A Comparison of BDD-Based Parity Game Solvers

Abstract

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.

Symbolic Parity Game Solvers that Yield Winning Strategies

“…Earlier work, e.g. [29,32], also considers fixpoint algorithms in their symbolic implementations. As demonstrated in [32], the symbolic implementation of the small progress measures algorithm often results in timeouts.…”

“…Often formal verification and also synthesis suffers from the state space explosion problem. Indeed, [29] reports that parity game solvers can require over 8 GB memory for large specifications. One method to alleviate this problem is to use binary decision diagrams [6].…”

“…One method to alleviate this problem is to use binary decision diagrams [6]. In the past, symbolic parity game solvers using binary decision diagrams have been explored [1,23,29,32]. Symbolic algorithms replace explicit data structures with implicit, symbolic representations such as binary decision diagrams, relying on optimised BDD implementations such as CUDD [31] and Sylvan [12].…”

“…Symbolic algorithms replace explicit data structures with implicit, symbolic representations such as binary decision diagrams, relying on optimised BDD implementations such as CUDD [31] and Sylvan [12]. Using binary decision diagrams can result in a massive difference in memory usage [29].…”

“…dfi: the standard symbolic DFI algorithm • dfi-ns: symbolic DFI with no strategy computation • fpj: symbolic FPJ • zlk: symbolic Zielonka's recursive algorithm, provided by Sanchez et al[29]. The main goals of the evaluations are to see whether the algorithms that compute strategies are competitive with state-of-the-art work, and furthermore to see whether not computing winning strategies influences the performance of symbolic DFI.…”