Finite partial-derivative carrier

Exact statement

For a regular expression $B$ , let $Q_B$ be a finite Antimirov partial-derivative carrier containing $B$ and closed under one-letter partial derivatives.

StatusClassical construction stated for the quotient proof

External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

The finite carrier supplies the states over which a quotienting expression can be interpreted as a relation.

Definitions

For a word $u$ , $\partial_u(P)$ denotes the finite set of Antimirov partial derivatives reached from $P$ .

Hypotheses and scope

The alphabet is finite and regular expressions use the ordinary 0, 1, letter, union, concatenation, and star constructors.

Proof or evidence

Finiteness is the standard partial-derivative theorem; the quotient construction uses only states reachable from B.

Finite derivative carrier →

Verification notes

The FPRD proof checked closure under letters and used the carrier only as a finite auxiliary object, not as an additional language operation.

Limitations

This record invokes the classical finiteness theorem rather than reproving it from first principles.

Open work

Make the carrier construction fully explicit in a mechanized implementation.