Applications and Optimizations for LTL Synthesis

LTL synthesis is the process of generating a reactive finite-state system from a formal specification written in Linear Temporal Logic (LTL). The idea of synthesis is to automatically construct a functional correct system from a behavioral description of the system. Even though the idea is nearly fifty years old and the underlying theory is well established, is has not be adapted to practice yet. The main reasons are the high complexity of the problem and intrinsic algorithms. This thesis follows along three different paths to bring LTL synthesis closer to practice. First, we present our synthesis tool Lily, a Linear Logic Synthesizer. Lily is the first implementation of a synthesis tool for full LTL. It is based on a recent approach to synthesis by Kupferman and Vardi that goes through a variety of alternating tree automata. Lily implements this approach and a set of optimizations necessary to make the approach applicable. Lily can only handle small examples, but since it imposes no restriction on the syntax of the LTL formula, it is easy to use and can help users to get familiar with LTL. In the second part, we state the repair problem and solve it for finite-state systems using synthesis techniques. In the repair problem, given a specification and faulty system, we search for slightly modifications of the system that make it correct with respect to the specification. We consider the repair problem as a game, which consists of a modified version of the faulty system and an automaton representing the specification. Every winning strategy of the game corresponds to a repair. However, a strategy with memory results in a repair that adds variables to the program, which we argue is undesirable. In order to avoid extra variables, we need a memoryless strategy. We show that the problem of finding a memoryless strategy is NP-complete and present a heuristic to compute such strategies. We have implemented the approach symbolically and present initial experimental results to show its usefulness. Finally, in the third part of the thesis we focus on the main application of synthesis: