An optimal arc consistency algorithm AC-4 was given by Mohr and Henderson [8]. AC4 has cost 0(ea), and cost (na) for scene labelling. Although their algorithm is indeed optimal, under certain conditions a constraint satisfaction problem can be transformed into a less complex problem. In this paper, we present conditions and mechanisms for such transformations, and show how to factor relations i...

Polycyclic aromatic hydrocarbons that we previously called total resonant sextet (TRS) benzenoids are revisited within the framework of recent experimental findings. A benzenoid transformation called leapfrogging generates TRS benzenoids. There are 13, 30, and 114 TRS benzenoid isomers with formulas C72H26, C96H30, and C102H32, respectively. “The leapfrogs of benzenoids are 2-factorable” is a s...

defined by a four-dimensional "triangular" matrix jamnkjjj (m, n, k, I = 1, 2, 3, ...; amnkl = O for k > m or I > n or both) of real or complex numbers. We showed (Theorem 2 of I) that if (A) is regular for bounded sequences, it is in general regular also for a large class of unbounded sequences. Special interest attaches to the type of transformation (A) for which we have amnklz = amk anl (m, ...

In the present paper, using result of Bennett [1] on characterization factorable matrices, we give necessary and sufficient conditions in order that Σλ_{n}x_{n} is summable |R,p_{n}|_{s} whenever Σμ_{n}x_{n} |C,0|_{k}, |C,0|_{s} |R,p_{n}|_{r},. where 1