Various models and languages for describing and manipulating hierarchically structured data have been proposed. Algebraic, calculus-based and logic-programming oriented languages have all been considered. This paper presents a general model for complex values (i.e., values with hierarchical structures), and languages for it based on the three paradigms. The algebraic language generalizes those ...

Cantor proved that the n−dimensional manyfold remains continuous if the set of points with purely algebraic coordinates is removed. This proof is simplified and it is shown, that continuity is also preserved if the set of points with purely transcendental coordinates is removed. Cantor’s first proof of the uncountability of real numbers is modified to cover the set of algebraic numbers and even...

A novel offline signature modeling is introduced and evaluated which attempts to advance a grid based feature extraction method uniting it with the use of an ordered powerset. Specifically, this work represents the pixel distribution of the signature trace by modeling specific predetermined paths having Chebyshev distance of two, as being members of alphabet subsets-events. In addition, it is p...

We address the strategy problem for parity games with partial information and observable colors, played on finite graphs of bounded graph complexity. We consider several measures for the complexity of graphs and analyze in which cases, bounding the measure decreases the complexity of the strategy problem on the corresponding classes of graphs. We prove or disprove that the usual powerset constr...

The aim of Coalgebraic Logic is to find formalisms that allow reasoning about T-coalgebras uniformly in the functor T. Moss' seminal idea was to consider the set functor T as providing a modality ∇ T , the semantics of which is given in terms of the relation lifting of T. The latter exists whenever T preserves weak pullbacks. In joint work with Marta Bílková, Alexander Kurz and Jiří Velebil, we...

The contravariant powerset, and its generalisations Σ to the lattices of open subsets of a locally compact topological space and of recursively enumerable subsets of numbers, satisfy the Euclidean principle that φ ∧ F (φ) = φ ∧ F (>). Conversely, when the adjunction Σ(−) a Σ(−) is monadic, this equation implies that Σ classifies some class of monos, and the Frobenius law ∃x.(φ(x) ∧ ψ) = (∃x.φ(x...

The powerset construction is a standard method for converting a nondeterministic automaton into a deterministic one recognizing the same language. In this paper, we lift the powerset construction from automata to the more general framework of coalgebras with structured state spaces. Coalgebra is an abstract framework for the uniform study of different kinds of dynamical systems. An endofunctor ...

Strong normalization results are obtained for a general language for collection types. An induced normal form for sets and bags is then used to show that the class of functions whose input has height (that is, the maximal depth of nestings of sets/bags/lists in the complex object) at most i and output has height at most o de nable in a nested relational query language without powerset operator ...