. The model is further enriched with abstract features such as term size, term depth, and the number of instances. To encode our problem into sparse vectors, we use three kinds of information available to the solver: the ground part of the formula (set of literals l 1 ,. .. , l m), the quantified formul

A Unifying Model of Genome Evolution Under Parsimony

We present a data structure called a history graph that offers a practical basis for the analysis of genome evolution. It conceptually simplifies the study of parsimonious evolutionary histories by representing both substitutions and double cut and join (DCJ) rearrangements in the presence of duplications. The problem of constructing parsimonious history graphs thus subsumes related maximum parsimony problems in the fields of phylogenetic reconstruction and genome rearrangement. We show that tractable functions can be used to define upper and lower bounds on the minimum number of substitutions and DCJ rearrangements needed to explain any history graph. These bounds become tight for a special type of unambiguous history graph called an ancestral variation graph (AVG), which constrains in its combinatorial structure the number of operations required. We finally demonstrate that for a given history graph $G$, a finite set of AVGs describe all parsimonious interpretations of $G$, and this set can be explored with a few sampling moves.Comment: 52 pages, 24 figure

A Lambda-Free Higher-Order Recursive Path Order

International audienceWe generalize the recursive path order (RPO) to higher-order terms without λ-abstraction. This new order fully coincides with the standard RPO on first-order terms also in the presence of currying, distinguishing it from previous work. It has many useful properties, including well-foundedness, transitivity, stability under substitution, and the subterm property. It appears promising as the basis of a higher-order superposition calculus

Finding a partner in the ocean: molecular and evolutionary bases of the response to sexual cues in a planktonic diatom

Microalgae play a major role as primary producers in aquatic ecosystems. Cell signalling regulates their interactions with the environment and other organisms, yet this process in phytoplankton is poorly defined. Using the marine planktonic diatom Pseudo-nitzschia multistriata, we investigated the cell response to cues released during sexual reproduction, an event that demands strong regulatory mechanisms and impacts on population dynamics. We sequenced the genome of P. multistriata and performed phylogenomic and transcriptomic analyses, which allowed the definition of gene gains and losses, horizontal gene transfers, conservation and evolutionary rate of sex-related genes. We also identified a small number of conserved noncoding elements. Sexual reproduction impacted on cell cycle progression and induced an asymmetric response of the opposite mating types. G protein-coupled receptors and cyclic guanosine monophosphate (cGMP) are implicated in the response to sexual cues, which overall entails a modulation of cell cycle, meiosis-related and nutrient transporter genes, suggesting a fine control of nutrient uptake even under nutrient-replete conditions. The controllable life cycle and the genome sequence of P. multistriata allow the reconstruction of changes occurring in diatoms in a key phase of their life cycle, providing hints on the evolution and putative function of their genes and empowering studies on sexual reproduction

Finding a partner in the ocean: molecular and evolutionary bases of the response to sexual cues in a planktonic diatom

Microalgae play a major role as primary producers in aquatic ecosystems. Cell signalling regulates their interactions with the environment and other organisms, yet this process in phytoplankton is poorly defined. Using the marine planktonic diatom Pseudo-nitzschia multistriata, we investigated the cell response to cues released during sexual reproduction, an event that demands strong regulatory mechanisms and impacts on population dynamics. We sequenced the genome of P. multistriata and performed phylogenomic and transcriptomic analyses, which allowed the definition of gene gains and losses, horizontal gene transfers, conservation and evolutionary rate of sex-related genes. We also identified a small number of conserved noncoding elements. Sexual reproduction impacted on cell cycle progression and induced an asymmetric response of the opposite mating types. G protein-coupled receptors and cyclic guanosine monophosphate (cGMP) are implicated in the response to sexual cues, which overall entails a modulation of cell cycle, meiosis-related and nutrient transporter genes, suggesting a fine control of nutrient uptake even under nutrient-replete conditions. The controllable life cycle and the genome sequence of P. multistriata allow the reconstruction of changes occurring in diatoms in a key phase of their life cycle, providing hints on the evolution and putative function of their genes and empowering studies on sexual reproduction

Machine Learning for Instance Selection in SMT Solving

International audienceSMT solvers are among the most suited tools for quantifier-free first-order problems, and their support for quantified formulas has been improving in recent years. To instantiate quantifiers, they rely on heuristic techniques that generate thousands of instances, most of them useless. We propose to apply state-of-the-art machine learning techniques as classifiers for instances on top of the instantiation process. We show that such techniques can indeed decrease the number of generated useless instances. We envision that this could lead to more efficient SMT solving for quantified problems. Satisfiability-modulo-theories (SMT) solvers are among the best backends for verification tools and "hammers" in proof assistants. When proof obligations contain quantified formulas, SMT solvers rely on instantiation, replacing quantified subformulas by sets of ground instances. Three main techniques have been designed: enumerative [11], trigger-based [4], and conflict-based [12] instantiation. Among these, only conflict-based instantiation computes instances that are guaranteed to be relevant, but it is incomplete and is normally used in combination with other techniques. Enumerative and trigger-based techniques are highly heuristic and generate a large number of instances, most of them useless. As a result, the search space of the solver explodes. Reducing the number of instances could improve the solver's efficiency and success rate within a given time limit. We propose to use a state-of-the-art machine learning algorithm as a predictor over the generated set of instances to filter out irrelevant instances, and thus decrease the number of instances given to the ground solver. The predictor is invoked after each instantiation round to rate the potential usefulness of each generated instance. Several strategies are then used to build a subset of potentially relevant instances that are immediately added to the ground solver. Adding the other instances is postponed. We conducted our experiment in veriT [2], an SMT solver that implements all three in-stantiation techniques described above. We chose as predictor the XGBoost gradient boosting toolkit [3] with the binary classification objective. This configuration had already been used successfully in the context of theorem proving [6, 10]. Choosing a suitable set of features is crucial for effective machine learning. The features determine how precise the representation of the problem is. Previous works already investigate features for theorem proving [1, 5, 6, 8-10]. Our features are more specifically inspired by ENIGMA [6] and RLCoP [7]. They are basically term symbols and term walks with symbol sequences projected to features using Vowpal Wabbit hashing. Term variables and Skolem constants are translated analogously to constants. The model is further enriched with abstract features such as term size, term depth, and the number of instances. To encode our problem into sparse vectors, we use three kinds of information available to the solver: the ground part of the formula (set of literals l 1 ,. .. , l m), the quantified formul