We develop an iterated homology theory for simplicial complexes. This theory is a variation on one due to Kalai. For 1 a simplicial complex of dimension d − 1, and each r = 0, . . . , d , we define r th iterated homology groups of 1. When r = 0, this corresponds to ordinary homology. If 1 is a cone over 1′, then when r = 1, we get the homology of 1′. If a simplicial complex is (nonpure) shellab...

In this paper we propose a conditional logic IBC to represent iterated belief revision. We define an iterated belief revision system by strengthening the postulates proposed by Darwiche and Pearl [3]. First, following the line of Darwiche and Pearl, we modify AGM postulates to make belief revision a function of epistemic states rather than of belief sets. Then we propose a set of postulates for...

The iterated diierence of polyhedra V = P1n(P2n independently in 11] and 7] as a suucient condition for V to be exactly computable by a two-layered neural network. An algorithm checking whether V I R d is an iterated diierence of polyhedra is proposed in 11]. However, this algorithm is not practically usable because it has a high computational complexity and it was only conjectured to stop with...

A new and efficient class of nonlinear receivers is introduced for digital communication systems. These “iterated-decision” receivers use optimized multipass algorithms to successively cancel interference from a block of received data and generate symbol decisions whose reliability increases monotonically with each iteration. Two variants of such receivers are discussed: the iterated-decision e...