Set-Based Invariants over Polynomial Systems

Dynamical systems model the time evolution of both natural and engineered processes. The automatic analysis of such models relies on different techniques ranging from reachability analysis, model checking, theorem proving, and abstractions. In this context, invariants are subsets of the state space containing all the states reachable from themself. The verification and synthesis of invariants is still a challenging problem over many classes of dynamical systems, since it involves the analysis of an infinite time horizon. In this paper we propose a method for computing invariants through sets of trajectories propagation. The method has been implemented and tested in the tool Sapo which provides reachability methods over discrete time polynomial dynamical systems

Fairness, assumptions, and guarantees for extended bounded response LTL+P synthesis

Realizability and reactive synthesis from temporal logics are fundamental problems in formal verification. The complexity of these problems for linear temporal logic with past (LTL+P) led to the identification of fragments with lower complexities and simpler algorithms. Recently, the logic of extended bounded response LTL+P (LTLEBR+ P for short) has been introduced. It allows one to express safety languages definable in LTL+P and it is provided with an efficient, fully symbolic algorithm for reactive synthesis. This paper features four related contributions. First, we introduce GR-EBR , an extension of LTLEBR+ P with fairness conditions, assumptions, and guarantees that, on the one hand, allows one to express properties beyond the safety fragment and, on the other, it retains the efficiency of LTLEBR+ P in practice. Second, we the expressiveness of GR-EBR starting from the expressiveness of its fragments. In particular, we prove that: (1) LTLEBR+ P is expressively complete with respect to the safety fragment of LTL+P , (2) the removal of past operators from LTLEBR+ P results into a loss of expressive power, and (3) GR-EBR is expressively equivalent to the logic GR(1) of Bloem et al. Third, we provide a fully symbolic algorithm for the realizability problem from GR-EBR specifications, that reduces it to a number of safety subproblems. Fourth, to ensure soundness and completeness of the algorithm, we propose and exploit a general framework for safety reductions in the context of realizability of (fragments of) LTL+P . The experimental evaluation shows promising results

A FIRST-ORDER LOGIC CHARACTERIZATION OF SAFETY AND CO-SAFETY LANGUAGES

Linear Temporal Logic (LTL) is one of the most popular temporal logics and comes into play in a variety of branches of computer science. Among the various reasons of its widespread use there are its strong foundational properties: LTL is equivalent to counter-free ω-automata, to star-free ω-regular expressions, and (by Kamp’s theorem) to the First-Order Theory of Linear Orders (FO-TLO). Safety and co-safety languages, where a finite prefix suffices to establish whether a word does not belong or belongs to the language, respectively, play a crucial role in lowering the complexity of problems like model checking and reactive synthesis for LTL. Safety-LTL (resp., coSafety-LTL) is a fragment of LTL where only the tomorrow, the weak tomorrow and the until temporal modalities (resp., the tomorrow, the weak tomorrow and the release temporal modalities) are allowed, that recognises safety (resp., co-safety) languages only. The main contribution of this paper is the introduction of a fragment of FO-TLO, called Safety-FO, and of its dual coSafety-FO, which are expressively complete with respect to the LTL-definable safety and co-safety languages. We prove that they exactly characterize Safety-LTL and coSafety-LTL, respectively, a result that joins Kamp’s theorem, and provides a clearer view of the characterization of (fragments of) LTL in terms of first-order languages. In addition, it gives a direct, compact, and self-contained proof that any safety language definable in LTL is definable in Safety-LTL as well. As a by-product, we obtain some interesting results on the expressive power of the weak tomorrow operator of Safety-LTL, interpreted over finite and infinite words. Moreover, we prove that, when interpreted over finite words, Safety-LTL (resp. coSafety-LTL) devoid of the tomorrow (resp., weak tomorrow) operator captures the safety (resp., co-safety) fragment of LTL over finite words. We then investigate some formal properties of Safety-FO and coSafety-FO: (i) we study their succinctness with respect to their modal counterparts, namely, Safety-LTL and coSafety-LTL; (ii) we illustrate an important practical application of them in the context of reactive synthesis; (iii) we compare them with expressively equivalent first-order fragments. Last but not least, we provide different characterizations of the (co-)safety fragment of LTL in terms of temporal logics, automata, and regular expressions

Distinctive effects of allochthonous and autochthonous organic matter on CDOM spectra in a tropical lake

Despite the increasing understanding about differences in carbon cycling between temperate and tropical freshwater systems, our knowledge on the importance of organic matter (OM) pools on light absorption properties in tropical lakes is very scarce. We performed a factorial mesocosm experiment in a tropical lake (Minas Gerais, Brazil) to evaluate the effects of increased concentrations of al-lochthonous and autochthonous OM, and differences in light availability on the light absorption characteristics of chromophoric dissolved organic matter (CDOM). Autochthonous OM deriving from phytoplankton (similar to Chl a) was stimulated by addition of nutrients, while OM from degradation of terrestrial leaves increased allochthonous OM, and neutral shading was used to manipulate light availability. Effects of the additions and shading on DOC, Chl a, nutrients, total suspended solid concentrations (TSM) and spectral CDOM absorption were monitored every 3 days. CDOM quality was characterized by spectral indices (S250-450, S275-295, S350-450, S-R and SUVA(254)). Effects of carbon sources and shading on the spectral CDOM absorption was investigated through principal component (PCA) and redundancy (RDA) analyses. The two different OM sources affected CDOM quality very differently and shading had minor effects on OM levels, but significant effects on OM quality, especially in combination with nutrient additions. Spectral indices (S250-450 and S-R) were mostly affected by allochthonous OM addition. The PCA showed that enrichment by allochthonous carbon had a strong effect on the CDOM spectra in the range between 300 and 400 nm, while the increase in autochthonous carbon increased absorption at wavelengths below 350 nm. Our study shows that small inputs of allochthonous OM can have large effects on the spectral light absorption compared to large production of autochthonous OM, with important implications for carbon cycling in tropical lakes.Peer reviewe

Linking shifts in bacterial community with changes in dissolved organic matter pool in a tropical lake

Bacterioplankton communities have a pivotal role in the global carbon cycle. Still the interaction between microbial community and dissolved organic matter (DOM) in freshwater ecosystems remains poorly understood. Here, we report results from a 12-day mesocosm study performed in the epilimnion of a tropical lake, in which inorganic nutrients and allochthonous DOM were supplemented under full light and shading. Although the production of autochthonous DOM triggered by nutrient addition was the dominant driver of changes in bacterial community structure, temporal covariations between DOM optical proxies and bacterial community structure revealed a strong influence of community shifts on DOM fate. Community shifts were coupled to a successional stepwise alteration of the DOM pool, with different fractions being selectively consumed by specific taxa Typical freshwater clades as Limnohabitans and Sporichthyaceae were associated with consumption of low molecular weight carbon, whereas Gammaproteobacteria and Flavobacteria utilized higher molecular weight carbon, indicating differences in DOM preference among Glades. Importantly. Verrucomicrobiaceae were important in the turnover of freshly produced autochthonous DOM, ultimately affecting light availability and dissolved organic carbon concentrations. Our findings suggest that taxonomically defined bacterial assemblages play definite roles when influencing DOM fate, either by changing specific fractions of the DOM pool or by regulating light availability and DOC levels. (C) 2019 Elsevier B.V. All rights reserved.Peer reviewe

Estrogen receptor transcription and transactivation: Estrogen receptor knockout mice - what their phenotypes reveal about mechanisms of estrogen action

Natural, synthetic and environmental estrogens have numerous effects on the development and physiology of mammals. Estrogen is primarily known for its role in the development and functioning of the female reproductive system. However, roles for estrogen in male fertility, bone, the circulatory system and immune system have been established by clinical observations regarding sex differences in pathologies, as well as observations following menopause or castration. The primary mechanism of estrogen action is via binding and modulation of activity of the estrogen receptors (ERs), which are ligand-dependent nuclear transcription factors. ERs are found in highest levels in female tissues critical to reproduction, including the ovaries, uterus, cervix, mammary glands and pituitary gland. Since other affected tissues have extremely low levels of ER, indirect effects of estrogen, for example induction of pituitary hormones that affect the bone, have been proposed. The development of transgenic mouse models that lack either estrogen or ER have proven to be valuable tools in defining the mechanisms by which estrogen exerts its effects in various systems. The aim of this article is to review the mouse models with disrupted estrogen signaling and describe the associated phenotypes

Quantifier-free encoding of invariants for hybrid systems

Hybrid systems are a clean modeling framework for embedded systems, which feature integrated discrete and continuous dynamics. A well-known source of complexity comes from the time invariants, which represent an implicit quan- tication of a constraint over all time points of a continuous transition. Emerging techniques based on Satisability Modulo Theory (SMT) have been found promising for the verication and validation of hybrid systems because they combine discrete reasoning with solvers for rst-order theories. However, these techniques are ecient for quantier-free theories and the current approaches have so far either ignored time invariants or have been limited to hybrid systems with linear constraints. In this paper, we propose a new method that encodes a class of hybrid systems into transition systems with quantier-free formulas. The method does not rely on expensive quantier elimination procedures. Rather, it exploits the sequential nature of the transition system to split the continuous evolution enforcing the invariants on the discrete time points. This way, we can encode all hybrid systems whose invariants can be expressed in terms of polynomial constraints. This pushes the application of SMT-based techniques beyond the standard linear case