Bella Abramovna Subbotovskaya (17 December 1937 – 23 September 1982)[1] was a Soviet mathematician who founded the short-lived Jewish People's University (1978–1983) in Moscow.

[2][3] The school's purpose was to offer free education to those affected by structured anti-Semitism within the Soviet educational system.

Its existence was outside Soviet authority and it was investigated by the KGB.

Subbotovskaya herself was interrogated a number of times by the KGB and shortly thereafter was hit by a truck and died, in what has been speculated was an assassination.

[4] Prior to founding the Jewish People's University, Subbotovskaya published papers in mathematical logic.

Her results on Boolean formulas written in terms of

were influential in the then nascent field of computational complexity theory.

Subbotovskaya invented the method of random restrictions to Boolean functions.

is a partial assignment to

variables, giving a function

Take the following function: The following is a restriction of one variable Under the usual identities of Boolean algebra this simplifies to

To sample a random restriction, retain

variables uniformly at random.

For each remaining variable, assign it 0 or 1 with equal probability.

As demonstrated in the above example, applying a restriction to a function can massively reduce the size of its formula.

is written with 7 variables, by only restricting one variable, we found that

Subbotovskaya proved something much stronger: if

variables, then the expected shrinkage between

is large, specifically where

is the minimum number of variables in the formula.

[5] Applying Markov's inequality we see Take

After applying a random restriction of

depending the parity of the assignments to the remaining variables.

Thus clearly the size of the circuit that computes

Then applying the probabilistic method, for sufficiently large

Thus we have proven that the smallest circuit to compute the parity of

[6] Although this is not an exceptionally strong lower bound, random restrictions have become an essential tool in complexity.

In a similar vein to this proof, the exponent

in the main lemma has been increased through careful analysis to

[5] Additionally, Håstad's Switching lemma (1987) applied the same technique to the much richer model of constant depth Boolean circuits.