Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 4 of 4
Full-Text Articles in Other Mathematics
A New Approach To Algebraic Coding Theory Through The Applications Of Soft Sets, Florentin Smarandache, Mumtaz Ali
A New Approach To Algebraic Coding Theory Through The Applications Of Soft Sets, Florentin Smarandache, Mumtaz Ali
Branch Mathematics and Statistics Faculty and Staff Publications
Algebraic codes play a signifcant role in the minimisation of data corruption which caused by defects such as inference, noise channel, crosstalk, and packet loss. In this paper, we introduce soft codes (soft linear codes) through the application of soft sets which is an approximated collection of codes. We also discuss several types of soft codes such as type-1 soft codes, complete soft codes etc. Further, we construct the soft generator matrix and soft parity check matrix for the soft linear codes. Moreover, we develop two techniques for the decoding of soft codes.
Relation Liftings On Preorders And Posets, Marta Bílková, Alexander Kurz, Daniela Petrişan, Jiří Velebil
Relation Liftings On Preorders And Posets, Marta Bílková, Alexander Kurz, Daniela Petrişan, Jiří Velebil
Engineering Faculty Articles and Research
The category Rel(Set) of sets and relations can be described as a category of spans and as the Kleisli category for the powerset monad. A set-functor can be lifted to a functor on Rel(Set) iff it preserves weak pullbacks. We show that these results extend to the enriched setting, if we replace sets by posets or preorders. Preservation of weak pullbacks becomes preservation of exact lax squares. As an application we present Moss’s coalgebraic over posets.
Towards Nominal Formal Languages, Alexander Kurz, Tomoyuki Suzuki, Emilio Tuosto
Towards Nominal Formal Languages, Alexander Kurz, Tomoyuki Suzuki, Emilio Tuosto
Engineering Faculty Articles and Research
We introduce formal languages over infinite alphabets where words may contain binders.We define the notions of nominal language, nominal monoid, and nominal regular expressions. Moreover, we extend history-dependent automata (HD-automata) by adding stack, and study the recognisability of nominal languages.
Generic Trace Logics, Christian Kissig, Alexander Kurz
Generic Trace Logics, Christian Kissig, Alexander Kurz
Engineering Faculty Articles and Research
We combine previous work on coalgebraic logic with the coalgebraic traces semantics of Hasuo, Jacobs, and Sokolova.