arXiv subjects

Tim A. C. Willemse

Publications and source records attributed to Tim A. C. Willemse.

28 records · Page 2Linked to original sources

arXiv2015

Improvement in Small Progress Measures

Small Progress Measures is one of the classical parity game solving algorithms. For games with n vertices, m edges and d different priorities, the original algorithm computes the winning regions and a winning strategy for one of the players in O(dm.(n/floor(d/2))^floor(d/2)) time. Computing a winning strategy for the other player requires a re-run of the algorithm on that player's winning region, thus increasing the runtime complexity to O(dm.(n/ceil(d/2))^ceil(d/2)) for computing the winning regions and winning strategies for both players. We modify the algorithm so that it derives the winning strategy for both players in one pass. This reduces the upper bound on strategy derivation for SPM to O(dm.(n/floor(d/2))^floor(d/2)). At the basis of our modification is a novel operational interpretation of the least progress measure that we provide.

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arXiv2015

Strategy Derivation for Small Progress Measures

Small Progress Measures is one of the most efficient parity game solving algorithms. The original algorithm provides the full solution (winning regions and strategies) in $O(dm \cdot (n/\lceil d / 2 \rceil)^{\lceil d/2 \rceil})$ time, and requires a re-run of the algorithm on one of the winning regions. We provide a novel operational interpretation of progress measures, and modify the algorithm so that it derives the winning strategies for both players in one pass. This reduces the upper bound on strategy derivation for SPM to $O(dm \cdot (n/\lfloor d / 2 \rfloor)^{\lfloor d/2 \rfloor})$.

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arXiv2014

Improved Static Analysis of Parameterised Boolean Equation Systems using Control Flow Reconstruction

We present a sound static analysis technique for fighting the combinatorial explosion of parameterised Boolean equation systems (PBESs). These essentially are systems of mutually recursive fixed point equations ranging over first-order logic formulae. Our method detects parameters that are not live by analysing a control flow graph of a PBES, and it subsequently eliminates such parameters. We show that a naive approach to constructing a control flow graph, needed for the analysis, may suffer from an exponential blow-up, and we define an approximate analysis that avoids this problem. The effectiveness of our techniques is evaluated using a number of case studies.

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arXiv2013

Zielonka's Recursive Algorithm: dull, weak and solitaire games and tighter bounds

Dull, weak and nested solitaire games are important classes of parity games, capturing, among others, alternation-free mu-calculus and ECTL* model checking problems. These classes can be solved in polynomial time using dedicated algorithms. We investigate the complexity of Zielonka's Recursive algorithm for solving these special games, showing that the algorithm runs in O(d (n + m)) on weak games, and, somewhat surprisingly, that it requires exponential time to solve dull games and (nested) solitaire games. For the latter classes, we provide a family of games G, allowing us to establish a lower bound of 2^(n/3). We show that an optimisation of Zielonka's algorithm permits solving games from all three classes in polynomial time. Moreover, we show that there is a family of (non-special) games M that permits us to establish a lower bound of 2^(n/3), improving on the previous lower bound for the algorithm.

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arXiv2013

Decomposability in Input Output Conformance Testing

We study the problem of deriving a specification for a third-party component, based on the specification of the system and the environment in which the component is supposed to reside. Particularly, we are interested in using component specifications for conformance testing of black-box components, using the theory of input-output conformance (ioco) testing. We propose and prove sufficient criteria for decompositionality, i.e., that components conforming to the derived specification will always compose to produce a correct system with respect to the system specification. We also study the criteria for strong decomposability, by which we can ensure that only those components conforming to the derived specification can lead to a correct system.

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arXiv2012

Expressiveness and Completeness in Abstraction

We study two notions of expressiveness, which have appeared in abstraction theory for model checking, and find them incomparable in general. In particular, we show that according to the most widely used notion, the class of Kripke Modal Transition Systems is strictly less expressive than the class of Generalised Kripke Modal Transition Systems (a generalised variant of Kripke Modal Transition Systems equipped with hypertransitions). Furthermore, we investigate the ability of an abstraction framework to prove a formula with a finite abstract model, a property known as completeness. We address the issue of completeness from a general perspective: the way it depends on certain abstraction parameters, as well as its relationship with expressiveness.

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arXiv2011

Stuttering Equivalence for Parity Games

We study the process theoretic notion of stuttering equivalence in the setting of parity games. We demonstrate that stuttering equivalent vertices have the same winner in the parity game. This means that solving a parity game can be accelerated by minimising the game graph with respect to stuttering equivalence. While, at the outset, it might not be clear that this strategy should pay off, our experiments using typical verification problems illustrate that stuttering equivalence speeds up solving parity games in many cases.

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arXiv2011

Analysing the Control Software of the Compact Muon Solenoid Experiment at the Large Hadron Collider

The control software of the CERN Compact Muon Solenoid experiment contains over 30,000 finite state machines. These state machines are organised hierarchically: commands are sent down the hierarchy and state changes are sent upwards. The sheer size of the system makes it virtually impossible to fully understand the details of its behaviour at the macro level. This is fuelled by unclarities that already exist at the micro level. We have solved the latter problem by formally describing the finite state machines in the mCRL2 process algebra. The translation has been implemented using the ASF+SDF meta-environment, and its correctness was assessed by means of simulations and visualisations of individual finite state machines and through formal verification of subsystems of the control software. Based on the formalised semantics of the finite state machines, we have developed dedicated tooling for checking properties that can be verified on finite state machines in isolation.

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arXiv2010

Structural Analysis of Boolean Equation Systems

We analyse the problem of solving Boolean equation systems through the use of structure graphs. The latter are obtained through an elegant set of Plotkin-style deduction rules. Our main contribution is that we show that equation systems with bisimilar structure graphs have the same solution. We show that our work conservatively extends earlier work, conducted by Keiren and Willemse, in which dependency graphs were used to analyse a subclass of Boolean equation systems, viz., equation systems in standard recursive form. We illustrate our approach by a small example, demonstrating the effect of simplifying an equation system through minimisation of its structure graph.

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arXiv2010

Analysis of Boolean Equation Systems through Structure Graphs

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