A Comparison of BDD-Based Parity Game Solvers

Parity games are two player games with omega-winning conditions, played on finite graphs. Such games play an important role in verification, satisfiability and synthesis. It is therefore important to identify algorithms that can efficiently deal with large games that arise from such applications. In this paper, we describe our experiments with BDD-based implementations of four parity game solving algorithms, viz. Zielonka's recursive algorithm, the more recent Priority Promotion algorithm, the Fixpoint-Iteration algorithm and the automata based APT algorithm. We compare their performance on several types of random games and on a number of cases taken from the Keiren benchmark set.Comment: In Proceedings GandALF 2018, arXiv:1809.0241

Partial-order reduction for parity games with an application on parameterised Boolean Equation Systems (Technical Report)

Partial-order reduction (POR) is a well-established technique to combat the problem of state-space explosion. Most approaches in literature focus on Kripke structures or labelled transition systems and preserve a form of stutter/weak trace equivalence or weak bisimulation. Therefore, they are at best applicable when checking weak modal mucalculus. We propose to apply POR on parity games, which can encode the combination of a transition system and a temporal property. Our technique allows one to apply POR in the setting of mu-calculus model checking. We show with an example that the reduction achieved on parity games can be significantly larger. Furthermore, we identify and repair an issue where stubborn sets do not preserve stutter equivalence

EufDpll - A Tool to Check Satisfiability of Equality Logic Formulas

Decision procedures for subsets of First-Order Logic form the core of many verification tools. Applications include hardware and software verification. The logic of Equality with Uninterpreted Functions (EUF) is a decidable subset of First-Order Logic. The EUF logic and its extensions have been applied for proving equivalence between systems. We present a branch and bound decision procedure for EUF logic based on the generalisation of the Davis-Putnam-Loveland-Logemann procedure (EUF-DPLL). EufDpll is a tool to check satisfiability of EUF formulas based on this procedure

Evidence extraction from parameterised Boolean equation systems

Model checking is a technique for automatically assessing the quality of software and hardware systems and designs. Given a formalisation of both the system behaviour and the requirements the system should meet, a model checker returns either a yes or a no. In case the answer is not as expected, it is desirable to provide feedback to the user as to why this is the case. Providing such feedback, however, is not straightforward if the requirement is expressed in a highly expressive logic such as the modal µ-calculus, and when the decision problem is solved using intermediate formalisms. In this paper, we show how to extract witnesses and counterexamples from parameterised Boolean equation systems encoding the model checking problem for the first-order modal µ-calculus. We have implemented our technique in the modelling and analysis toolset mCRL2 and showcase our approach on a few illustrative examples.</p

A formal analysis of a dynamic distributed spanning tree algorithm

Abstract. We analyze the spanning tree algorithm in the IEEE 1394.1 draft standard, which correctness has not previously been proved. This algorithm is a fully-dynamic distributed graph algorithm, which, in general, is hard to develop. The approach we use is to formally develop an algorithm that is almost equivalent to it: First, based on a formal specification and an abstraction of the network, we systematically construct an algorithm including its correctness proof. Afterwards we implement this algorithm in terms of IEEE 1394 devices under maintenance of its correctness.

Evidence extraction from parameterised Boolean equation systems

\u3cp\u3eModel checking is a technique for automatically assessing the quality of software and hardware systems and designs. Given a formalisation of both the system behaviour and the requirements the system should meet, a model checker returns either a yes or a no. In case the answer is not as expected, it is desirable to provide feedback to the user as to why this is the case. Providing such feedback, however, is not straightforward if the requirement is expressed in a highly expressive logic such as the modal µ-calculus, and when the decision problem is solved using intermediate formalisms. In this paper, we show how to extract witnesses and counterexamples from parameterised Boolean equation systems encoding the model checking problem for the first-order modal µ-calculus. We have implemented our technique in the modelling and analysis toolset mCRL2 and showcase our approach on a few illustrative examples.\u3c/p\u3

Partial-order reduction for parity games with an application on parameterised Boolean Equation Systems (Technical Report)

Partial-order reduction (POR) is a well-established technique to combat the problem of state-space explosion. Most approaches in literature focus on Kripke structures or labelled transition systems and preserve a form of stutter/weak trace equivalence or weak bisimulation. Therefore, they are at best applicable when checking weak modal mucalculus. We propose to apply POR on parity games, which can encode the combination of a transition system and a temporal property. Our technique allows one to apply POR in the setting of mu-calculus model checking. We show with an example that the reduction achieved on parity games can be significantly larger. Furthermore, we identify and repair an issue where stubborn sets do not preserve stutter equivalence