Symbolic Parity Game Solvers that Yield Winning Strategies

Abstract

Parity games play an important role for LTL synthesis as evidenced by recent breakthroughs on LTL synthesis, which rely in part on parity game solving. Yet state space explosion remains a major issue if we want to scale to larger systems or specifications. In order to combat this problem, we need to investigate symbolic methods such as BDDs, which have been successful in the past to tackle exponentially large systems. It is therefore essential to have symbolic parity game solving algorithms, operating using BDDs, that are fast and that can produce the winning strategies used to synthesize the controller in LTL synthesis. Current symbolic parity game solving algorithms do not yield winning strategies. We now propose two symbolic algorithms that yield winning strategies, based on two recently proposed fixpoint algorithms. We implement the algorithms and empirically evaluate them using benchmarks obtained from SYNTCOMP 2020. Our conclusion is that the algorithms are competitive with or faster than an earlier symbolic implementation of Zielonka's recursive algorithm, while also providing the winning strategies.

Knor: reactive synthesis using Oink

“…strategy iteration (psi) [11,19] tangle learning (tl) [10] priority promotion (npp) [2,11] -Zielonka's recursive algorithm (zlk) [11,35] fixpoint iteration using freezing (fpi) [16] fixpoint iteration using justifications (fpj) [24] We also implement a symbolic solver based on [25]. This symbolic solver implements fixpoint iteration with freezing using BDD operations, and operates directly on the BDD obtained by the fully-symbolic translation.…”

“…Knor leverages Oink to solve parity games with state-of-the-art parity game solvers [16], and the Sylvan binary decision diagrams (BDD) package [14] to implement most of the steps before and after solving and a purely symbolic parity game solver based on [25]. The techniques implemented in Knor have secured us multiple victories in the SYNTCOMP competition, in 2021, 2022 and 2023.…”

The Reactive Synthesis Competition (SYNTCOMP): 2018-2021

“…Importantly, the chosen variable ordering encodes first source states, then uncontrollable inputs, controllable inputs, and finally the target states. The resulting symbolic parity automaton can then be treated in two ways: First, it can be solved directly using a symbolic parity game algorithm (Lijzenga and van Dijk, 2020b) optimized to utilize the aforementioned variable ordering. This solution immediately yields a controller that can be dumped as an AIG.…”