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Minimum vertex ranking spanning tree problem for chordal and proper interval graphs

Dariusz Dereniowski (2009)

Discussiones Mathematicae Graph Theory

A vertex k-ranking of a simple graph is a coloring of its vertices with k colors in such a way that each path connecting two vertices of the same color contains a vertex with a bigger color. Consider the minimum vertex ranking spanning tree (MVRST) problem where the goal is to find a spanning tree of a given graph G which has a vertex ranking using the minimal number of colors over vertex rankings of all spanning trees of G. K. Miyata et al. proved in [NP-hardness proof and an approximation algorithm...

Modeling of distributed objects computing design pattern combinations using a formal specification language

Toufik Taibi, David Ngo (2003)

International Journal of Applied Mathematics and Computer Science

Design patterns help us to respond to the challenges faced while developing Distributed Object Computing (DOC) applications by shifting developers' focus to high-level design concerns, rather than platform specific details. However, due to the inherent ambiguity of the existing textual and graphical descriptions of the design patterns, users are faced with difficulties in understanding when and how to use them. Since design patterns are seldom used in isolation but are usually combined to solve...

Modeling shortest path games with Petri nets: a Lyapunov based theory

Julio Clempner (2006)

International Journal of Applied Mathematics and Computer Science

In this paper we introduce a new modeling paradigm for shortest path games representation with Petri nets. Whereas previous works have restricted attention to tracking the net using Bellman's equation as a utility function, this work uses a Lyapunov-like function. In this sense, we change the traditional cost function by a trajectory-tracking function which is also an optimal cost-to-target function. This makes a significant difference in the conceptualization of the problem domain, allowing the...

Modelling integer linear programs with petri nets*

P. Richard (2010)

RAIRO - Operations Research

We show in this paper that timed Petri nets, with one resource shared by all the transitions, are directly connected to the modelling of integer linear programs (ILP). To an ILP can be automatically associated an equivalent Petri net. The optimal reachability delay is an optimal solution of the ILP. We show next that a net can model any ILP. I order to do this, we give a new sufficient reachability condition for the marking equation, which also holds for general Petri nets without timed transitions. ...

Monoid presentations of groups by finite special string-rewriting systems

Duncan W. Parkes, V. Yu. Shavrukov, Richard M. Thomas (2004)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We show that the class of groups which have monoid presentations by means of finite special [ λ ] -confluent string-rewriting systems strictly contains the class of plain groups (the groups which are free products of a finitely generated free group and finitely many finite groups), and that any group which has an infinite cyclic central subgroup can be presented by such a string-rewriting system if and only if it is the direct product of an infinite cyclic group and a finite cyclic group.

Monoid presentations of groups by finite special string-rewriting systems

Duncan W. Parkes, V. Yu. Shavrukov, Richard M. Thomas (2010)

RAIRO - Theoretical Informatics and Applications

We show that the class of groups which have monoid presentations by means of finite special [λ]-confluent string-rewriting systems strictly contains the class of plain groups (the groups which are free products of a finitely generated free group and finitely many finite groups), and that any group which has an infinite cyclic central subgroup can be presented by such a string-rewriting system if and only if it is the direct product of an infinite cyclic group and a finite cyclic group.

Monotone (co)inductive types and positive fixed-point types

Ralph Matthes (2010)

RAIRO - Theoretical Informatics and Applications

We study five extensions of the polymorphically typed lambda-calculus (system F) by type constructs intended to model fixed-points of monotone operators. Building on work by Geuvers concerning the relation between term rewrite systems for least pre-fixed-points and greatest post-fixed-points of positive type schemes (i.e., non-nested positive inductive and coinductive types) and so-called retract types, we show that there are reduction-preserving embeddings even between systems of monotone (co)inductive...

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