Search results for "SETS"
showing 10 items of 592 documents
Uncertainty measures—Problems concerning additivity
2009
Additivity of an uncertainty measure on an MV-algebra has a clear meaning. If the divisibility is dropped, we come up to a so-called Girard algebra. There we discuss strong resp. weak additivity based on so-called divisible disjoint unions resp. on additivity for all sub-MV-algebras. We obtain a description of those extensions from additive measures on an MV-algebra to the canonical Girard algebra extension of pairs which are strongly additive and valuation measures. Finally, we prove the non-existence of strongly additive measure extensions, if the underlying MV-algebra is a finite chain with more than two non-trivial elements.
Category, Measure, Inductive Inference: A Triality Theorem and Its Applications
2002
The famous Sierpinski-Erdos Duality Theorem [Sie34b, Erd43] states, informally, that any theorem about effective measure 0 and/or first category sets is also true when all occurrences of "effective measure 0" are replaced by "first category" and vice versa. This powerful and nice result shows that "measure" and "category" are equally useful notions neither of which can be preferred to the other one when making formal the intuitive notion "almost all sets." Effective versions of measure and category are used in recursive function theory and related areas, and resource-bounded versions of the same notions are used in Theory of Computation. Again they are dual in the same sense.We show that in…
Unavoidable sets and circular splicing languages
2017
Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. They are defined by a finite alphabet A, an initial set I of circular words, and a set R of rules. In this paper, we focus on the still unknown relations between regular languages and circular splicing systems with a finite initial set and a finite set R of rules represented by a pair of letters ( ( 1 , 3 ) -CSSH systems). When R = A × A , it is known that the set of all words corresponding to the splicing language belongs to the class of pure unitary languages, introduced by Ehrenfeucht, Haussler, Rozenberg in 1983. They also provided a characteriza…
On a generalization of Goguen's category Set(L)
2007
The paper considers a category which generalizes Goguen's category Set(L) of L-fuzzy sets with a fixed basis L. We show the necessary and sufficient conditions for the generalized category to be a quasitopos and consider additional inner structure supplied by the latter property.
Dimensions of random affine code tree fractals
2014
We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.
Introduction to generalized topological spaces
2011
[EN] We introduce the notion of generalized topological space (gt-space). Generalized topology of gt-space has the structure of frame and is closed under arbitrary unions and finite intersections modulo small subsets. The family of small subsets of a gt-space forms an ideal that is compatible with the generalized topology. To support the definition of gt-space we prove the frame embedding modulo compatible ideal theorem. Weprovide some examples of gt-spaces and study key topological notions (continuity, separation axioms, cardinal invariants) in terms of generalized spaces.
Some remarks on the category SET(L), part III
2004
This paper considers the category SET(L) of L-subsets of sets with a fixed basis L and is a continuation of our previous investigation of this category. Here we study its general properties (e.g., we derive that the category is a topological construct) as well as some of its special objects and morphisms.
On the computational power of affine automata
2017
We investigate the computational power of affine automata (AfAs) introduced in [4]. In particular, we present a simpler proof for how to change the cutpoint for any affine language and a method how to reduce error in bounded error case. Moreover, we address to the question of [4] by showing that any affine language can be recognized by an AfA with certain limitation on the entries of affine states and transition matrices. Lastly, we present the first languages shown to be not recognized by AfAs with bounded-error.
Character sums and double cosets
2008
Abstract If G is a p-solvable finite group, P is a self-normalizing Sylow p-subgroup of G with derived subgroup P ′ , and Ψ is the sum of all the irreducible characters of G of degree not divisible by p, then we prove that the integer Ψ ( P ′ z P ′ ) is divisible by | P | for all z ∈ G . This answers a question of J. Alperin.
Nondeterministic operations on finite relational structures
1998
Abstract This article builds on a tutorial introduction to universal algebra for language theory (Courcelle, Theoret. Comput. Sci. 163 (1996) 1–54) and extends it in two directions. First, nondeterministic operations are considered, i.e., operations which give a set of results instead of a single one. Most of their properties concerning recognizability and equational definability carry over from the ordinary case with minor modifications. Second, inductive sets of evaluations are studied in greater detail. It seems that they are handled most naturally in the framework presented here. We consider the analogues of top-down and bottom-up tree transducers. Again, most of their closure propertie…