Topological automata
Topological complexity of motion planning and Massey products
We employ Massey products to find sharper lower bounds for the Schwarz genus of a fibration than those previously known. In particular we give examples of non-formal spaces X for which the topological complexity TC(X) (defined to be the genus of the free path fibration on X) is greater than the zero-divisors cup-length plus one.
Topological deformation of higher dimensional automata.
Topological Interpretation of Rough Sets
Rough sets, developed by Pawlak, are an important model of incomplete or partially known information. In this article, which is essentially a continuation of [11], we characterize rough sets in terms of topological closure and interior, as the approximations have the properties of the Kuratowski operators. We decided to merge topological spaces with tolerance approximation spaces. As a testbed for our developed approach, we restated the results of Isomichi [13] (formalized in Mizar in [14]) and...
Topological views on computational complexity.
Topologies, continuity and bisimulations
Topologies, Continuity and Bisimulations
The notion of a bisimulation relation is of basic importance in many areas of computation theory and logic. Of late, it has come to take a particular significance in work on the formal analysis and verification of hybrid control systems, where system properties are expressible by formulas of the modal μ-calculus or weaker temporal logics. Our purpose here is to give an analysis of the concept of bisimulation, starting with the observation that the zig-zag conditions are suggestive of some...
Topologies on free monoids induced by closure operators of a special type
Torus knots extremizing the Möbius energy.
Totally coherent set-valued probability assessments
We introduce the concept of total coherence of a set-valued probability assessment on a family of conditional events. In particular we give sufficient and necessary conditions of total coherence in the case of interval-valued probability assessments. Some relevant cases in which the set-valued probability assessment is represented by the unitary hypercube are also considered.
Totally greedy coin sets and greedy obstructions.
Tournaments as feedback arc sets.
Tours de Hanoï et automates
Toward a semantics for the QUEST language
Towards a Digital Mathematical Library
The workshop’s objectives were to formulate the strategy and goals of a global mathematical digital library and to summarize the current successes and failures of ongoing technologies and related projects. There is already some experience with building smaller DMLs and/or building big thematical scientific digital libraries. Why there are already big fulltext digital library in some domains like PubMed in biomedical one, but none in others? We try to pose such and other questions, and try to find...
Towards a Digital Mathematics Library. On the Crossroad
The DML workshop’s objectives were to formulate the strategy and goals of a global mathematical digital library and to summarize the current successes and failures of ongoing technologies and related projects. There is already experience with building regional DMLs or building big thematic scientific digital libraries. EuDML project reached it halflife period. While there are already big fulltext digital libraries in some domains like PubMed Central in the biomedical domain, Inspire in high-energy...
Towards a Flexible Author Name Disambiguation Framework
In this paper we propose a flexible, modular framework for author name disambiguation. Our solution consists of the core which orchestrates the disambiguation process, and replaceable modules performing concrete tasks. The approach is suitable for distributed computing, in particular it maps well to the MapReduce framework. We describe each component in detail and discuss possible alternatives. Finally, we propose procedures for calibration and evaluation of the described system.
Towards a general principle of evaluation for approximate algorithms
Towards a linguistic description of dependencies in data
The problem of a linguistic description of dependencies in data by a set of rules R_k: “If X is T_k then Y is S_k” is considered, where T_k’s are linguistic terms like SMALL, BETWEEN 5 AND 7 describing some fuzzy intervals A_k. S_k’s are linguistic terms like DECREASING and QUICKLY INCREASING describing the slopes p_k of linear functions y_k = p_{k}x + q_k approximating data on A_k. The decision of this problem is obtained as a result of a fuzzy partition of the domain X on fuzzy intervals A_k,...
Towards a logic of semiotic systems
The rationalistic denotational approach to semantics is not adequate for capturing the structural dimension of meaning, which is immanent in semiotic systems. The demand for a structural approach to semantics is intensified by a turn in Artificial Intelligence, introduced by Connectionism and Information Retrieval. This paper presents such a structural approach to semantics founded on the phenomenological and autopoietic paradigms and proposes a formalization with the help of category theory.