Learning-Based Synthesis of Safety Controllers

Abstract

We propose a machine learning framework to synthesize reactive controllers for systems whose interactions with their adversarial environment are modeled by infinite-duration, two-player games over (potentially) infinite graphs. Our framework targets safety games with infinitely many vertices, but it is also applicable to safety games over finite graphs whose size is too prohibitive for conventional synthesis techniques. The learning takes place in a feedback loop between a teacher component, which can reason symbolically about the safety game, and a learning algorithm, which successively learns an approximation of the winning region from various kinds of examples provided by the teacher. We develop a novel decision tree learning algorithm for this setting and show that our algorithm is guaranteed to converge to a reactive safety controller if a suitable approximation of the winning region can be expressed as a decision tree. Finally, we empirically compare the performance of a prototype implementation to existing approaches, which are based on constraint solving and automata learning, respectively.

GenSys: a scalable fixed-point engine for maximal controller synthesis over infinite state spaces

“…These tools include SimSynth [9] and ConSynth [2], which are based on logic-based synthesis, just like GenSys and JSyn-VG. We also consider the tool DT-Synth [17], which is based on decision tree learning, and the tools SAT-Synth and RPI-Synth, which are based on automaton based learning [18]. The numbers we show for the SimSynth tool are from their paper itself [9], the numbers for ConSynth are taken from [17], while the numbers for all other tools mentioned above are run on a machine with an Intel i5-6400 processor and 8 GB RAM.…”

“…We also consider the tool DT-Synth [17], which is based on decision tree learning, and the tools SAT-Synth and RPI-Synth, which are based on automaton based learning [18]. The numbers we show for the SimSynth tool are from their paper itself [9], the numbers for ConSynth are taken from [17], while the numbers for all other tools mentioned above are run on a machine with an Intel i5-6400 processor and 8 GB RAM. 4 Results for the Cinderella game are not available from the learning-based approaches(i.e., they time out after 900 seconds) and from SimSynth results are available only for Cinderella among the benchmarks we consider.…”

“…We were unable to get access to ConSynth even after mailing the authors. Thus, we used the numbers for ConSynth from the DT-Synth[17] paper which is the latest paper that evaluates ConSynth. They also describe the difficulty in reproducing the original ConSynth results.…”

Synthesis of infinite-state systems with random behavior

“…Program synthesis aims at automated generation of implementations that meet formal specifications. It has been thoroughly explored in various contexts, such as controller synthesis and automated program repair [2,3,11,14,24,35,37]. The implementations are generated from of the specification's realizability and have the form of deterministic witnesses.…”

“…Thus, the procedure remains completely automated, unlike previous work on infinite-state synthesis that requires additional templates, or the user's intervention [3,7,17,42]. More importantly, our work imposes no performance overheads over JSyn-vg, remaining thus competitive with other state-of-the-art tools which could be considered for random synthesis [35]. We implemented the Skolem extraction algorithm and applied it in two distinct case studies.…”