1. Apparatus for self-testing a system which includes a plurality of functional network interconnected by interface networks comprising: a first plurality of dual mode feedback shift registers, each connected to the input of respective ones of said plurality of functional networks, each of said feedback shift registers having a first mode of operation for generating a pseudo-random binary test sequence and a second mode of operation for evaluating responses by polynomial division to produce a succession of quotient bits; a second plurality of dual mode feedback shift registers, each connected to the output of respective ones of said plurality of functional networks and to the input of a respective one of a plurality of interface networks, each of said feedback shift registers having a first mode of operation for evaluating responses by polynomial division to produce a succession of quotient bits and a second mode of operation for generating a pseudo-random binary test sequence; and a central signature processor comprising: compressor means for receiving quotient bit data output from each of said feedback shift registers when evaluating responses and generating a system-response signature by recursively compressing said quotient bit data from all of said plurality of feedback shift registers by polynomial division; and signature-verifying means for comparing said system-response signature with an expected fault-free signature and providing an output signal indicative of system status; and control means for controlling the mode of operation of each of said feedback shift registers.