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Some complexity results in topology and analysis

Steve Jackson, R. Mauldin (1992)

Fundamenta Mathematicae

If X is a compact metric space of dimension n, then K(X), the n- dimensional kernel of X, is the union of all n-dimensional Cantor manifolds in X. Aleksandrov raised the problem of what the descriptive complexity of K(X) could be. A straightforward analysis shows that if X is an n-dimensional complete separable metric space, then K(X) is a Σ 2 1 or PCA set. We show (a) there is an n-dimensional continuum X in ℝ n + 1 for which K(X) is a complete Π 1 1 set. In particular, K ( X ) ∈ Π 1 1 - Σ 1 1 ; K(X) is coanalytic but is not an analytic...

Some decidable congruences of free monoids

Jaroslav Ježek (1999)

Czechoslovak Mathematical Journal

Let W be the free monoid over a finite alphabet A . We prove that a congruence of W generated by a finite number of pairs 〈 a u , u 〉 , where a ∈ A and u ∈ W , is always decidable.

Some decidable theories with finitely many covers which are decidable and algorithmically found

Cornelia Kalfa (1994)

Colloquium Mathematicae

In any recursive algebraic language, I find an interval of the lattice of equational theories, every element of which has finitely many covers. With every finite set of equations of this language, an equational theory of this interval is associated, which is decidable with decidable covers that can be algorithmically found. If the language is finite, both this theory and its covers are finitely based. Also, for every finite language and for every natural number n, I construct a finitely based decidable...

Some distributivities in GBbi-QRs characterizing Boolean rings

Joanna Kaleta (2004)

Discussiones Mathematicae - General Algebra and Applications

This paper presents some manner of characterization of Boolean rings. These algebraic systems one can also characterize by means of some distributivities satisfied in GBbi-QRs.

Some examples of true F σ δ sets

Marek Balcerzak, Udayan Darji (2000)

Colloquium Mathematicae

Let K(X) be the hyperspace of a compact metric space endowed with the Hausdorff metric. We give a general theorem showing that certain subsets of K(X) are true F σ δ sets.

Some Facts about Trigonometry and Euclidean Geometry

Roland Coghetto (2014)

Formalized Mathematics

We calculate the values of the trigonometric functions for angles: [XXX] , by [16]. After defining some trigonometric identities, we demonstrate conventional trigonometric formulas in the triangle, and the geometric property, by [14], of the triangle inscribed in a semicircle, by the proposition 3.31 in [15]. Then we define the diameter of the circumscribed circle of a triangle using the definition of the area of a triangle and prove some identities of a triangle [9]. We conclude by indicating that...

Some issues of fuzzy querying in relational databases

Miroslav Hudec, Miljan Vučetić (2015)

Kybernetika

Fuzzy logic has been used for flexible database querying for more than 30 years. This paper examines some of the issues of flexible querying which seem to have potential for further research and development from theoretical and practical points of view. More precisely, defining appropriate fuzzy sets for queries, calculating matching degrees for commutative and non-commutative query conditions, preferences, merging constraints and wishes, empty and overabundant answers, and views on practical realizations...

Some key research problems in automated theorem proving for hardware and software verification.

Matt Kaufmann, J. Strother Moore (2004)

RACSAM

This paper sketches the state of the art in the application of mechanical theorem provers to the verification of commercial computer hardware and software. While the paper focuses on the theorem proving system ACL2, developed by the two authors, it references much related work in formal methods. The paper is intended to satisfy the curiosity of readers interested in logic and artificial intelligence as to the role of mechanized theorem proving in hardware and software design today. In addition,...

Some methods to obtain t-norms and t-conorms on bounded lattices

Gül Deniz Çaylı (2019)

Kybernetika

In this study, we introduce new methods for constructing t-norms and t-conorms on a bounded lattice L based on a priori given t-norm acting on [ a , 1 ] and t-conorm acting on [ 0 , a ] for an arbitrary element a ∈ L ∖ { 0 , 1 } . We provide an illustrative example to show that our construction methods differ from the known approaches and investigate the relationship between them. Furthermore, these methods are generalized by iteration to an ordinal sum construction for t-norms and t-conorms on a bounded lattice.

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