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Combinatorial aspects of code loops

Petr Vojtěchovský (2000)

Commentationes Mathematicae Universitatis Carolinae

The existence and uniqueness (up to equivalence defined below) of code loops was first established by R. Griess in [3]. Nevertheless, the explicit construction of code loops remained open until T. Hsu introduced the notion of symplectic cubic spaces and their Frattini extensions, and pointed out how the construction of code loops followed from the (purely combinatorial) result of O. Chein and E. Goodaire contained in [2]. Within this paper, we focus on their combinatorial construction and prove...

Compatibility relations on codes and free monoids

Tomi Kärki (2008)

RAIRO - Theoretical Informatics and Applications

A compatibility relation on letters induces a reflexive and symmetric relation on words of equal length. We consider these word relations with respect to the theory of variable length codes and free monoids. We define an (R,S)-code and an (R,S)-free monoid for arbitrary word relations R and S. Modified Sardinas-Patterson algorithm is presented for testing whether finite sets of words are (R,S)-codes. Coding capabilities of relational codes are measured algorithmically by finding minimal and maximal relations....

Completing codes

A. Restivo, S. Salemi, T. Sportelli (1989)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Complexity theoretical results on nondeterministic graph-driven read-once branching programs

Beate Bollig (2003)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Branching programs are a well-established computation model for boolean functions, especially read-once branching programs (BP1s) have been studied intensively. Recently two restricted nondeterministic (parity) BP1 models, called nondeterministic (parity) graph-driven BP1s and well-structured nondeterministic (parity) graph-driven BP1s, have been investigated. The consistency test for a BP-model M is the test whether a given BP is really a BP of model M . Here it is proved that the consistency test...

Complexity Theoretical Results on Nondeterministic Graph-driven Read-Once Branching Programs

Beate Bollig (2010)

RAIRO - Theoretical Informatics and Applications

Branching programs are a well-established computation model for boolean functions, especially read-once branching programs (BP1s) have been studied intensively. Recently two restricted nondeterministic (parity) BP1 models, called nondeterministic (parity) graph-driven BP1s and well-structured nondeterministic (parity) graph-driven BP1s, have been investigated. The consistency test for a BP-model M is the test whether a given BP is really a BP of model M. Here it is proved that the consistency...

Computation of centralizers in Braid groups and Garside groups.

Nuno Franco, Juan González-Meneses (2003)

Revista Matemática Iberoamericana

We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. This method, together with the solution of the conjugacy problem given by the authors in [9], are two main steps for solving conjugacy systems, thus breaking recently discovered cryptosystems based in braid groups [2]. We also present the result of our computations, where we notice that our algorithm yields surprisingly small generating sets for the centralizers.

Computing with the Square Root of NOT

De Vos, Alexis, De Beule, Jan, Storme, Leo (2009)

Serdica Journal of Computing

To the two classical reversible 1-bit logic gates, i.e. the identity gate (a.k.a. the follower) and the NOT gate (a.k.a. the inverter), we add an extra gate, the square root of NOT. Similarly, we add to the 24 classical reversible 2-bit circuits, both the square root of NOT and the controlled square root of NOT. This leads to a new kind of calculus, situated between classical reversible computing and quantum computing.

Conditional distributivity of overlap functions over uninorms with continuous underlying operators

Hui Liu, Wenle Li (2024)

Kybernetika

The investigations of conditional distributivity are encouraged by distributive logical connectives and their generalizations used in fuzzy set theory and were brought into focus by Klement in the closing session of Linzs 2000. This paper is mainly devoted to characterizing all pairs ( O , F ) of aggregation functions that are satisfying conditional distributivity laws, where O is an overlap function, and F is a continuous t-conorm or a uninorm with continuous underlying operators.

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