Search results for " Computer"

Additivity of affine designs

2020

We show that any affine block design $$\mathcal{D}=(\mathcal{P},\mathcal{B})$$ is a subset of a suitable commutative group $${\mathfrak {G}}_\mathcal{D},$$ with the property that a k-subset of $$\mathcal{P}$$ is a block of $$\mathcal{D}$$ if and only if its k elements sum up to zero. As a consequence, the group of automorphisms of any affine design $$\mathcal{D}$$ is the group of automorphisms of $${\mathfrak {G}}_\mathcal{D}$$ that leave $$\mathcal P$$ invariant. Whenever k is a prime p,  $${\mathfrak {G}}_\mathcal{D}$$ is an elementary abelian p-group.

On monadic quantale algebras: basic properties and representation theorems

2010

Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new structures.

Symmetric and asymmetric cryptographic key exchange protocols in the octonion algebra

2019

AbstractWe propose three cryptographic key exchange protocols in the octonion algebra. Using the totient function, defined for integral octonions, we generalize the RSA public-key cryptosystem to the octonion arithmetics. The two proposed symmetric cryptographic key exchange protocols are based on the automorphism and the derivation of the octonion algebra.

Finitary shadows of compact subgroups of $$S(\omega )$$

2020

AbstractLet LF be the lattice of all subgroups of the group $$SF(\omega )$$SF(ω) of all finitary permutations of the set of natural numbers. We consider subgroups of $$SF(\omega )$$SF(ω) of the form $$C\cap SF(\omega )$$C∩SF(ω), where C is a compact subgroup of the group of all permutations. In particular, we study their distribution among elements of LF. We measure this using natural relations of orthogonality and almost containedness. We also study complexity of the corresponding families of compact subgroups of $$S(\omega )$$S(ω).

Arithmetical Analysis of Biomolecular Finite Automaton

2013

In the paper we present a theoretical analysis of extension of the finite automaton built on DNA (introduced by the Shapiro team) to an arbitrary number of states and symbols. In the implementation we use a new idea of several restriction enzymes instead of one. We give arithmetical conditions for the existence of such extensions in terms of ingredients used in the implementation.

Forcing for First-Order Languages from the Perspective of Rasiowa–Sikorski Lemma

2017

The paper is concerned with the problem of building models for first-order languages from the perspective of the classic paper of Rasiowa and Sikorski [9]. The central idea, developed in this paper, consists in constructing first-order models from individual variables. The key notion of a Rasiowa–Sikorski set of formulas for an arbitrary countable language L is examined. Each Rasiowa–Sikorski set defines a countable model for L . Conversely, every countable model for L is determined by a Rasiowa–Sikorski set. The focus is on constructing Rasiowa–Sikorski sets by applying forcing techniques restricted to Boolean algebras arising from the subsets of the set of atomic formulas of L .

TWO-DIMENSIONAL FINITE STATE RECOGNIZABILITY

1996

The purpose of this paper is to investigate about a new notion of finite state recognizability for two-dimensional (picture) languages. This notion takes as starting point the characterization of one-dimensional recognizable languages in terms of local languages and projections. Such notion can be extended in a natural way to the two-dimensional case. We first introduce a notion of local picture language and then we define,a recognizable picture language as a projection of a local picture language. The family of recognizable picture languages is denoted by REC. We study some combinatorial and language-theoretic properties of family REC. In particular we prove some closure properties with re…

A Survey on Nature-Inspired Medical Image Analysis: A Step Further in Biomedical Data Integration

2019

Natural phenomena and mechanisms have always intrigued humans, inspiring the design of effective solutions for real-world problems. Indeed, fascinating processes occur in nature, giving rise to an ever-increasing scientific interest. In everyday life, the amount of heterogeneous biomedical data is increasing more and more thanks to the advances in image acquisition modalities and high-throughput technologies. The automated analysis of these large-scale datasets creates new compelling challenges for data-driven and model-based computational methods. The application of intelligent algorithms, which mimic natural phenomena, is emerging as an effective paradigm for tackling complex problems, by…

Stubborn sets, frozen actions, and fair testing

2021

Many partial order methods use some special condition for ensuring that the analysis is not terminated prematurely. In the case of stubborn set methods for safety properties, implementation of the condition is usually based on recognizing the terminal strong components of the reduced state space and, if necessary, expanding the stubborn sets used in their roots. In an earlier study it was pointed out that if the system may execute a cycle consisting of only invisible actions and that cycle is concurrent with the rest of the system in a non-obvious way, then the method may be fooled to construct all states of the full parallel composition. This problem is solved in this study by a method tha…

Bornological structures on many-valued sets

2017