# Sequential dynamical systems with threshold functions.

### Description

A sequential dynamical system (SDS) (see [BH+01] and the references therein) consists of an undirected graph G(V,E) where each node {nu} {epsilon} V is associated with a Boolean state (s{sub {nu}}) and a symmetric Boolean function f{sub {nu}} (called the local transition function at {nu}). The inputs to f{sub {nu}} are s{sub {nu}} and the states of all the nodes adjacent to {nu}. In each step of the SDS, the nodes update their state values using their local transition functions in the order specified by a given permutation {pi} of the nodes. A configuration of the SDS is an n-tuple ... continued below

3 p.

## Who

People and organizations associated with either the creation of this article or its content.

### Provided By

#### UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

## What

### Description

A sequential dynamical system (SDS) (see [BH+01] and the references therein) consists of an undirected graph G(V,E) where each node {nu} {epsilon} V is associated with a Boolean state (s{sub {nu}}) and a symmetric Boolean function f{sub {nu}} (called the local transition function at {nu}). The inputs to f{sub {nu}} are s{sub {nu}} and the states of all the nodes adjacent to {nu}. In each step of the SDS, the nodes update their state values using their local transition functions in the order specified by a given permutation {pi} of the nodes. A configuration of the SDS is an n-tuple (b{sub 1}, b{sub 2}...,b{sub n}) where n = |V| and b{sub i} {epsilon} {l_brace}0,1{r_brace} is the state value of node {nu}{sub i}. The system starts in a specified initial configuration and each step of the SDS produces a (possibly new) configuration.

3 p.

### Source

• Submitted to: ACM-SIAM Symposium on Discrete Algorithms (SODA 02) San Fransisco, CA, January 2002

### Identifier

Unique identifying numbers for this article in the Digital Library or other systems.

• Report No.: LA-UR-01-4696
• Grant Number: none
• Office of Scientific & Technical Information Report Number: 975700

### Collections

#### Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

## When

### Creation Date

• January 1, 2001

### Added to The UNT Digital Library

• Nov. 13, 2016, 7:26 p.m.

### Description Last Updated

• Dec. 12, 2016, 6:17 p.m.

Yesterday: 0
Past 30 days: 0
Total Uses: 3