scholarly journals A Behavioural Theory of Recursive Algorithms

2020 ◽  
Vol 177 (1) ◽  
pp. 1-37
Author(s):  
Egon Börger ◽  
Klaus-Dieter Schewe
Keyword(s):  
Recursive Algorithm ◽  
Recursive Algorithms ◽  
State Machines ◽  
Abstract State Machines ◽  
Sequential Algorithms ◽  
Machine Model ◽  
Behavioural Theory ◽  
Concurrent Algorithms ◽  
Definition Of

“What is an algorithm?” is a fundamental question of computer science. Gurevich’s behavioural theory of sequential algorithms (aka the sequential ASM thesis) gives a partial answer by defining (non-deterministic) sequential algorithms axiomatically, without referring to a particular machine model or programming language, and showing that they are captured by (nondeterministic) sequential Abstract State Machines (nd-seq ASMs). However, recursive algorithms such as mergesort are not covered by this theory, as has been pointed out by Moschovakis, who had independently developed a different framework to mathematically characterize the concept of (in particular recursive) algorithm. In this article we propose an axiomatic definition of the notion of sequential recursive algorithm which extends Gurevich’s axioms for sequential algorithms by a Recursion Postulate and allows us to prove that sequential recursive algorithms are captured by recursive Abstract State Machines, an extension of nd-seq ASMs by a CALL rule. Applying this recursive ASM thesis yields a characterization of sequential recursive algorithms as finitely composed concurrent algorithms all of whose concurrent runs are partial-order runs.

Modelling general recursion in type theory

2005 ◽  
Vol 15 (4) ◽  
pp. 671-708 ◽  
Author(s):  
ANA BOVE ◽  
VENANZIO CAPRETTA
Keyword(s):  
Programming Language ◽  
Type Theory ◽  
Functional Programming ◽  
Recursive Algorithm ◽  
Recursive Algorithms ◽  
Constructive Type Theory ◽  
Structural Recursion ◽  
Constructive Type ◽  
Definition Of ◽  
Theoretic Version

Constructive type theory is an expressive programming language in which both algorithms and proofs can be represented. A limitation of constructive type theory as a programming language is that only terminating programs can be defined in it. Hence, general recursive algorithms have no direct formalisation in type theory since they contain recursive calls that satisfy no syntactic condition guaranteeing termination. In this work, we present a method to formalise general recursive algorithms in type theory. Given a general recursive algorithm, our method is to define an inductive special-purpose accessibility predicate that characterises the inputs on which the algorithm terminates. The type-theoretic version of the algorithm is then defined by structural recursion on the proof that the input values satisfy this predicate. The method separates the computational and logical parts of the definitions and thus the resulting type-theoretic algorithms are clear, compact and easy to understand. They are as simple as their equivalents in a functional programming language, where there is no restriction on recursive calls. Here, we give a formal definition of the method and discuss its power and its limitations.

scholarly journals Experimental Evaluation of Shear Behavior of Stone Masonry Wall

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2313
Author(s):  
Maria Luisa Beconcini ◽  
Pietro Croce ◽  
Paolo Formichi ◽  
Filippo Landi ◽  
Benedetta Puccini
Keyword(s):  
Shear Behavior ◽  
Stone Masonry ◽  
Masonry Walls ◽  
Mechanical Parameters ◽  
In Situ Tests ◽  
Capacity Curves ◽  
Historical Structures ◽  
Definition Of

The evaluation of the shear behavior of masonry walls is a first fundamental step for the assessment of existing masonry structures in seismic zones. However, due to the complexity of modelling experimental behavior and the wide variety of masonry types characterizing historical structures, the definition of masonry’s mechanical behavior is still a critical issue. Since the possibility to perform in situ tests is very limited and often conflicting with the needs of preservation, the characterization of shear masonry behavior is generally based on reference values of mechanical properties provided in modern structural codes for recurrent masonry categories. In the paper, a combined test procedure for the experimental characterization of masonry mechanical parameters and the assessment of the shear behavior of masonry walls is presented together with the experimental results obtained on three stone masonry walls. The procedure consists of a combination of three different in situ tests to be performed on the investigated wall. First, a single flat jack test is executed to derive the normal compressive stress acting on the wall. Then a double flat jack test is carried out to estimate the elastic modulus. Finally, the proposed shear test is performed to derive the capacity curve and to estimate the shear modulus and the shear strength. The first results obtained in the experimental campaign carried out by the authors confirm the capability of the proposed methodology to assess the masonry mechanical parameters, reducing the uncertainty affecting the definition of capacity curves of walls and consequently the evaluation of seismic vulnerability of the investigated buildings.

Fundamental relations and identities of fuzzy hyperalgebras

2021 ◽  
pp. 1-10
Author(s):  
Narjes Firouzkouhi ◽  
Abbas Amini ◽  
Chun Cheng ◽  
Mehdi Soleymani ◽  
Bijan Davvaz
Keyword(s):  
Universal Algebra ◽  
Equivalence Relation ◽  
Polynomial Function ◽  
Equivalence Relations ◽  
Fundamental Relation ◽  
Term Function ◽  
Biological Phenomena ◽  
Definition Of

Inspired by fuzzy hyperalgebras and fuzzy polynomial function (term function), some homomorphism properties of fundamental relation on fuzzy hyperalgebras are conveyed. The obtained relations of fuzzy hyperalgebra are utilized for certain applications, i.e., biological phenomena and genetics along with some elucidatory examples presenting various aspects of fuzzy hyperalgebras. Then, by considering the definition of identities (weak and strong) as a class of fuzzy polynomial function, the smallest equivalence relation (fundamental relation) is obtained which is an important tool for fuzzy hyperalgebraic systems. Through the characterization of these equivalence relations of a fuzzy hyperalgebra, we assign the smallest equivalence relation α i 1 i 2 ∗ on a fuzzy hyperalgebra via identities where the factor hyperalgebra is a universal algebra. We extend and improve the identities on fuzzy hyperalgebras and characterize the smallest equivalence relation α J ∗ on the set of strong identities.

scholarly journals Genomic Tackling of Human Satellite DNA: Breaking Barriers through Time

2021 ◽  
Vol 22 (9) ◽  
pp. 4707
Author(s):  
Mariana Lopes ◽  
Sandra Louzada ◽  
Margarida Gama-Carvalho ◽  
Raquel Chaves
Keyword(s):  
Human Genome ◽  
Satellite Dna ◽  
Repetitive Sequences ◽  
Nucleotide Composition ◽  
Genomic Component ◽  
Genomic Studies ◽  
Human Genomic ◽  
Definition Of ◽  
High Degree

(Peri)centromeric repetitive sequences and, more specifically, satellite DNA (satDNA) sequences, constitute a major human genomic component. SatDNA sequences can vary on a large number of features, including nucleotide composition, complexity, and abundance. Several satDNA families have been identified and characterized in the human genome through time, albeit at different speeds. Human satDNA families present a high degree of sub-variability, leading to the definition of various subfamilies with different organization and clustered localization. Evolution of satDNA analysis has enabled the progressive characterization of satDNA features. Despite recent advances in the sequencing of centromeric arrays, comprehensive genomic studies to assess their variability are still required to provide accurate and proportional representation of satDNA (peri)centromeric/acrocentric short arm sequences. Approaches combining multiple techniques have been successfully applied and seem to be the path to follow for generating integrated knowledge in the promising field of human satDNA biology.

scholarly journals A lattice-theoretic characterization of pure subgroups of Abelian groups

2021 ◽  
Author(s):  
M. Ferrara ◽  
M. Trombetti
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Subgroup Lattice ◽  
General Definition ◽  
Short Paper ◽  
Theoretic Characterization ◽  
Definition Of

AbstractLet G be an abelian group. The aim of this short paper is to describe a way to identify pure subgroups H of G by looking only at how the subgroup lattice $$\mathcal {L}(H)$$ L ( H ) embeds in $$\mathcal {L}(G)$$ L ( G ) . It is worth noticing that all results are carried out in a local nilpotent context for a general definition of purity.

scholarly journals Characterization of Spent Ni-MH Batteries

2012 ◽  
Vol 730-732 ◽  
pp. 569-574
Author(s):  
Marta Cabral ◽  
Fernanda Margarido ◽  
Carlos A. Nogueira
Keyword(s):  
Quantitative Analysis ◽  
Electrode Materials ◽  
Phase Identification ◽  
Recycling Process ◽  
X Ray ◽  
Leaching Experiments ◽  
Plastic Components ◽  
Definition Of ◽  
Physical And Chemical

Spent Ni-MH batteries are not considered too dangerous for the environment, but they have a considerable economical value due to the chemical composition of electrodes which are highly concentrated in metals. The present work aimed at the physical and chemical characterisation of spent cylindrical and thin prismatic Ni-MH batteries, contributing for a better definition of the recycling process of these spent products. The electrode materials correspond to more than 50% of the batteries weight and contain essentially nickel and rare earths (RE), and other secondary elements (Co, Mn, Al). The remaining components are the steel parts from the external case and supporting grids (near 30%) containing Fe and Ni, and the plastic components (<10%). Elemental quantitative analysis showed that the electrodes are highly concentrated in metals. Phase identification by X-ray powder diffraction combined with chemical analysis and leaching experiments allowed advancing the electrode materials composition. The cathode is essentially constituted by 6% metallic Ni, 66% Ni(OH)2, 4.3% Co(OH)2 and the anode consists mainly in 62% RENi5 and 17% of substitutes and/or additives such as Co, Mn and Al.

scholarly journals Surface and Underground Geomechanical Characterization of an Area Affected by Instability Phenomena in Zaruma Mining Zone (Ecuador)

2021 ◽  
Vol 13 (6) ◽  
pp. 3272
Author(s):  
Paúl Carrión-Mero ◽  
Maribel Aguilar-Aguilar ◽  
Fernando Morante-Carballo ◽  
María José Domínguez-Cuesta ◽  
Cristhian Sánchez-Padilla ◽  
...  
Keyword(s):  
Mass Movement ◽  
Mining Activity ◽  
Mining District ◽  
Mean Values ◽  
Surface Areas ◽  
Definition Of ◽  
Action Measures ◽  
Geomechanical Characterization ◽  
The City

In the last decade, in the mining district of Zaruma-Portovelo, there has been significant land subsidence related to uncontrolled mining activity. The purpose of this work was to carry out a surface and underground geomechanical characterization of a mining sector north of the city of Zaruma that allows the definition of potentially unstable areas susceptible to the mass movement. The methodology used consists of the following stages: (i) compilation of previous studies; (ii) surface and underground characterization of rocky material to establish its susceptibility to mass movement; (iii) interpretation of results; and (iv) proposal of action measures. Among the most relevant results, it stands out that 26.1% of the 23 stations characterized on the surface present conditions that vary from potentially unstable to unstable. In underground galleries, the studied mean values of the 17 stations indicate that the rock has a medium to good quality, representing a medium susceptibility to gallery destabilization. The results obtained for the surface areas (depths up to 50 m, where altered materials predominate) and the underground areas (depths > 50 m, where the alterations are specific) can be used to identify the areas with a more significant potential for instability. For both cases, it has been possible to define specific monitoring, control, and planning actions for sensitive areas.

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