We determine set-theoretic defining equations for the variety Dualk,d,N ⊂ P(S d C N ) of hypersurfaces of degree d in C that have dual variety of dimension at most k. We apply these equations to the Mulmuley-Sohoni variety GLn2 · [detn] ⊂ P(S n C n2), showing it is an irreducible component of the variety of hypersurfaces of degree n in C 2 with dual of dimension at most 2n − 2. We establish add...

In this paper we study program checking (in the sense of Blum and Kannan 7]) using AC 0 circuits as checkers. Our focus is on the number of queries made by the checker to the program being checked and we term this as the query complexity of the checker for the given problem. We study the query complexity of both deterministic and randomized AC 0 checkers. We show that, for each > 0, (n 1?) is a...

ACTION When one brings Occam up, one first must choose between two Occam “actions”: “Do Fit” and “Do Search”. Occam then returns a window specific to the choice made. Search assesses many models either from the full set of all possible models or from various partial subsets of models. Fit examines one model (or a few models) in greater detail. In an exploratory mode, one would do Search first, ...

Although natural selection does not guarantee that organisms will increase in complexity as they evolve, it is apparent that the complexity of certain lineages, such as our own, has increased during evolution. Although we have an intuitive appreciation of biological complexity--often thinking in terms of morphological or behavioral complexity, or the variety of cell types in an organism--the te...

Kolmogorov complexity, which is also called algorithmic (descriptive) complexity is an object, such as a piece of text, to measure the computational resources needed, which are mostly the length of the shortest binary program to specify an object. Strings whose Kolmogorov complexity is small relative to the string’s size are not considered to be complex and easy to use a short program to specif...

Maintaining behavior change is one of the major challenges in weight management and long-term weight loss. We investigated the impact of the cognitive complexity of eating rules on adherence to weight management programs. We studied whether popular weight management programs can fail if participants find the rules too complicated from a cognitive perspective, meaning that individuals are not ab...

Intuitively, if we can prove that a program terminates, we expect some conclusion regarding its complexity. But the passage from termination proofs to complexity bounds is not always clear. In this work we consider Monotonicity Constraint Transition Systems, a program abstraction where termination is decidable (based on the size-change termination principle). We show that these programs also ha...

We consider a generalization of heterogeneous meta-programs by (1) introducing an extra level of abstraction within the meta-program structure, and (2) meta-program transformations. We define basic terms, formalize transformation tasks, consider properties of meta-program transformations and rules to manage complexity through the following transformation processes: (1) reverse transformation, w...