On the Expressive Power of Multiple Heads in CHR

Constraint Handling Rules (CHR) is a committed-choice declarative language which has been originally designed for writing constraint solvers and which is nowadays a general purpose language. CHR programs consist of multi-headed guarded rules which allow to rewrite constraints into simpler ones until a solved form is reached. Many empirical evidences suggest that multiple heads augment the expressive power of the language, however no formal result in this direction has been proved, so far. In the first part of this paper we analyze the Turing completeness of CHR with respect to the underneath constraint theory. We prove that if the constraint theory is powerful enough then restricting to single head rules does not affect the Turing completeness of the language. On the other hand, differently from the case of the multi-headed language, the single head CHR language is not Turing powerful when the underlying signature (for the constraint theory) does not contain function symbols. In the second part we prove that, no matter which constraint theory is considered, under some reasonable assumptions it is not possible to encode the CHR language (with multi-headed rules) into a single headed language while preserving the semantics of the programs. We also show that, under some stronger assumptions, considering an increasing number of atoms in the head of a rule augments the expressive power of the language. These results provide a formal proof for the claim that multiple heads augment the expressive power of the CHR language.Comment: v.6 Minor changes, new formulation of definitions, changed some details in the proof

Breaking the power-of-two barrier: noise estimation for BGV in NTT-friendly rings

The Brakerski-Gentry-Vaikuntanathan (BGV) scheme is a Fully Homomorphic Encryption (FHE) cryptosystem based on the Ring Learning With Error (RLWE) problem. Ciphertexts in this scheme contain an error term that grows with operations and causes decryption failure when it surpasses a certain threshold. For this reason, the parameters of BGV need to be estimated carefully, with a trade-off between security and error margin. The ciphertext space of BGV is the ring $\mathcal R_q=\mathbb Z_q[x]/(\Phi_m(x))$, where usually the degree $n$ of the cyclotomic polynomial $\Phi_m(x)$ is chosen as a power of two for efficiency reasons. However, the jump between two consecutive powers-of-two polynomials can sometimes also cause a jump of the security, resulting in parameters that are much bigger than what is needed. In this work, we explore the non-power-of-two instantiations of BGV. Although our theoretical research encompasses results applicable to any cyclotomic ring, our main investigation is focused on the case of $m=2^s 3^t$, i.e., cyclotomic polynomials with degree $n=2^s 3^{t-1}$. We provide a thorough analysis of the noise growth in this new setting using the canonical norm and compare our results with the power-of-two case considering practical aspects like NTT algorithms. We find that in many instances, the parameter estimation process yields better results for the non-power-of-two setting

Decidability properties for fragments of CHR

We study the decidability of termination for two CHR dialects which, similarly to the Datalog like languages, are defined by using a signature which does not allow function symbols (of arity >0). Both languages allow the use of the = built-in in the body of rules, thus are built on a host language that supports unification. However each imposes one further restriction. The first CHR dialect allows only range-restricted rules, that is, it does not allow the use of variables in the body or in the guard of a rule if they do not appear in the head. We show that the existence of an infinite computation is decidable for this dialect. The second dialect instead limits the number of atoms in the head of rules to one. We prove that in this case, the existence of a terminating computation is decidable. These results show that both dialects are strictly less expressive than Turing Machines. It is worth noting that the language (without function symbols) without these restrictions is as expressive as Turing Machines

Advancements in Forest Fire Prevention: A Comprehensive Survey

Nowadays, the challenges related to technological and environmental development are becoming increasingly complex. Among the environmentally significant issues, wildfires pose a serious threat to the global ecosystem. The damages inflicted upon forests are manifold, leading not only to the destruction of terrestrial ecosystems but also to climate changes. Consequently, reducing their impact on both people and nature requires the adoption of effective approaches for prevention, early warning, and well-coordinated interventions. This document presents an analysis of the evolution of various technologies used in the detection, monitoring, and prevention of forest fires from past years to the present. It highlights the strengths, limitations, and future developments in this field. Forest fires have emerged as a critical environmental concern due to their devastating effects on ecosystems and the potential repercussions on the climate. Understanding the evolution of technology in addressing this issue is essential to formulate more effective strategies for mitigating and preventing wildfires

Bismuth exposure affects morpho-physiological performances and the ionomic profile in garden cress (Lepidium sativum L.) plants

Environmental pollution caused by heavy metals has long been considered a relevant threat to ecosystem survival and human health. The use of safer substitutes for the most toxic heavy metals in many industrial applications is discussed as a potential way to face this issue. In this regard, Bi has been proposed for replacing Pb in several production processes. However, few literature records reported on the effects of Bi on living organisms, particularly on plants. In this study, garden cress (Lepidium sativum L.) plants were exposed to different concentrations of Bi nitrate added to soil in growth chambers for 21 days. Results evidenced the toxic effect of Bi on shoot growth, regardless of the Bi nitrate concentration in the soil, paralleled by a similar reduction in the chlorophyll and carotenoid content, a decrease in the nitrogen balance index values, and an impairment of the photosynthetic machinery evaluated by chlorophyll fluorescence image analysis. The presence of Bi in the soil was shown to affect element accumulation in roots and translocation to shoots, with micronutrient content particularly reduced in the leaves of Bi-treated plants. A dose-dependent plant accumulation of Bi to metal concentration in the soil was observed, even if very low metal bioconcentration ability was highlighted. The reduced Bi translocation from roots to shoots in plants exposed to increasing Bi concentrations in the soil is discussed as a possible defense mechanism likely associated with the observed increase of anthocyan and flavonol contents and the activation of photoprotection mechanisms preventing higher damages to the photosynthetic apparatus

Towards Optimal Graph Coloring Using Rydberg Atoms

Quantum mechanics is expected to revolutionize the computing landscape in the near future. Among the many candidate technologies for building universal quantum computers, Rydberg atoms-based systems stand out for being capable of performing both quantum simulations and working as gate-based universal quantum computers while operating at room temperature through an optical system. Moreover, they can potentially scale up to hundreds of quantum bits (qubits). In this work, we solve a Graph Coloring problem by iteratively computing the solutions of Maximal Independent Set (MIS) problems, exploiting the Rydberg blockade phenomenon. Experimental results using a simulation framework on the CINECA Marconi-100 supercomputer demonstrate the validity of the proposed approach

A Social IoT-Based Solution for Real-Time Forest Fire Detection

Conservation of the natural ecosystem is a hot topic that is receiving increasing attention not only from the scientific community, but from the entire world population. Forests and woodlands are major contributors to climate change mitigation, able to absorb significant amounts of carbon dioxide. This paper proposes a novel real-time fire monitoring and detection system based on Digital Mobile Radio (DMR) nodes and a Social Internet of Things (SIoT) platform on which fire detection decision making algorithms have been implemented. The results obtained by employing a K-Nearest Neighbors (KNN) algorithm and a Recurrent Neural Network (RNN) show the ability to detect the slightest variation in the observed parameters, determining the direction and speed of fire propagation with an accuracy of more than 98%

Spectroscopic Kernel Quality From A Symbiotic Corn Production

The management of the inoculation of a plant's roots, by means of biofertilizers (BF) containing arbuscular mycorrhizal (AM) fungi, is aimed at inducing modifications of the quality of the seeds. It is here shown that a seed-soil treatment can be elicited in the fingerprints of a symbiotic treatment using Near Infra Red (NIR)-SCiO NIR-SCiO spectra collections of single kernels: overall, a sensitivity of 73% and a specificity of 73% have been achieved, thus suggesting that it may be possible to assign the symbiotic origin of corn from just twenty kernels, provided that the dataset is adequately representative of the cultivar and AM. A global correlation study has shown a positive general trend (R2 0.45) of quality vs. quantity, in the sense that an increase in yield corresponded to an increase in the spectral differences between the symbiotic spectra and the control ones, but the inverse was also true, as a result of the parasitic behaviour of the BF treatments. The efficacy of the symbiosis can be back predicted from the NIR spectra; in fact, around 90% of the positive yield outcome results were discriminated from the negative ones. A reduction in the foliar pH (R2 0.37) and an increase in the foliar protein (R2 0.43) were observed as immediate phenotypic signs of a productive symbiosis. The commercial raw composition of the kernels appeared to only be affected slightly by the BF treatments; thus, till now uncharted secondary compounds of the maize kernels are involved, as supported by animal performances