Synthesis of Large Dynamic Concurrent Programs from Dynamic Specifications

We present a tractable method for synthesizing arbitrarily large concurrent programs, for a shared memory model with common hardware-available primitives such as atomic registers, compare-and-swap, load-linked/store conditional, etc. The programs we synthesize are dynamic: new processes can be created and added at run-time, and so our programs are not finite-state, in general. Nevertheless, we successfully exploit automatic synthesis and model-checking methods based on propositional temporal logic. Our method is algorithmically efficient, with complexity polynomial in the number of component processes (of the program) that are alive'' at any time. Our method does not explicitly construct the automata-theoretic product of all processes that are alive, thereby avoiding \intr{state explosion}. Instead, for each pair of processes which interact, our method constructs an automata-theoretic product (\intr{pair-machine}) which embodies all the possible interactions of these two processes. From each pair-machine, we can synthesize a correct \intr{pair-program} which coordinates the two involved processes as needed. We allow such pair-programs to be added dynamically at run-time. They are then composed conjunctively’’ with the currently alive pair-programs to re-synthesize the program as it results after addition of the new pair-program. We are thus able to add new behaviors, which result in new properties being satisfied, at run-time. We establish a ``large model’’ theorem which shows that the synthesized large program inherits correctness properties from the pair-programs.