Language Equation Solving via Boolean Automata Manipulation

Language equations are a powerful tool for compositional synthesis, modeled as the unknown component problem. Given a (sequential) system specification S and a fixed component F, we are asked to synthesize an unknown component X such that whose composition with F fulfills S. The synthesis of X can be formulated with language equation solving. Although prior work exploits partitioned representation for effective finite automata manipulation, it remains challenging to solve language equations involving a large number of states. In this work, we propose variants of Boolean automata as the underlying succinct representation for regular languages. They admit logic circuit manipulation and extend the scalability for solving language equations. Experimental results demonstrate the superiority of our method to the state-of-the-art in solving nine more cases out of the 36 studied benchmarks and achieving an average of 740× speedup.