Theoretical Computer Science and Discrete Mathematics

2017 ◽  
Keyword(s):  
Computer Science ◽  
Theoretical Computer Science ◽  
Discrete Mathematics ◽  
Theoretical Computer

scholarly journals Foreword to the special issue dedicated to the tenth ''Journées montoises d'informatique théorique''

2007 ◽  
Vol Vol. 9 no. 2 ◽  
Author(s):  
Véronique Bruyère ◽  
Michel Rigo
Keyword(s):  
Computer Science ◽  
Coding Theory ◽  
Theoretical Computer Science ◽  
Discrete Mathematics ◽  
Combinatorics On Words ◽  
Special Issue ◽  
Theoretical Computer ◽  
Universitair Centrum ◽  
Numeration Systems ◽  
The University

Held at the Institute of Mathematics of the University of Liège, Liège, September 8―11, 2004 International audience This special issue of Discrete Mathematics & Theoretical Computer Science is dedicated to the tenth "Journées montoises d'informatique théorique" conference (Mons theoretical computer science days) which was held, for the first time, at the Institute of Mathematics of the University of Liège, Belgium, From 8th to 11th September 2004. Previous editions of this conference took place in Mons 1990, 1992, 1994, 1998, in Rouen 1991, in Bordeaux 1993, Marseille 1995, Marne-La-Vallée 2000 and Montpellier 2002.<p> This tenth edition can be considered as a widely international one. We were lucky to have almost 85 participants from fourteen different countries: Austria, Belgium, Burkina Faso, Canada, Czech republic, Finland, France, Germany, Israel, Italy, Japan, Norway, Poland and Portugal. The main proportion of researchers participating to this event was coming from France and Italy where a long tradition of combinatorics on words is well established. During four days, 42 contributed talks and 7 invited talks were given, the main topics being combinatorics on words, numeration systems, automata and formal languages theory, coding theory, verification, bio-informatics, number theory, grammars, text algorithms, symbolic dynamics and tilings. The invited speakers were: J. Cassaigne (CNRS, Luminy-Marseille), D. Caucal (IRISIA-CNRS, Rennes), C. Frougny (LIAFA, Université Paris 8), T. Helleseth (University of Bergen), S. Langerman (FNRS, Université Libre de Bruxelles), F. Neven (Limburgs Universitair Centrum, Diepenbeek), M.-F. Sagot (Inria Rhône-Alpes, Université Lyon I).<p> We would like to thanks all the participants, the invited speakers and the anonymous referees who made possible this event and special issue. Each paper has been refereed using high scientific standard by two independent referees. Readers of this special issue may wonder why it took so long to obtain it. We have encountered some problems with the formerly chosen journal and for the benefit of the contributors to this issue, we have chosen Discrete Mathematics & Theoretical Computer Science to publish their work.

scholarly journals Open k-monopolies in graphs: complexity and related concepts

2016 ◽  
Vol Vol. 18 no. 3 (Graph Theory) ◽  
Author(s):  
Dorota Kuziak ◽  
Iztok Peterin ◽  
Ismael G. Yero
Keyword(s):  
Positive Integer ◽  
Computer Science ◽  
Long Range ◽  
Theoretical Computer Science ◽  
Chordal Graphs ◽  
Discrete Mathematics ◽  
Voting Systems ◽  
Minimum Cardinality ◽  
Theoretical Computer ◽  
Np Complete

Closed monopolies in graphs have a quite long range of applications in several problems related to overcoming failures, since they frequently have some common approaches around the notion of majorities, for instance to consensus problems, diagnosis problems or voting systems. We introduce here open $k$-monopolies in graphs which are closely related to different parameters in graphs. Given a graph $G=(V,E)$ and $X\subseteq V$, if $\delta_X(v)$ is the number of neighbors $v$ has in $X$, $k$ is an integer and $t$ is a positive integer, then we establish in this article a connection between the following three concepts: - Given a nonempty set $M\subseteq V$ a vertex $v$ of $G$ is said to be $k$-controlled by $M$ if $\delta_M(v)\ge \frac{\delta_V(v)}{2}+k$. The set $M$ is called an open $k$-monopoly for $G$ if it $k$-controls every vertex $v$ of $G$. - A function $f: V\rightarrow \{-1,1\}$ is called a signed total $t$-dominating function for $G$ if $f(N(v))=\sum_{v\in N(v)}f(v)\geq t$ for all $v\in V$. - A nonempty set $S\subseteq V$ is a global (defensive and offensive) $k$-alliance in $G$ if $\delta_S(v)\ge \delta_{V-S}(v)+k$ holds for every $v\in V$. In this article we prove that the problem of computing the minimum cardinality of an open $0$-monopoly in a graph is NP-complete even restricted to bipartite or chordal graphs. In addition we present some general bounds for the minimum cardinality of open $k$-monopolies and we derive some exact values. Comment: 18 pages, Discrete Mathematics & Theoretical Computer Science (2016)

scholarly journals Snow Leopard Permutations and Their Even and Odd Threads

2016 ◽  
Vol Vol. 18 no. 2, Permutation... (Permutation Patterns) ◽  
Author(s):  
Eric S. Egge ◽  
Kailee Rubin
Keyword(s):  
Computer Science ◽  
Pattern Avoidance ◽  
Theoretical Computer Science ◽  
Catalan Number ◽  
The Other ◽  
Discrete Mathematics ◽  
Snow Leopard ◽  
Theoretical Computer ◽  
Set Of Permutations ◽  
Motzkin Paths

Caffrey, Egge, Michel, Rubin and Ver Steegh recently introduced snow leopard permutations, which are the anti-Baxter permutations that are compatible with the doubly alternating Baxter permutations. Among other things, they showed that these permutations preserve parity, and that the number of snow leopard permutations of length $2n-1$ is the Catalan number $C_n$. In this paper we investigate the permutations that the snow leopard permutations induce on their even and odd entries; we call these the even threads and the odd threads, respectively. We give recursive bijections between these permutations and certain families of Catalan paths. We characterize the odd (resp. even) threads which form the other half of a snow leopard permutation whose even (resp. odd) thread is layered in terms of pattern avoidance, and we give a constructive bijection between the set of permutations of length $n$ which are both even threads and odd threads and the set of peakless Motzkin paths of length $n+1$. Comment: 25 pages, 6 figures. Version 3 is modified to use standard Discrete Mathematics and Theoretical Computer Science but is otherwise unchanged

scholarly journals $2\times 2$ monotone grid classes are finitely based

2016 ◽  
Vol Vol. 18 no. 2, Permutation... (Permutation Patterns) ◽  
Author(s):  
Michael Albert ◽  
Robert Brignall
Keyword(s):  
Computer Science ◽  
General Result ◽  
Theoretical Computer Science ◽  
Discrete Mathematics ◽  
Finite Collection ◽  
Permutation Patterns ◽  
Finitely Based ◽  
Special Issue ◽  
Theoretical Computer

In this note, we prove that all $2 \times 2$ monotone grid classes are finitely based, i.e., defined by a finite collection of minimal forbidden permutations. This follows from a slightly more general result about certain $2 \times 2$ (generalized) grid classes having two monotone cells in the same row. Comment: 10 pages, 5 figures. To appear in Discrete Mathematics and Theoretical Computer Science, special issue for Permutation Patterns 2015

scholarly journals Impact of Mathematics on the Theoretical Computer Science Course Units in the General Degree Program in Computer Science at Sri Lankan State Universities

10.28945/4057 ◽  
2018 ◽  
Keyword(s):  
Academic Performance ◽  
Computer Science ◽  
Degree Program ◽  
Theoretical Computer Science ◽  
Discrete Mathematics ◽  
Sri Lankan ◽  
Theoretical Computer ◽  
Advanced Level ◽  
And Mathematics ◽  
Mathematics Course

[This Proceedings paper was revised and published in the 2018 issue of the journal Issues in Informing Science and Information Technology, Volume 15] ABSTRACT Mathematics is fundamental to the study of Computer Science. In Sri Lankan state universities, students have been enrolled only from the Physical Science stream with minimum ‘C’ grade in Mathematics in the advanced level examination to do a degree program in Computer Science. In addition to that universities have been offering some course units in Mathematics covering basis in Discrete Mathematics, Calculus, and Algebra to provide the required mathematical maturity to Computer Science under-graduates. Despite of this it is observed that the failure rate in fundamental theoretical Computer Science course units are much higher than other course units offered in the general degree program every year. The purpose of this study is to identify how Advanced level Mathematics and Mathematics course units offered at university level do impact on the academic performance of theoretical Computer Science course units and to make appropriate recommendations based on our findings. Academic records comprised of 459 undergraduates from three consecutive batches admitted to the degree program in Computer Science from a university was considered for this study. Results indicated that Advanced level Mathematics does not have any significant effect on the academic performance of theoretical Computer Science course units. Even though all Mathematics course units offered in the first and second year of studies were significantly correlated with academic performance of every theoretical Computer Science course unit, only the Discrete Mathematics course unit highly impact-ed on the academic performance of all three theoretical Computer Science course units. Further this study indicates that the academic performance of female undergraduates is better than males in all theoretical Computer Science and Mathematics course units.

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