Topic
Average-case complexity
About: Average-case complexity is a research topic. Over the lifetime, 1749 publications have been published within this topic receiving 44972 citations.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: This paper presents a new quantitative definition of organized complexity that simultaneously captures all of the three key features of complexity for the first time and is based on circuits rather than Turing machines and ɛ-machines.
Abstract: One of the most fundamental problems in science is to define the complexity of organized matters quantitatively, that is, organized complexity. Although many definitions have been proposed toward this aim in previous decades (e.g., logical depth, effective complexity, natural complexity, thermodynamics depth, effective measure complexity, and statistical complexity), there is no agreed-upon definition. The major issue of these definitions is that they captured only a single feature among the three key features of complexity, descriptive, computational, and distributional features, for example, the effective complexity captured only the descriptive feature, the logical depth captured only the computational, and the statistical complexity captured only the distributional. In addition, some definitions were not computable; some were not rigorously specified; and any of them treated either probabilistic or deterministic forms of objects, but not both in a unified manner. This paper presents a new quantitative definition of organized complexity. In contrast to the existing definitions, this new definition simultaneously captures all of the three key features of complexity for the first time. In addition, the proposed definition is computable, is rigorously specified, and can treat both probabilistic and deterministic forms of objects in a unified manner or seamlessly. The proposed definition is based on circuits rather than Turing machines and ɛ-machines. We give several criteria required for organized complexity definitions and show that the proposed definition satisfies all of them.
1 citations
••
1 citations
01 May 2002
TL;DR: This abstract sketches a way of reducing item generation through grammar transformation by using Schema-TAGs (STAGs), which in contrast to TIGs keeps weak equivalence and performs better than factoring as proposed by (Harbusch, Widmann and Woch, 1998), and provides a proof of the average case time complexity of STAGs based on the proposed transformation.
Abstract: The introduction of the adjoining operation to context-free grammars comes at high costs: The worst case time complexity of (Earley, 1968) is O n 3 ¡ , whereas Tree Adjoining Grammars have O n 6 ¡ ((Schabes, 1990)). Thus, avoiding adjoining as far as possible seems to be a good idea for reducing costs (e.g.) address this problem more radically by restricting the adjoining operation of TAGs such that it is no context-sensitive operation anymore. The result is O n 3 ¡ worst case parseability which stems from TIG's context-freeness. However, to preserve TAG's mildly context-sensitiveness the adjoining operation must not be restricted in any way. Another solution would be simply to call the adjoining operation less frequently: The production of items directly depends on the fashion of the underlying grammar and often adjoining is used to make the grammar more comprehensible or more adequate to the linguistic phenomenon even if there would be simpler representations as, for instance, left-or right recursion. This abstract (1st) sketches a way of reducing item generation through grammar transformation by using Schema-TAGs (STAGs , as introduced by (Weir, 1987), where tree sets are enumerated by regular expressions) which in contrast to TIGs keeps weak equivalence and performs better than factoring as proposed by (Harbusch, Widmann and Woch, 1998), and (2nd) provides a proof of the average case time complexity of STAGs based on the proposed transformation. In the following, adressing of nodes occurs in the fashion of (Gorn, 1967), i.e. each node of a tree gets a unique number – beginning with zero – which preserves the structure of the tree. For example, 1¢ 2 points to the second daughter of the first daughter of a root node, and in grammar G 1 of Fig. 2,
1 citations