Bas Ploeger

Correcting a Space-Efficient Simulation Algorithm

Although there are many efficient algorithms for calculating the simulation preorder on finite Kripke structures, only two have been proposed of which the space complexity is of the same order as the size of the output of the algorithm. Of these, the one with the best time complexity exploits the representation of the simulation problem as a generalised coarsest partition problem. It is based on a fixed-point operator for obtaining a generalised coarsest partition as the limit of a sequence of partition pairs. We show that this fixed-point theory is flawed, and that the algorithm is incorrect. Although we do not see how the fixed-point operator can be repaired, we correct the algorithm without affecting its space and time complexity.

Instantiation for Parameterised Boolean Equation Systems

Verification problems for finite- and infinite-state processes, like model checking and equivalence checking, can effectively be encoded in Parameterised Boolean Equation Systems (PBESs). Solving the PBES solves the encoded problem. The decidability of solving a PBES depends on the data sorts that occur in the PBES. We describe a manipulation for transforming a given PBES to a simpler PBES that may admit solution methods that are not applicable to the original one. Depending on whether the data sorts occurring in the PBES are finite or countable, the resulting PBES can be a Boolean Equation System (BES) or an Infinite Boolean Equation System (IBES). Computing the solution to a BES is decidable. Computing the global solution to an IBES is still undecidable, but for partial solutions (which suffices for e.g.local model checking), effective tooling is possible. We give examples that illustrate the efficacy of our techniques.

Five Determinisation Algorithms

Determinisation of nondeterministic finite automata is a well-studied problem that plays an important role in compiler theory and system verification. In the latter field, one often encounters automata consisting of millions or even billions of states. On such input, the memory usage of analysis tools becomes the major bottleneck. In this paper we present several determinisation algorithms, all variants of the well-known subset construction, that aim to reduce memory usage and produce smaller output automata. One of them produces automata that are already minimal. We apply our algorithms to determinise automata that describe the possible sequences appearing after a fixed-length run of cellular automaton 110, and obtain a significant improvement in both memory and time efficiency.

Improving an interactive visualization of transition systems

A transition system can be used to model the behaviour of a software system. A popular way of analysing this behaviour is by studying the corresponding transition system. An interactive visualization technique for showing the global structure of a transition system has been proposed by Van Ham et al. This technique clusters states and forms these clusters into a 3D structure similar to a cone tree, with the emphasis on symmetry. The technique has been used by analysts to study real-world systems. In this paper we solve a number of problems related to the symmetry of the visual representation and the misrepresentation of cluster sizes. This results in more effective and less misleading visualizations. In addition, we also extend the original technique by providing simulation facilities and a more effective state and cluster marking technique. These enhance the way in which a user can interact with the visualization.

Verification of reactive systems via instantiation of Parameterised Boolean Equation Systems

Verification problems for finite- and infinite-state processes, like model checking and equivalence checking, can effectively be encoded in Parameterised Boolean Equation Systems (PBESs). Solving the PBES then solves the encoded problem. The decidability of solving a PBES depends on the data sorts that occur in the PBES. We describe a pragmatic methodology for solving PBESs, viz., by attempting to instantiate them to the sub-fragment of Boolean Equation Systems (BESs). Unlike solving PBESs, solving BESs is a decidable problem. Based on instantiation, verification using PBESs can effectively be done fully automatically in most practical cases. We demonstrate this by solving several complex verification problems using a prototype implementation of our instantiation technique. In addition, practical issues concerning this implementation are addressed. Furthermore, we illustrate the effectiveness of instantiation as a transformation on PBESs when solving verification problems involving systems of infinite size.

Switching Graphs

Switching graphs are graphs containing switches. By using boolean functions called switch settings, these switches can be put in a fixed direction to obtain an ordinary graph. For many problems, switching graphs are a remarkable straightforward and natural model, but they have hardly been studied. We study the complexity of several natural questions in switching graphs of which some are polynomial, and others are NP-complete. We started investigating switching graphs because they turned out to be a natural framework for studying the problem of solving Boolean equation systems, which is equivalent to model checking of the modal @m-calculus and deciding the winner in parity games. We give direct, polynomial encodings of Boolean equation systems in switching graphs and vice versa, and prove correctness of the encodings.