An O(mlog⁡n)O(m\log n) Algorithm for Stuttering Equivalence and Branching Bisimulation

We provide a new algorithm to determine stuttering equivalence with time complexity $O(m \log n)$, where $n$ is the number of states and $m$ is the number of transitions of a Kripke structure. This algorithm can also be used to determine branching bisimulation in $O(m(\log |\mathit{Act}|+ \log n))$ time where $\mathit{Act}$ is the set of actions in a labelled transition system. Theoretically, our algorithm substantially improves upon existing algorithms which all have time complexity $O(m n)$ at best. Moreover, it has better or equal space complexity. Practical results confirm these findings showing that our algorithm can outperform existing algorithms with orders of magnitude, especially when the sizes of the Kripke structures are large. The importance of our algorithm stretches far beyond stuttering equivalence and branching bisimulation. The known $O(m n)$ algorithms were already far more efficient (both in space and time) than most other algorithms to determine behavioural equivalences (including weak bisimulation) and therefore it was often used as an essential preprocessing step. This new algorithm makes this use of stuttering equivalence and branching bisimulation even more attractive.Comment: A shortened version of this technical report has been published in the proceedings of TACAS 201

Norm Functions for Probabilistic Bisimulations with Delays

In this paper, we consider action-labelled systems with non-deterministic and probabilistic choice. Using the concept of norm functions [GV98], we introduce two types of bisimulations that allow for delays when simulating a transition. The so obtained equivalences (called (strict) normed bisimulation equivalence) are strictly between strong and weak bisimulation equivalence `a la [LS89, SL94, SL95]. Using a suitable modification of the prominent splitter/partitioning technique [KS83, PT87], we present polynomial-time algorithms that constructs the quotient space of the (strict) normed bisimulation equivalence classes. Moreover, we briefly discuss other aspects such as the soundness for establishing linear time properties and compositiality

Energy Security as a Priority for CEE Countries. Is the King Naked?

The aim of this article is to assess the implementation process of the EU energy security policy in Central and Eastern European (CEE) countries. In the EU, energy security remains a crucial issue for European Energy Strategy, the fundamental goals of which include the security of supply, sustainability and competitiveness. Security of supply should be considered the most important aspect in this context, because it is connected to deep interdependencies between markets and economies, often based on political or even geo-political considerations. This is currently particularly noticeable, among other things, in the relations between the EU and Russia, where – in the event of any potential energy supply disturbances – some CEE countries are considered to be the most exposed. By analysing matters referred to the security of energy supplies, the article aims to determine the scope of activities undertaken by selected CEE countries which are also EU Member States in order to achieve this goal. The paper stresses the significance of cooperation by CEE countries at regional level, and focuses on initiatives and projects meant to ensure the security of their energy supplies. The conclusions of the paper assess some of the success stories as well as failures experienced by CEE countries in the process of building their energy independence.Le but de cet article est d'évaluer la mise en oeuvre de la politique de sécurité énergétique de l’Union européenne dans les pays de l’Europe centrale et orientale (PECO). Dans l'UE, la sécurité énergétique est un enjeu crucial pour la Stratégie énergétique européenne qui contient parmi ces objectifs fondamentaux la sécurité de l'approvisionnement, la durabilité et la compétitivité. La sécurité de l’approvisionnement doit être considérée comme l'aspect le plus important dans ce contexte, car elle est liée aux interdépendances profondes entre les marchés et les économies, souvent basées sur des considérations politiques ou même géo-politiques. Ceci est actuellement particulièrement visible, entre autres, dans les relations entre l'UE et la Russie, où - dans le cas de perturbations concernant l'approvisionnement en énergie - certains PECO sont considérés comme le plus exposés. En analysant les questions concernant la sécurité de l’approvisionnement énergétique, l'article vise à déterminer l’étendue des activités entreprises par certains PECO [qui sont aussi les États Membres de l’Union européenne] afin d’atteindre cet objectif. L’article souligne l'importance de la coopération des PECO au niveau régional et se focalise sur les initiatives et les projets visés à assurer la sécurité de l’approvisionnement énergétique de ces pays. Les conclusions de cet article évaluent des réussites, ainsi que les échecs des PECO, dans le processus de la construction de leur indépendance énergétique