1. Generic term for a program that assists in debugging other programs by showing individual machine instructions in a readable symbolic form and letting the user change them. In this sense the term DDT is now archaic, having been widely displaced by "debugger" or names of individual programs like "adb", "sdb", "dbx", or "gdb".
3. Any one of several specific debuggers supported on early DEC hardware. The DEC PDP-10 Reference Handbook (1969) contained a footnote on the first page of the documentation for DDT that illuminates the origin of the term:
Historical footnote: DDT was developed at MIT for the PDP-1 computer in 1961. At that time DDT stood for "DEC Debugging Tape". Since then, the idea of an on-line debugging program has propagated throughout the computer industry. DDT programs are now available for all DEC computers. Since media other than tape are now frequently used, the more descriptive name "Dynamic Debugging Technique" has been adopted, retaining the DDT abbreviation. Confusion between DDT-10 and another well known pesticide, dichloro-diphenyl-trichloroethane (C14-H9-Cl5) should be minimal since each attacks a different, and apparently mutually exclusive, class of bugs.
(The "tape" referred to was, incidentally, not magnetic but paper.) Sadly, this quotation was removed from later editions of the handbook after the suits took over and DEC became much more "businesslike".
The history above is known to many old-time hackers. But there's more: Peter Samson, compiler of the original TMRC lexicon, reports that he named "DDT" after a similar tool on the TX-0 computer, the direct ancestor of the PDP-1 built at MIT's Lincoln Lab in 1957. The debugger on that ground-breaking machine (the first transistorised computer) rejoiced in the name FLIT (FLexowriter Interrogation Tape).