Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games

Parameterised Boolean Equation Systems (PBESs) are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal μ-calculus formulae for process algebraic specifications with data. Solving a PBES is usually done by instantiation to a Parity Game and then solving the game. Practical game solvers exist, but the instantiation step is the bottleneck. We enhance the instantiation in two steps. First, we transform the PBES to a Parameterised Parity Game (PPG), a PBES with each equation either conjunctive or disjunctive. Then we use LTSmin, that offers transition caching, efficient storage of states and both distributed and symbolic state space generation, for generating the game graph. To that end we define a language module for LTSmin, consisting of an encoding of variables with parameters into state vectors, a grouped transition relation and a dependency matrix to indicate the dependencies between parts of the state vector and transition groups. Benchmarks on some large case studies, show that the method speeds up the instantiation significantly and decreases memory usage drastically

Generating and Solving Symbolic Parity Games

We present a new tool for verification of modal mu-calculus formulae for process specifications, based on symbolic parity games. It enhances an existing method, that first encodes the problem to a Parameterised Boolean Equation System (PBES) and then instantiates the PBES to a parity game. We improved the translation from specification to PBES to preserve the structure of the specification in the PBES, we extended LTSmin to instantiate PBESs to symbolic parity games, and implemented the recursive parity game solving algorithm by Zielonka for symbolic parity games. We use Multi-valued Decision Diagrams (MDDs) to represent sets and relations, thus enabling the tools to deal with very large systems. The transition relation is partitioned based on the structure of the specification, which allows for efficient manipulation of the MDDs. We performed two case studies on modular specifications, that demonstrate that the new method has better time and memory performance than existing PBES based tools and can be faster (but slightly less memory efficient) than the symbolic model checker NuSMV.Comment: In Proceedings GRAPHITE 2014, arXiv:1407.767

Soliton solutions of 3D Gross-Pitaevskii equation by a potential control method

We present a class of three-dimensional solitary waves solutions of the Gross-Pitaevskii (GP) equation, which governs the dynamics of Bose-Einstein condensates (BECs). By imposing an external controlling potential, a desired time-dependent shape of the localized BEC excitation is obtained. The stability of some obtained localized solutions is checked by solving the time-dependent GP equation numerically with analytic solutions as initial conditions. The analytic solutions can be used to design external potentials to control the localized BECs in experiment.Comment: 11 pages, 5 figures, submitted to Phys. Rev.

Drawings of Planar Graphs with Few Slopes and Segments

We study straight-line drawings of planar graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on $n$ vertices has a plane drawing with at most ${5/2}n$ segments and at most $2n$ slopes. We prove that every cubic 3-connected plane graph has a plane drawing with three slopes (and three bends on the outerface). In a companion paper, drawings of non-planar graphs with few slopes are also considered.Comment: This paper is submitted to a journal. A preliminary version appeared as "Really Straight Graph Drawings" in the Graph Drawing 2004 conference. See http://arxiv.org/math/0606446 for a companion pape

Compact Floor-Planning via Orderly Spanning Trees

Floor-planning is a fundamental step in VLSI chip design. Based upon the concept of orderly spanning trees, we present a simple O(n)-time algorithm to construct a floor-plan for any n-node plane triangulation. In comparison with previous floor-planning algorithms in the literature, our solution is not only simpler in the algorithm itself, but also produces floor-plans which require fewer module types. An equally important aspect of our new algorithm lies in its ability to fit the floor-plan area in a rectangle of size (n-1)x(2n+1)/3. Lower bounds on the worst-case area for floor-planning any plane triangulation are also provided in the paper.Comment: 13 pages, 5 figures, An early version of this work was presented at 9th International Symposium on Graph Drawing (GD 2001), Vienna, Austria, September 2001. Accepted to Journal of Algorithms, 200

Un Algorithme Évolutionnaire pour Trouver des Politiques Optimales avec un Simulateur Multi-Agent

International audienceIn this paper, we introduce a new agent-based method to build a decision-aid tool aimed to improve policy design. In our approach, a policy is defined as a set of levers, modelling the set of actions, the means to impact a complex system. Our method is generic, as it could be applied to any domain, and be coupled with any agent-based simulator. We could deal not only with simple levers (a single variable whose value is modified) but also complex ones (multiple variable modifications, qualitative effects, ...), unlike most optimization methods. It is based on the evolutionary algorithm CMA-ES, coupled with a normalized and aggregated fitness function. The fitness is normalized using estimated Ideal (best policy) and Nadir (worst policy) values, these values being dynamically computed during the execution of CMA-ES through a Pareto Front estimated with the ABM simulation. Moreover , to deal with complex levers, we introduce the FSM-branching algorithm, where a Finite State Machine (FSM) determines whether a complex policy can potentially be improved or has to be aborted. We tested our method with Economic Policies on the French Labor Market (FLM), allowing the modification of multiple elements of the FLM, and we compared the results to the reference, the FLM without any policy applied. The policies studied here comprise simple and complex levers. This experience shows the viability of our approach, the efficiency of our algorithms and illustrates how this combination of evolutionary optimization, multi-criteria aggregation and agent-based simulation could help any policy-maker to design better policies

Kant’s Causal Power Argument Against Empirical Affection

A well-known trilemma faces the interpretation of Kant’s theory of affection, namely whether the objects that affect us are empirical, noumenal, or both. I argue that according to Kant, the things that affect us and cause representations in us are not empirical objects. I articulate what I call the Causal Power Argument, according to which empirical objects cannot affect us because they do not have the right kind of power to cause representations. All the causal powers that empirical objects have are moving powers, and such powers can only have spatial effects. According to Kant, however, the representations that arise in us as a result of the affection of our sensibility are non-spatial. I show that this argument is put forward by Kant in a number of passages, and figures as a decisive reason for rejecting empirical affection and instead endorsing affection by the things in themselves

Combinatorial Properties of Triangle-Free Rectangle Arrangements and the Squarability Problem

We consider arrangements of axis-aligned rectangles in the plane. A geometric arrangement specifies the coordinates of all rectangles, while a combinatorial arrangement specifies only the respective intersection type in which each pair of rectangles intersects. First, we investigate combinatorial contact arrangements, i.e., arrangements of interior-disjoint rectangles, with a triangle-free intersection graph. We show that such rectangle arrangements are in bijection with the 4-orientations of an underlying planar multigraph and prove that there is a corresponding geometric rectangle contact arrangement. Moreover, we prove that every triangle-free planar graph is the contact graph of such an arrangement. Secondly, we introduce the question whether a given rectangle arrangement has a combinatorially equivalent square arrangement. In addition to some necessary conditions and counterexamples, we show that rectangle arrangements pierced by a horizontal line are squarable under certain sufficient conditions.Comment: 15 pages, 13 figures, extended version of a paper to appear at the International Symposium on Graph Drawing and Network Visualization (GD) 201

Time equals money?: A randomized controlled field experiment on the effects of four types of training vouchers on training participation

Organizations aiming to help their employees in fostering their human capital offer training, but not all employees participate. Some organizations therefore experiment with training vouchers that typically offer financial means for training to motivate training participation. However, the effectiveness of such vouchers remains suboptimal, arguably due to lack of clarity on- and variation in the mechanisms of such vouchers. The present paper uniquely employs Conservation of Resources theory to compare the effectiveness of four types of vouchers with different combinations of money and time as well as different (i.e. firm internal and external) governance on training participation. To this end, 230 employees in a large Dutch insurance company were randomly assigned to one of the four voucher types or a control group. For eleven months, training participation was monitored and a concurrent questionnaire measured several personal characteristics as potential covariates and moderators. We find that the voucher type that allows employees to freely choose between a training budget and training days most strongly encourages training participation. Vouchers that provide employees with either working days or a training budget did not improve training participation significantly compared to the control group. Moreover, moderation analyses suggested that the training participation of employees provided with non-flexible vouchers appears to depend more strongly on personal characteristics, and particularly components from the Reasoned Action Approach. These findings suggest that to encourage training participation organizations should best offer flexible vouchers that provide employees a free choice between money and working time to spend on training. Moreover, the findings demonstrate the applicability of Conservation of Resource theory to training vouchers and address the need for recognizing subjectivity within this theoretical framework