We introduce the notion of natural proof. We argue that the known proofs of lower bounds on the complexity of explicit Boolean functions in non-monotone models fall within our definition of natural. We show based on a hardness assumption that natural proofs can't prove super

Razborov and Rudich have shown that so-called natural proofs are not useful for separating P from NP unless hard pseudorandom number generators do not exist. This famous result is widely regarded as a serious barrier to proving strong lower bounds in circuit complexity theory. By definition, a

We study connections between Natural Proofs, derandomization, and the problem of proving “weak” circuit lower bounds such as NEXP ⊂ TC 0, which are still wide open. Natural Proofs have three properties: they are constructive (an efficient algorithm A is embedded in them), have largeness (A accepts

We propose natural proofs for reasoning with programs that manipulate data-structures against specifications that describe the structure of the heap, the data stored within it, and separation and framing of sub-structures. Natural proofs are a subclass of proofs that are amenable to completely

Summary. Some fundamental properties of addition, multiplication, order relations, exact division, the remainder, divisibility, the least common multiple, the greatest common divisor are presented. A proof of Euclid algorithm is also given. MML Identifier:NAT_1. WWW:http://mizar.org/JFM/Vol1/nat_1

Consider a committee which must select one alternative from a set of three or more alternatives. Committee members each cast a ballot which the voting procedure counts. The voting procedure is strategy-proof if it always induces every committee member to cast a ballot revealing his preference. I

Abstract: Muscadet is a knowledge-based theorem prover based on natural deduction. Its results show its complementarity with regard to resolution-based provers. This paper presents some Muscadet results and points out some of its characteristics.

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Categorizations which humans make of the concrete world are not arbitrary but highly determined. In taxonomies of concrete objects, there is one level of abstraction at which the most basic category cuts are made. Basic categories are those which carry the most information, possess the highest category cue validity, and are, thus, the most differentiated from one another. The four experiments of Part I define basic objects by demonstrating that in taxonomies of common concrete nouns in English based on class inclusion, basic objects are the most inclusive categories whose members: (a) possess significant numbers of attributes in common, (b) have motor programs which are similar to one another, (c) have similar shapes, and (d) can be identified from averaged shapes of members of the class. The eight experiments of Part II explore implications of the structure of categories. Basic objects are shown to be the most inclusive categories for which a concrete image of the category as a whole can be formed, to be the first categorizations made during perception of the environment, to be the earliest categories sorted and earliest named by children, and to be the categories

Abstract: We introduce the input-output automaton, a simple but powerful model of computation in asynchronous distributed networks. With this model we are able to construct modular, hierarchical correctness proofs for distributed algorithms. We de ne this model, and give aninteresting example