A Typical Verification Challenge for the GRID

A typical verification challenge for the GRID community is\ud presented. The concrete challenge is to implement a simple recursive algorithm for finding the strongly connected components in a graph. The graph is typically stored in the collective memory of a number of computers, so a distributed algorithm is necessary.\ud \ud The implementation should be efficient and scalable, and separate synchronization and implementation details from the purely algorithmic aspects. In the end, a framework is envisaged for distributed algorithms on very large graphs. This would be useful to explore various alternative algorithmic choices

Floral induction, floral hormones and flowering

The factors, influencing the synthesis and action of floral hormones, and possible differences between floral hormones in different plants were studied. The experimental results are summarized in the conclusions 1-20, on pages 35-36 (Crassulaceae'); 21-39 on pages 58-59 ('Xanthium strumarium') and 40-50 on pages 74-75 ('Caryophyllaceae').General conclusions are as follows:1. The processes leading to flower formation of plants with a floral hormone can be roughly divided in induction and realization, the latter subdivided in synthesis, transport and action of floral hormone as initiation of flower buds in the receptive meristems. These processes are called the 'floral chain'.2. In the long-short-day plant Bryophyllum daigremontianum neither the LD, nor the SD induction were influenced qualitatively by temperature, but the resulting inductive state and the already synthesized floral hormone were destructed by too high a temperature.3. In the short-day plant Kalanchoë blossfeldiana the induction was influenced by temperature, so that in individual species different processes of the floral chain may be influenced.4. In the LSDP B. daigremontianum no 2 separate components of the floral hormone are formed.5. The transmission of floral hormone by grafting is influenced by the direction of movement of the hormone in B. daigremontianum and by the age of the receptor in the SDP Xanthium strumarium. Presence of the leaves in X. strumarium strongly stimulates the growth of the axillary shoots and reduces the flowering-reaction, while defoliation of receptors promotes the transmission of flowering.6. In K. blossfeldiana and X.strumarium early lines need less floral hormone for a flowering-reaction than late ones. The former have a lower threshold value of the hormone.7. The good donor capacity of B. daigremontianum towards K. blossfeldiana in contrast to the reverse combination suggests a lower level of floral hormone in K. blossfeldiana than in B. daigremontianum.8. Also in X. strumarium different levels of floral hormone, corresponding with different floral stages and different donor capacities, could be distinguished.9. The factors influencing the flowering of a receptor, grafted with a donor, mentioned sub 5, 6, 7 and 8, make it questionable to assume that plants without demonstrable transmission of flowering do not have a floral hormone, while negative results of interspecies graftings need not be caused by differences in floral hormones. New successful combinations between graft partners of different photoperiodic response types suggest a more universal floral hormone.10. The action of floral hormone is not restricted to floral initiation. In K. blossfeldiana the presence of sufficient floral hormone is also necessary for Rower development, while in K.blossfeldiana and in X. strumarium the number of flowers depend on the level of floral hormone. In B. daigremontianum the presence of floral hormone is a condition for continued flowering.11. The term 'non-localized synthesis of floral hormone' was introduced for the phenomenon that receptors of some species brought into flowering by grafting, can act as a donor in a next grafting. It is likely that the difference between B. daigremontianum and K.blossfeldiana concerning localized synthesis of floral hormone is caused by differences in internal conditions between these plants rather than by different floral hormones. Also the case of Silene armeria, brought into flowering by Perilla crispa, suggests this explanation.12. Since differences in flowering-reactions can be explained by different levels of floral hormone and/or by differences in internal conditions of the plants in which the floral hormone has to act, the existence of one universal floral hormone remains possible

A Multi-Core Solver for Parity Games

We describe a parallel algorithm for solving parity games,\ud with applications in, e.g., modal mu-calculus model\ud checking with arbitrary alternations, and (branching) bisimulation\ud checking. The algorithm is based on Jurdzinski's Small Progress\ud Measures. Actually, this is a class of algorithms, depending on\ud a selection heuristics.\ud \ud Our algorithm operates lock-free, and mostly wait-free (except for\ud infrequent termination detection), and thus allows maximum\ud parallelism. Additionally, we conserve memory by avoiding storage\ud of predecessor edges for the parity graph through strictly\ud forward-looking heuristics.\ud \ud We evaluate our multi-core implementation's behaviour on parity games\ud obtained from mu-calculus model checking problems for a set of\ud communication protocols, randomly generated problem instances, and\ud parametric problem instances from the literature.\ud \u

Computing Weakest Strategies for Safety Games of Imperfect Information

CEDAR (Counter Example Driven Antichain Refinement) is a new symbolic algorithm for computing weakest strategies for safety games of imperfect information. The algorithm computes a fixed point over the lattice of contravariant antichains. Here contravariant antichains are antichains over pairs consisting of an information set and an allow set representing the associated move. We demonstrate how the richer structure of contravariant antichains for representing antitone functions, as opposed to standard antichains for representing sets of downward closed sets, allows CEDAR to apply a significantly less complex controllable predecessor step than previous algorithms

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

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

Action with Manifest Duality for Maximally Supersymmetric Six-dimensional Supergravity

We perform explicitly the toroidal compactification of eleven dimensional supergravity to six dimensions and present its action in a manifestly $SO(5,5)\over SO(5)\times SO(5)$ invariant form using the recently proposed covariant formulation of theories involving chiral fields.Comment: 19 pages, late

Bridging the Gap between Enumerative and Symbolic Model Checkers

We present a method to perform symbolic state space generation for languages with existing enumerative state generators. The method is largely independent from the chosen modelling language. We validated this on three different types of languages and tools: state-based languages (PROMELA), action-based process algebras (muCRL, mCRL2), and discrete abstractions of ODEs (Maple).\ud Only little information about the combinatorial structure of the\ud underlying model checking problem need to be provided. The key enabling data structure is the "PINS" dependency matrix. Moreover, it can be provided gradually (more precise information yield better results).\ud \ud Second, in addition to symbolic reachability, the same PINS matrix contains enough information to enable new optimizations in state space generation (transition caching), again independent from the chosen modelling language. We have also based existing optimizations, like (recursive) state collapsing, on top of PINS and hint at how to support partial order reduction techniques.\ud \ud Third, PINS allows interfacing of existing state generators to, e.g., distributed reachability tools. Thus, besides the stated novelties, the method we propose also significantly reduces the complexity of building modular yet still efficient model checking tools.\ud \ud Our experiments show that we can match or even outperform existing tools by reusing their own state generators, which we have linked into an implementation of our ideas