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1

Rough Approximation Operators in Group Mapping and Their Applications to Coding Theory

Xu J., Qiu R., Tao Z.

Fundamenta Informaticae

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2016

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Vol. 145, nr 1

93--109

EN

This paper focuses on rough approximation operators in group mapping. The relationships between rough set theory and group theory are considered from a novel perspective. The necessary and sufficient conditions for the upper approximation and lower approximation of a group to be groups are analyzed. In addition, the homomorphism and isomorphism between two groups which have related upper or lower approximations are investigated. Finally, the applications of rough approximation operators in group mapping to coding theory are developed.

2

Combinatorial Geometry and Coding Theory

Raigorodskii A. M.

Fundamenta Informaticae

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2016

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Vol. 145, nr 3

359--369

EN

In this paper, we overview three closely related problems: Nelson-Hadwiger problem on coloring spaces with forbidden monochromatics distances; Borsuk's problem on partitioning sets in spaces into parts of smaller diameter; problem of finding codes with forbidden Hamming distances.

3

Coding Theory : A General Framework and Two Inverse Problems

Bortolussi L., Dinu L. P., Franzoi L., Sgarro A.

Fundamenta Informaticae

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2015

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Vol. 141, nr 4

297--310

EN

We put forward an ample framework for coding based on upper probabilities, or more generally on normalized monotone set-measures, and model accordingly noisy transmission channels and decoding errors. Two inverse problems are considered. In the first case, a decoder is given and one looks for channels of a specified family over which that decoder would work properly. In the second and more ambitious case, it is codes which are given, and one looks for channels over which those codes would ensure the required error correction capabilities. Upper probabilities allow for a solution of the two inverse problems in the case of usual codes based on checking Hamming distances between codewords: one can equivalently check suitable upper probabilities of the decoding errors. This soon extends to “odd” codeword distances for DNA strings as used in DNA word design, where instead, as we prove, not even the first unassuming inverse problem admits of a solution if one insists on channel models based on ”usual” probabilities.

4

Synthesis of Reo Connectors for Strategies and Controllers

Baier Ch., Klein J., Klüppelholz S.

Fundamenta Informaticae

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2014

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Vol. 130, nr 1

1--20

EN

In controller synthesis, i.e., the question whether there is a controller or strategy to achieve some objective in a given system, the controller is often realized as some kind of automaton. In the context of the exogenous coordination language Reo, where the coordination glue code between the components is realized as a network of channels, it is desirable for such synthesized controllers to also take the form of a Reo connector built from a repertoire of basic channels. In this paper, we address the automatic construction of such Reo connectors directly from a constraint automaton representation.

5

More About Converting BNF to PEG

Redziejowski R. R.

Fundamenta Informaticae

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2014

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Vol. 133, nr 2/3

257--270

EN

Parsing Expression Grammar (PEG) encodes a recursive-descent parser with limited backtracking. The parser has many useful properties. Converting PEG to an executable parser is a rather straightforward task. Unfortunately, PEG is not well understood as a language definition tool. It is thus of a practical interest to construct PEGs for languages specified in some familiar way, such as Backus-Naur Form (BNF). The problem was attacked by Medeiros in an elegant way by noticing that both PEG and BNF can be formally defined in a very similar way. Some of his results were extended in a previous paper by this author. We continue here with further extensions.

6

Construction of modular number systems with arbitrary finite ranges

Selyaninov M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2009

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Vol. 14

105-115

EN

In the present paper, we deal with the methodology of constructing modular number systems (MNS), named also residue number systems, on arbitrary mathematical structures such as finite groups, rings and Galois fields.

7

A pragmatic approach to extending provers by computer algebra-with applications to coding theory

Ballarin C., Paulson L.C.

Fundamenta Informaticae

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1999

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Vol. 39, Nr 1,2

1-20

EN

The use of computer algebra is usually considered beneficial for mechanised reasoning in mathematical domains. We present a case study, in the application domain of coding theory, that supports this claim: the mechanised proofs depend on non-trivial algorithms from computer algebra and increase the reasoning power of the theorem prover. The unsoundness of computer algebra systems is a major problem in interfacing them to theorem provers. Our approach to obtaining a sound overall system is not blanket distrust but based on the distinction between algorithms we call sound and ad hoc respectively. This distinction is blurred in most computer algebra systems. Our experimental interface therefore uses a computer algebra library. It is based on formal specifications for the algorithms, and links the computer algebra library Sumit to the prover Isabelle. We give details of the interface, the use of the computer algebra system on the tactic-level of Isabelle and its integration into proof procedures.