Oscillator-searching method with SAT

[testitemqlstudop]

This might sound ridiculous, but I think that there is a feasible method for row-by-row (wide and high period) oscillator searching with SAT solvers.

Specifically, given the first two rows (in all phases), we want to find the all possible collection of phases for the next row such that the evolution sequence for the previous row is correct.

For example, if we are searching for a p4 (mold):

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......   ....o.   ...oo.   ..o.o.
...ooo   ..oo.o   ..ooo.   .....o
.o.ooo   .o....   .o.oo.   .o..o.
abcdef   ghijkl   mnopqr   stuvwx

we want to find sets {a-x} such that

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...ooo
.o.ooo
abcdef

evolves into

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??????
..oo.o
??????

and

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.....o
.o..o.
stuvwx

evolves into

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??????
.o.ooo
??????

and so on.
This is where the SAT solvers come into play. For wide/high-period oscillators there may be too many variables to try with standard methods. we can construct a SAT problem where the variables are the phases of the next row and the clauses ensure the correct evolution sequence.

Is this a feasible method or is it impossible?

[Bullet51]

I have done some experiments on it, and it certainly works in P3 and P4.

[testitemqlstudop]

I think that this will especially be helpful with higher periods, and it can also help to find oscillators with special properties , particularly noticeable sparks from the top (i.e. t-nosed, pipsquirter, etc.)

Any ideas on efficient implementation?