Design procedure on a newly developed paper craft.
We report on a new project to design a semantic ground truth set for mathematical document analysis. The ground truth set will be generated by annotating recognised mathematical symbols with respect to both their global meaning in the context of the considered documents and their local function within the particular mathematical formula they occur. The aim of our work is to have a reliable database available for semantic classification during the formula recognition process with the aim of enabling...
Detecting a cluster structure is considered. This means solving either the problem of discovering a natural decomposition of data points into groups (clusters) or the problem of detecting clouds of data points of a specific form. In this paper both these problems are considered. To discover a cluster structure of a specific arrangement or a cloud of data of a specific form a class of nonlinear projections is introduced. Fitness functions that estimate to what extent a given subset of data points...
A new method of detecting deadlocks and traps in Petri nets is presented. Deadlocks and traps in Petri nets can be represented by the roots of special equations in CNF form. Such equations can be solved by using the search tree algorithm proposed by Thelen. In order to decrease the tree size and to accelerate the computations, some heuristics for Thelen's method are presented.
The paper treats the question whether there always exists a minimal nondeterministic finite automaton of n states whose equivalent minimal deterministic finite automaton has α states for any integers n and α with n ≤ α ≤ 2n. Partial answers to this question were given by Iwama, Kambayashi, and Takaki (2000) and by Iwama, Matsuura, and Paterson (2003). In the present paper, the question is completely solved by presenting appropriate automata for all values of n and α. However, in order to...
This paper describes an effort to develop a metadata element set for the exchange of descriptive metadata about mathematical literature. The approach taken uses the Dublin Core Application Profile (DCAP) framework, based on the DC Abstract Model. A fully developed DCAP for mathematical literature would be valuable, as both a guide and constraint in the creation of metadata records suitable for harvesting via OAI or sharing through other means. Adhering to the DCAP model would also enhance global...
The research on incomplete soft sets is an integral part of the research on soft sets and has been initiated recently. However, the existing approach for dealing with incomplete soft sets is only applicable to decision making and has low forecasting accuracy. In order to solve these problems, in this paper we propose a novel data filling approach for incomplete soft sets. The missing data are filled in terms of the association degree between the parameters when a stronger association exists between...
We study diagonalization in the context of implicit proofs of [10]. We prove that at least one of the following three conjectures is true: ∙ There is a function f: 0,1* → 0,1 computable in that has circuit complexity . ∙ ≠ co . ∙ There is no p-optimal propositional proof system. We note that a variant of the statement (either ≠ co or ∩ co contains a function hard on average) seems to have a bearing on the existence of good proof complexity generators. In particular, we prove that if a minor variant...