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Deterministic blow-ups of minimal NFA's

Galina Jirásková (2006)

RAIRO - Theoretical Informatics and Applications

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...

Developing a Metadata Exchange Format for Mathematical Literature

Ruddy, David (2010)

Towards a Digital Mathematics Library. Paris, France, July 7-8th, 2010

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...

DFIS: A novel data filling approach for an incomplete soft set

Hongwu Qin, Xiuqin Ma, Tutut Herawan, Jasni Mohamad Zain (2012)

International Journal of Applied Mathematics and Computer Science

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...

Diagonalization in proof complexity

Jan Krajíček (2004)

Fundamenta Mathematicae

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 2 Ω ( n ) . ∙ ≠ co . ∙ There is no p-optimal propositional proof system. We note that a variant of the statement (either ≠ co or ∩ co contains a function 2 Ω ( n ) 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...

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