[2] In 1962, Brzozowski earned his PhD in the field of electrical engineering at Princeton University under Edward J. McCluskey.

Brzozowski worked on regular expressions and on syntactic semigroups of formal languages.

[3] The result was Characterizations of locally testable events written together with Imre Simon, which had a similar impact[4] on the development of the algebraic theory of formal languages as Marcel-Paul Schützenberger's characterization of the star-free languages.

Notably, Brzozowski was not only co-author of the paper that defined the dot-depth hierarchy and raised the question whether this hierarchy is strict,[8] he later also was co-author of the paper resolving that problem after roughly ten years.

[9] The Brzozowski hierarchy gained further importance after Wolfgang Thomas discovered a relation between the algebraic concept of dot-depth and the alternation depth of quantifiers in first-order logic via Ehrenfeucht–Fraïssé games.