Abstract: Technologies are described herein for generating uniformly random passwords by the use of regular expressions. One or more regular expressions are used to define a constraint on a string or password. The regular expressions are processed into one or more symbolic finite automata (SFA). The one or more SFAs are exposed to a combination of operations to produce a determinized, minimized SFA. Provided techniques generate probability data associated with individual state transitions of the SFA, and optionally, probability data is generated for one or more binary decision diagrams (BDD). Passwords or strings can be generated by traversing the SFA using the probability data. In some embodiments, the process for selecting characters at each state transition of the determinized, minimized SFA may utilize a binary decision diagram (BDD). Techniques disclosed herein also minimize SFAs by use of an over-approximation method.