Arithmetic circuit complexity
In computational complexity theory, standard circuit complexity studies the sizes and depths of boolean circuits needed to solve various problems. Arithmetic circuit complexity replaces the abstract logic gates of boolean circuits with "arithmetic gates" that compute (iterated) sums and products over some arbitrary semiring. The choice of semiring may either be left unspecified, as in a circuit that computed products of matrices with entries from the semiring [1]; or may be fixed, as when showing that arithmetic circuits over finite fields can be reduced to boolean circuits using threshold gates.[2]