µ-calculus synthesis

In system synthesis, we transform a specification into a system that is guaranteed to satisfy the specification. When the system is open, it interacts with an environment via input and output signals and its behavior depends on this interaction. An open system should satisfy its specification in all possible environments. In addition to the input signals that the system can read, an environment can also have internal signals that the system cannot read. In the above setting, of synthesis with incomplete information, we should transform a specification that refers to both readable and unreadable signals into a system whose behavior depends only on the readable signals. In this work we solve the problem of synthesis with incomplete information for specifications in µ-calculus. Since many properties of systems are naturally specified by means of fixed points, the µ-calculus is an expressive and important specification language. Our results and technique generalize and simplify previous work on synthesis. In particular, we prove that the problem of µ-calculus synthesis with incomplete information is EXPTIME-complete. Thus, it is not harder than the satisfiability or the synthesis problems for this logic.