In this paper we describe a method that estimates the motion of a calibrated camera (settled
on an experimental vehicle) and the tridimensional geometry of the environment. The only …

We develop the theory of holographic algorithms. We definea basis manifold and give
characterizations of algebraic varieties of realizable symmetric generators and recognizers …

We propose and explore a novel alternative framework to study the complexity of counting
problems, called Holant Problems. Compared to counting Constrained Satisfaction …

We propose a new method to prove complexity dichotomy theorems. First we introduce
Fibonacci gates which provide a new class of polynomial time holographic algorithms. Then …

We propose and explore a novel alternative framework to study the complexity of counting
problems, called Holant problems. Compared to counting constraint satisfaction problems (# …

We explore the intricate interdependent relationship among counting problems, considered
from three frameworks for such problems: Holant Problems, counting CSP and weighted H …

Valiant has proposed a new theory of algorithmic computation based on perfect matchings
and Pfaffians. We study the properties of matchgates—the basic building blocks in this new …

Valiant introduced match gate computation and holographic algorithms. A number of
seemingly exponential time problems can be solved by this novel algorithmic paradigm in …

We prove a complexity dichotomy for complex-weighted Holant problems with an arbitrary
set of symmetric constraint functions on Boolean variables. In the study of counting …

Let TG (x, y) be the Tutte polynomial of a graph G. In this paper we show that if (G n) n is a
sequence of d-regular graphs with girth g (G n)→∞, then for x≥ 1 and 0≤ y≤ 1 we have lim …