An input gives the number p of predicates, a finite transition table, and accepting state numbers. Its alphabet is the full powerset of {0,…,p−1}. Letters index columns by their binary masks. The initial state is 0.

A table with s rows uses states 0,…,s. A missing entry returns 0; targets are reduced modulo s+1. This total convention assigns a finite automaton to every input, without a separate promise of well-formedness. Every ordinary DFA can be represented (renumber its initial state to 0 and provide its table). The computability encoding is the standard encoding of natural numbers and lists, explicitly transported to this record.