Symbolic Algorithms for Language Equivalence and Kleene Algebra with Tests

We first propose algorithms for checking language equivalence of finite automata over a large alphabet. We use symbolic automata, where the transition function is compactly represented using a (multi-terminal) binary decision diagrams (BDD). The key idea consists in computing a bisimulation by exploring reachable pairs symbolically, so as to avoid redundancies. This idea can be combined with already existing optimisations, and we show in particular a nice integration with the disjoint sets forest data-structure from Hopcroft and Karp's standard algorithm. Then we consider Kleene algebra with tests (KAT), an algebraic theory that can be used for verification in various domains ranging from compiler optimisation to network programming analysis. This theory is decidable by reduction to language equivalence of automata on guarded strings, a particular kind of automata that have exponentially large alphabets. We propose several methods allowing to construct symbolic automata out of KAT expressions, based either on Brzozowski's derivatives or standard automata constructions. All in all, this results in efficient algorithms for deciding equivalence of KAT expressions

Applying relational algebra and RelView to coalition formation

We present an application of relational algebra to coalition formation. This leads to specifications, which can be executed with the help of the RelView tool after a simple translation into the tool's programming language. As an example we consider a simplification of the situation in Poland after the 2001 elections.RelView; relational algebra; coalition formation; feasible government; dominance; stable government

An Interdisciplinary Approach to Coalition Formation

A stable government is by definition not dominated by any other government. However, it may happen that all governments are dominated. In graph-theoretic terms this means that the dominance graph does not possess a source. In this paper we are able to deal with this case by a clever combination of notions from different fields, such as relational algebra, graph theory and social choice theory, and by using the computer support system RelView for computing solutions and visualizing the results. Using relational algorithms, in such a case we break all cycles in each initial strongly connected component by removing the vertices in an appropriate minimum feedback vertex set. In this way we can choose a government that is as close as possible to being un-dominated. To achieve unique solutions, we additionally apply the majority ranking recently introduced by Balinski and Laraki. The main parts of our procedure can be executed using the RelView tool. Its sophisticated implementation of relations allows to deal with graph sizes that are sufficient for practical applications of coalition formation.Graph theory; RelView; relational algebra; dominance; stable government

Applications of Relations and Graphs to Coalition Formation

A stable government is by definition not dominated by any other government. However, it may happen that all governments are dominated. In graph-theoretic terms this means that the dominance graph does not possess a source. In this paper we are able to deal with this case by a clever combination of notions from different fields, such as relational algebra, graph theory, social choice and bargaining theory, and by using the computer support system RelView for computing solutions and visualizing the results. Using relational algorithms, in such a case we break all cycles in each initial strongly connected component by removing the vertices in an appropriate minimum feedback vertex set. So, we can choose an un-dominated government. To achieve unique solutions, we additionally apply social choice rules. The main parts of our procedure can be executed using the RelView tool. Its sophisticated implementation of relations allows to deal with graph sizes that are sufficient for practical applications of coalition formation.Graph Theory, RELVIEW, Relational Algebra, Dominance, Stable Government

Negotiating a stable government - an application of bargaining theory to a coalition formation model

In this paper, we apply bargaining theory to a certain model of coalition formation. The notions of a feasible government and a stable government are central in the model considered. By a government, we mean a pair consisting of a majority coalition and a policy supported by this coalition. The aim of this paper is to establish which stable government should be created if more than one stable government exists or, in case there is no stable one, which feasible government should be formed if more than one feasible government exists. Several bargaining procedures leading to the choice of one stable (or feasible) government are proposed. We define bargaining games in which only parties belonging to at least one stable (or feasible) government bargain over the creation of a government. We consider different bargaining costs. We investigate subgame perfect equilibria of the bargaining games defined. It turns out that the prospects of a party depend on the procedure applied, and on the bargaining costs assumed. We also apply the coalition formation model to the Polish Parliament after the 2001 elections and apply the different bargaining games for the creation of a government to this example.stable government; bargaining game; subgame perfect equilibrium

Applying Formal Methods to Networking: Theory, Techniques and Applications

Despite its great importance, modern network infrastructure is remarkable for the lack of rigor in its engineering. The Internet which began as a research experiment was never designed to handle the users and applications it hosts today. The lack of formalization of the Internet architecture meant limited abstractions and modularity, especially for the control and management planes, thus requiring for every new need a new protocol built from scratch. This led to an unwieldy ossified Internet architecture resistant to any attempts at formal verification, and an Internet culture where expediency and pragmatism are favored over formal correctness. Fortunately, recent work in the space of clean slate Internet design---especially, the software defined networking (SDN) paradigm---offers the Internet community another chance to develop the right kind of architecture and abstractions. This has also led to a great resurgence in interest of applying formal methods to specification, verification, and synthesis of networking protocols and applications. In this paper, we present a self-contained tutorial of the formidable amount of work that has been done in formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial

Applying Relation Algebra and RelView to Measures in aSocial Network

We present an application of relation algebra to measure players' ‘strength' in a social network with influence between players. In particular, we deal with power, success, and influence of a player as measured by the Hoede-Bakker index, its generalization and modifications, and by the influence indices. We also apply relation algebra to determine followers of a coalition and the kernel of an influence function. This leads to specifications, which can be executed with the help of the BDDbased tool RelView after a simple translation into the tool's programming language. As an example we consider the present Dutch parliament.RelView ; relation algebra ; social network ; the Hoede-Bakker index ; influence index ;follower ; kernel

CrocoPat 2.1 Introduction and Reference Manual

CrocoPat is an efficient, powerful and easy-to-use tool for manipulating relations of arbitrary arity, including directed graphs. This manual provides an introduction to and a reference for CrocoPat and its programming language RML. It includes several application examples, in particular from the analysis of structural models of software systems.Comment: 19 pages + cover, 2 eps figures, uses llncs.cls and cs_techrpt_cover.sty, for downloading the source code, binaries, and RML examples, see http://www.software-systemtechnik.de/CrocoPat

A relation-algebraic approach to simple games

Simple games are a powerful tool to analyze decision - making and coalition formation in social and political life. In this paper, we present relation-algebraic models of simple games and develop relational specifications for solving some basic problems of them. In particular, we test certain fundamental properties of simple games and compute specific players and coalitions. We also apply relation algebra to determine power indices. This leads to relation-algebraic specifications, which can be evaluated with the help of the BDD-based tool RelView after a simple translation into the tool's programming language. In order to demonstrate the visualization facilities of RelView, we consider an example of the Catalonian Parliament after the 2003 election.Relation algebra ; RelView ; simple game ; winning coalition ; swinger ; dominant player ; central player ; power index