Topic
Structural complexity theory
About: Structural complexity theory is a research topic. Over the lifetime, 1108 publications have been published within this topic receiving 41190 citations.
Papers published on a yearly basis
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Papers
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TL;DR: Several properties of the graph-theoretic complexity are proved which show, for example, that complexity is independent of physical size and complexity depends only on the decision structure of a program.
Abstract: This paper describes a graph-theoretic complexity measure and illustrates how it can be used to manage and control program complexity. The paper first explains how the graph-theory concepts apply and gives an intuitive explanation of the graph concepts in programming terms. The control graphs of several actual Fortran programs are then presented to illustrate the correlation between intuitive complexity and the graph-theoretic complexity. Several properties of the graph-theoretic complexity are then proved which show, for example, that complexity is independent of physical size (adding or subtracting functional statements leaves complexity unchanged) and complexity depends only on the decision structure of a program.
6,047 citations
Book•
30 Oct 1997TL;DR: This chapter discusses decision problems and Complexity over a Ring and the Fundamental Theorem of Algebra: Complexity Aspects.
Abstract: 1 Introduction.- 2 Definitions and First Properties of Computation.- 3 Computation over a Ring.- 4 Decision Problems and Complexity over a Ring.- 5 The Class NP and NP-Complete Problems.- 6 Integer Machines.- 7 Algebraic Settings for the Problem "P ? NP?".- 8 Newton's Method.- 9 Fundamental Theorem of Algebra: Complexity Aspects.- 10 Bezout's Theorem.- 11 Condition Numbers and the Loss of Precision of Linear Equations.- 12 The Condition Number for Nonlinear Problems.- 13 The Condition Number in ?(H(d).- 14 Complexity and the Condition Number.- 15 Linear Programming.- 16 Deterministic Lower Bounds.- 17 Probabilistic Machines.- 18 Parallel Computations.- 19 Some Separations of Complexity Classes.- 20 Weak Machines.- 21 Additive Machines.- 22 Nonuniform Complexity Classes.- 23 Descriptive Complexity.- References.
1,770 citations
5 May 1982
TL;DR: The pattern which will be shown is that the expression complexity of the investigated languages is one exponential higher then their data complexity, and for both types of complexity the authors show completeness in some complexity class.
Abstract: Two complexity measures for query languages are proposed. Data complexity is the complexity of evaluating a query in the language as a function of the size of the database, and expression complexity is the complexity of evaluating a query in the language as a function of the size of the expression defining the query. We study the data and expression complexity of logical languages - relational calculus and its extensions by transitive closure, fixpoint and second order existential quantification - and algebraic languages - relational algebra and its extensions by bounded and unbounded looping. The pattern which will be shown is that the expression complexity of the investigated languages is one exponential higher then their data complexity, and for both types of complexity we show completeness in some complexity class.
1,683 citations
IBM1
TL;DR: The problem of deciding validity in the theory of equality is shown to be complete in polynomial-space, and close upper and lower bounds on the space complexity of this problem are established.
1,579 citations
TL;DR: Several complexity measures for Boolean functions are discussed: certificate complexity, sensitivity, block sensitivity, and the degree of a representing or approximating polynomial, and how they give bounds for the decision tree complexity of Boolean functions on deterministic, randomized, and quantum computers.
929 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2022 | 5 |
| 2021 | 1 |
| 2020 | 2 |
| 2019 | 2 |
| 2018 | 5 |