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Extensions of Büchi's problem: Questions of decidability for addition and kth powers

Thanases Pheidas, Xavier Vidaux (2005)

Fundamenta Mathematicae

We generalize a question of Büchi: Let R be an integral domain, C a subring and k ≥ 2 an integer. Is there an algorithm to decide the solvability in R of any given system of polynomial equations, each of which is linear in the kth powers of the unknowns, with coefficients in C? We state a number-theoretical problem, depending on k, a positive answer to which would imply a negative answer to the question for R = C = ℤ. We reduce a negative answer for k = 2 and for...

Extensions of fuzzy connectives on ACDL

Hui Liu, Bin Zhao (2019)

Kybernetika

The main goal of this paper is to construct fuzzy connectives on algebraic completely distributive lattice(ACDL) by means of extending fuzzy connectives on the set of completely join-prime elements or on the set of completely meet-prime elements, and discuss some properties of the new fuzzy connectives. Firstly, we present the methods to construct t-norms, t-conorms, fuzzy negations valued on ACDL and discuss whether De Morgan triple will be kept. Then we put forward two ways to extend fuzzy implications...

Extraction of fuzzy logic rules from data by means of artificial neural networks

Martin Holeňa (2005)

Kybernetika

The extraction of logical rules from data has been, for nearly fifteen years, a key application of artificial neural networks in data mining. Although Boolean rules have been extracted in the majority of cases, also methods for the extraction of fuzzy logic rules have been studied increasingly often. In the paper, those methods are discussed within a five-dimensional classification scheme for neural-networks based rule extraction, and it is pointed out that all of them share the feature of being...

Fermat’s Little Theorem via Divisibility of Newton’s Binomial

Rafał Ziobro (2015)

Formalized Mathematics

Solving equations in integers is an important part of the number theory [29]. In many cases it can be conducted by the factorization of equation’s elements, such as the Newton’s binomial. The article introduces several simple formulas, which may facilitate this process. Some of them are taken from relevant books [28], [14]. In the second section of the article, Fermat’s Little Theorem is proved in a classical way, on the basis of divisibility of Newton’s binomial. Although slightly redundant in...

Finite Product of Semiring of Sets

Roland Coghetto (2015)

Formalized Mathematics

We formalize that the image of a semiring of sets [17] by an injective function is a semiring of sets.We offer a non-trivial example of a semiring of sets in a topological space [21]. Finally, we show that the finite product of a semiring of sets is also a semiring of sets [21] and that the finite product of a classical semiring of sets [8] is a classical semiring of sets. In this case, we use here the notation from the book of Aliprantis and Border [1].

Finite Symmetric Functions with Non-Trivial Arity Gap

Shtrakov, Slavcho, Koppitz, Jörg (2012)

Serdica Journal of Computing

Given an n-ary k-valued function f, gap(f) denotes the essential arity gap of f which is the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f. In the present paper we study the properties of the symmetric function with non-trivial arity gap (2 ≤ gap(f)). We prove several results concerning decomposition of the symmetric functions with non-trivial arity gap with its minors or subfunctions. We show that all non-empty sets of...

First Order Languages: Further Syntax and Semantics

Marco Caminati (2011)

Formalized Mathematics

Third of a series of articles laying down the bases for classical first order model theory. Interpretation of a language in a universe set. Evaluation of a term in a universe. Truth evaluation of an atomic formula. Reassigning the value of a symbol in a given interpretation. Syntax and semantics of a non atomic formula are then defined concurrently (this point is explained in [16], 4.2.1). As a consequence, the evaluation of any w.f.f. string and the relation of logical implication are introduced....

Fixpoints, games and the difference hierarchy

Julian C. Bradfield (2003)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Drawing on an analogy with temporal fixpoint logic, we relate the arithmetic fixpoint definable sets to the winning positions of certain games, namely games whose winning conditions lie in the difference hierarchy over Σ 2 0 . This both provides a simple characterization of the fixpoint hierarchy, and refines existing results on the power of the game quantifier in descriptive set theory. We raise the problem of transfinite fixpoint hierarchies.

Fixpoints, games and the difference hierarchy

Julian C. Bradfield (2010)

RAIRO - Theoretical Informatics and Applications

Drawing on an analogy with temporal fixpoint logic, we relate the arithmetic fixpoint definable sets to the winning positions of certain games, namely games whose winning conditions lie in the difference hierarchy over Σ 2 0 . This both provides a simple characterization of the fixpoint hierarchy, and refines existing results on the power of the game quantifier in descriptive set theory. We raise the problem of transfinite fixpoint hierarchies.

Folding theory applied to BL-algebras

Young Jun, Jung Ko (2004)

Open Mathematics

The notion of n-fold grisly deductive systems is introduced. Some conditions for a deductive system to be an n-fold grisly deductive system are provided. Extension property for n-fold grisly deductive system is established.

Fopid Controller Design for Robust Performance Using Particle Swarm Optimization

Zamani, Majid, Karimi-Ghartemani, Masoud, Sadati, Nasser (2007)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33; 93C15, 93C55, 93B36, 93B35, 93B51; 03B42; 70Q05; 49N05This paper proposes a novel method to design an H∞ -optimal fractional order PID (FOPID) controller with ability to control the transient, steady-state response and stability margins characteristics. The method uses particle swarm optimization algorithm and operates based on minimizing a general cost function. Minimization of the cost function is carried out subject to the H∞ -norm; this norm is also...

Formalization of Generalized Almost Distributive Lattices

Adam Grabowski (2014)

Formalized Mathematics

Almost Distributive Lattices (ADL) are structures defined by Swamy and Rao [14] as a common abstraction of some generalizations of the Boolean algebra. In our paper, we deal with a certain further generalization of ADLs, namely the Generalized Almost Distributive Lattices (GADL). Our main aim was to give the formal counterpart of this structure and we succeeded formalizing all items from the Section 3 of Rao et al.’s paper [13]. Essentially among GADLs we can find structures which are neither V-commutative...

Currently displaying 361 – 380 of 1305