Valiant transform of forney graphs

Abstract

In his recent work, Valiant presented a powerful family of new algorithms, which he calls holographic algorithms. The mathematical foundation of holographic algorithms is what is known as Holant Theorem. Synthesizing from Valiant's work, in this paper, we introduce the notion of Valiant transform for normal graphs. Exploiting this synthesis, we establish a more general version of Holant Theorem, which allows an alternative interpretation of the duality results on normal graphs.