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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.

Connections between object classification criteria using an ultrasonic bi-sonar system

Bogdan Kreczmer (2016)

International Journal of Applied Mathematics and Computer Science

The paper presents connections between the criteria which make three types of objects possible to be recognized, namely, edges, planes and corners. These criteria can be applied while a binaural sonar system is used. It is shown that the criteria are specific forms of a general equation. The form of the equation depends on a single coefficient. In the paper, the meaning of this coefficient is discussed. The constructions of the arrangement of objects are presented and are bound with values of the...

Consensus and trajectory tracking of SISO linear multi-agent systems under switching communication topologies and formation changes

Carlos López-Limón, Javier Ruiz, Alejandro Cervantes-Herrera, Antonio Ramírez-Treviño (2013)

Kybernetika

The simultaneous problem of consensus and trajectory tracking of linear multi-agent systems is considered in this paper, where the dynamics of each agent is represented by a single-input single-output linear system. In order to solve this problem, a distributed control strategy is proposed in this work, where the trajectory and the formation of the agents are achieved asymptotically even in the presence of switching communication topologies and smooth formation changes, and ensuring the closed-loop...

Construction of Optimal Linear Codes by Geometric Puncturing

Maruta, Tatsuya (2013)

Serdica Journal of Computing

Dedicated to the memory of S.M. Dodunekov (1945–2012)Abstract. Geometric puncturing is a method to construct new codes. ACM Computing Classification System (1998): E.4.∗This research was partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 24540138.

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