ConwayLife.com

When synthesising an oscillator it is always desirable to find an immediate predecessor, or even better one some generations back which can be constructed. Is there a script or program that does this already?

Win Life Search (WLS) can find predecessors with the "find parents only" option in the search settings. Pick the number of generations you want and put your target pattern in the last generation. It can also help to limit the number of active cells in generation 0 to avoid an unwieldy mess. As for whether these predecessors are any good for synthesis, WLS won't tell you, and not having synthesis experience myself, I don't know if this is a useful way to approach the problem. There may be other utilities better suited for the problem.

In addition to WinLifeSeach, there is Karel Suhajda's JavaLifeSearch (JLS). To search for predecessors in JLS, go to Edit -> Properties -> Tiling/translation tab and under "After last generation is..." select "Unknown".

Edit: You can download WinLifeSearch here.