An RTL hardware description language simulation accelerator and circuit emulator which operates on data driven asynchronous completion handshaking principles. Deploying Muller C elements to control latches, the system does not depend on externally provided clocks or internal timing circuits with delay logic or clock generators. Each levelized domain of logic signals a successor level to begin execution of instructions with a level complete message produced when all its input operands have produced a completion message. Each predecessor stage holds back data production until the successor stage is ready. Each levelized data-driven asynchronous domain evaluation processor is self-timed receiving completion messages from its predecessors, and sending completion messages to its successors.