On the complexity of acyclic modules in automata networks

Modules were introduced as an extension of Boolean automata networks. They have inputs which are used in the computation said modules perform, and can be used to wire modules with each other. In the present paper we extend this new formalism and study the specific case of acyclic modules. These modules prove to be well described in their limit behavior by functions called output functions. We provide other results that offer an upper bound on the number of attractors in an acyclic module when wired recursively into an automata network, alongside a diversity of complexity results around the difficulty of deciding the existence of cycles depending on the number of inputs and the size of said cycle.Comment: 21 page

Kernels for Feedback Arc Set In Tournaments

A tournament T=(V,A) is a directed graph in which there is exactly one arc between every pair of distinct vertices. Given a digraph on n vertices and an integer parameter k, the Feedback Arc Set problem asks whether the given digraph has a set of k arcs whose removal results in an acyclic digraph. The Feedback Arc Set problem restricted to tournaments is known as the k-Feedback Arc Set in Tournaments (k-FAST) problem. In this paper we obtain a linear vertex kernel for k-FAST. That is, we give a polynomial time algorithm which given an input instance T to k-FAST obtains an equivalent instance T' on O(k) vertices. In fact, given any fixed e>0, the kernelized instance has at most (2+e)k vertices. Our result improves the previous known bound of O(k^2) on the kernel size for k-FAST. Our kernelization algorithm solves the problem on a subclass of tournaments in polynomial time and uses a known polynomial time approximation scheme for k-FAST

The hardness of perfect phylogeny, feasible register assignment and other problems on thin colored graphs

AbstractIn this paper, we consider the complexity of a number of combinatorial problems; namely, Intervalizing Colored Graphs (DNA physical mapping), Triangulating Colored Graphs (perfect phylogeny), (Directed) (Modified) Colored Cutwidth, Feasible Register Assignment and Module Allocation for graphs of bounded pathwidth. Each of these problems has as a characteristic a uniform upper bound on the tree or path width of the graphs in “yes”-instances. For all of these problems with the exceptions of Feasible Register Assignment and Module Allocation, a vertex or edge coloring is given as part of the input. Our main results are that the parameterized variant of each of the considered problems is hard for the complexity classes W[t] for all t∈N. We also show that Intervalizing Colored Graphs, Triangulating Colored Graphs, and Colored Cutwidth are NP-Complete

Distributed synchronous diagnosis of discrete-event systems

Recently, the centralized and decentralized synchronous diagnosis of discreteevent systems have been proposed in the literature. In this work, we propose a di erent synchronous diagnosis strategy called distributed synchronous diagnosis. In this scheme, local diagnosers are computed based on the observation of the fault-free behavior models of the system components. It is considered that these local diagnosers are separated into networks, and are capable of communicating the occurrence of events and their current state estimate to other local diagnosers that belong to the same network. The diagnosers are implemented considering an speci c communication protocol that re nes the state estimate of the faultfree behavior of the system modules, reducing, therefore, the augmented fault-free language considered for synchronous diagnosis. In order to do so, boolean conditions are added to the transitions of the fault-free component models, which check if the occurrence of an observable event is possible according to the current state estimate of other local diagnosers. This leads to the notion of distributed synchronous diagnosability. An algorithm to verify the distributed synchronous diagnosability with polynomial complexity in the state-space of the system component models is proposed.Recentemente, o diagnóstico síncrono centralizado e descentralizado de sistemas a eventos discretos foi proposto na literatura. Neste trabalho, propomos uma estratégia de diagnóstico síncrono diferente, denominada diagnóstico síncrono distribuído. Neste esquema, diagnosticadores locais são construídos com base na observação do comportamento livre de falha dos componentes do sistema. Considera-se que esses diagnosticadores locais são agrupados em redes de comunicação e capazes de informar a ocorrência de eventos e sua estimativa de estado atual a outros diagnosticadores locais pertencentes à mesma rede. Os diagnosticadores são implementados considerando um protocolo de comunicação específico, o qual refina a estimativa de estado do comportamento livre de falha dos módulos do sistema, reduzindo, portanto, a linguagem aumentada livre de falha considerada no diagnóstico síncrono. Isso é feito com a adição de condições booleanas para a transposição de transições dos modelos livre de falha dos componentes do sistema, as quais verificam se a ocorrência de um evento observável é possível de acordo com a estimativa do estado atual dos outros diagnosticadores locais. Isso leva à noção de diagnosticabilidade síncrona distribuída. Um algoritmo para verificar a diagnosticabilidade síncrona distribuída com complexidade polinomial no espaço de estados dos modelos dos componentes do sistema é proposto

Model-based dependability analysis : state-of-the-art, challenges and future outlook

Abstract: Over the past two decades, the study of model-based dependability analysis has gathered significant research interest. Different approaches have been developed to automate and address various limitations of classical dependability techniques to contend with the increasing complexity and challenges of modern safety-critical system. Two leading paradigms have emerged, one which constructs predictive system failure models from component failure models compositionally using the topology of the system. The other utilizes design models - typically state automata - to explore system behaviour through fault injection. This paper reviews a number of prominent techniques under these two paradigms, and provides an insight into their working mechanism, applicability, strengths and challenges, as well as recent developments within these fields. We also discuss the emerging trends on integrated approaches and advanced analysis capabilities. Lastly, we outline the future outlook for model-based dependability analysis

Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version)

Although the ``scale-free'' literature is large and growing, it gives neither a precise definition of scale-free graphs nor rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many inherent contradictions and verifiably false claims. In this paper, we propose a new, mathematically precise, and structural definition of the extent to which a graph is scale-free, and prove a series of results that recover many of the claimed properties while suggesting the potential for a rich and interesting theory. With this definition, scale-free (or its opposite, scale-rich) is closely related to other structural graph properties such as various notions of self-similarity (or respectively, self-dissimilarity). Scale-free graphs are also shown to be the likely outcome of random construction processes, consistent with the heuristic definitions implicit in existing random graph approaches. Our approach clarifies much of the confusion surrounding the sensational qualitative claims in the scale-free literature, and offers rigorous and quantitative alternatives.Comment: 44 pages, 16 figures. The primary version is to appear in Internet Mathematics (2005

Finding and counting vertex-colored subtrees

The problems studied in this article originate from the Graph Motif problem introduced by Lacroix et al. in the context of biological networks. The problem is to decide if a vertex-colored graph has a connected subgraph whose colors equal a given multiset of colors $M$. It is a graph pattern-matching problem variant, where the structure of the occurrence of the pattern is not of interest but the only requirement is the connectedness. Using an algebraic framework recently introduced by Koutis et al., we obtain new FPT algorithms for Graph Motif and variants, with improved running times. We also obtain results on the counting versions of this problem, proving that the counting problem is FPT if M is a set, but becomes W[1]-hard if M is a multiset with two colors. Finally, we present an experimental evaluation of this approach on real datasets, showing that its performance compares favorably with existing software.Comment: Conference version in International Symposium on Mathematical Foundations of Computer Science (MFCS), Brno : Czech Republic (2010) Journal Version in Algorithmic

When Are Behaviour Networks Well-Behaved?

Agents operating in the real world have to deal with a constantly changing and only partially predictable environment and are nevertheless expected to choose reasonable actions quickly. This problem is addressed by a number of action-selection mechanisms. Behaviour networks as proposed by Maes are one such mechanism, which is quite popular. In general, it seems not possible to predict when behaviour networks are well-behaved. However, they perform quite well in the robotic soccer context. In this paper, we analyse the reason for this success by identifying conditions that make behaviour networks goal converging, i.e., force them to reach the goals regardless of the details of the action selection scheme. In terms of STRIPS domains one could talk of self-solving planning domains