Quantitative measurements of system complexity

• US 8,244,503 B1
• Filed: 08/30/2007
• Issued: 08/14/2012
• Est. Priority Date: 08/30/2007
• Status: Expired due to Fees

• Current Assignee: United States Of America As Represented By The Secretary Of The Air Force
• Original Assignee: United States Of America As Represented By The Secretary Of The Air Force
• Inventors: Repperger, Daniel W., Roberts, Rodney G., Koepke, Corbin G.
• Primary Examiner(s): Thangavelu, Kandasamy
• Assistant Examiner(s): MOLL, NITHYA JANAKIRAMAN
• Application Number:
  US11/900,137
• Time in Patent Office: 1,811 Days
• Field of Search: 703/2, 703/6, 703/13, 703/22, 702/182, 702/183, 702/186, 702/194, 702/196, 706/45
• US Class Current: 703/2
• CPC Class Codes: G06F 17/10 Complex mathematical operations function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544

Abstract

A method is provided for determining the complexity of a system. The method includes creating a response matrix for the system, creating a contingency matrix, C_n, from the response matrix, and calculating the complexity of the system from the formula: Complexity=[α/det(C_n^TC_n)]*Log₂([(H(x)/H(y))]) wherein H(x) is the input information quantity, H(y) is the output information quantity, and α is a dimensionless system constant. The method also includes displaying the complexity of the system.

Claims

1. An apparatus for measuring a complexity of a system, the apparatus comprising a computer programmed to:

create a response matrix for the system;

create a contingency matrix, C_n, from the response matrix;

calculate the complexity of the system from a formula;

Complexity=[α

/det(C_n^TC_n)]*Log₂([(H(x)/H(y)])

wherein

H(x) is an input information quantity

H(y) is an output information quantity

α

is a dimensionless system constant; and

,

display the complexity of the system.

2. The apparatus of claim 1, wherein:

3. The apparatus of claim 2, wherein creating the response matrix includes determining a number of inputs and outputs of the system and determining a frequency of each input for each output.

4. The apparatus of claim 3, wherein creating the contingency matrix includes dividing each frequency by a summation of the frequencies.

5. The apparatus of claim 2, wherein α

=1.

6. An apparatus for comparing a complexity of a system in first and second configurations, the apparatus comprising a computer programmed to:

create a first response matrix for the system in the first configuration;

create a first contingency matrix, C_n, from the first response matrix;

calculate a first complexity of the system in the first configuration from a formula;

First Complexity=[α

/det(C_n^TC_n)]*Log₂([(H(x)/H(y)])

wherein

H(x) is an input information quantity

H(y) is an output information quantity

α

is a dimensionless system constant;

create a second response matrix for the system in the second configuration;

create a second contingency matrix, C_n, from the second response matrix;

calculate a second complexity of the system in the second configuration from a formula;

Second Complexity=[α

/det(C_n^TC_n)]*Log₂([(H(x)/H(y)])

wherein

H(x) is an input information quantity

H(y) is an output information quantity

α

is a dimensionless system constant; and

,

output the first and second complexities of the system.

7. The apparatus of claim 6, wherein for the first and second complexities:

8. The apparatus of claim 7, wherein creating the first response matrix includes determining a number of inputs and outputs of the system in the first configuration and determining a frequency of each input for each output.

9. The apparatus of claim 8, wherein creating the first contingency matrix includes dividing each frequency by a summation of the frequencies.

10. The apparatus of claim 7, wherein α

=1.

11. A process for measuring a complexity of a system, comprising;

using a computer programmed to perform the following steps;

creating a response matrix for the system;

creating a contingency matrix, C_n, from the response matrix;

calculating the complexity of the system from a formula;

Complexity=[α

/det(C_n^TC_n)]*Log₂([(H(x)/H(y)]),

wherein;

H(x) is an input information quantity;

H(y) is an output information quantity; and

,

α

is a dimensionless system constant; and

,

outputting the measured system complexity.

12. The process for measuring a complexity of a system of claim 11, wherein:

13. The process for measuring a complexity of a system of claim 12, wherein creating the response matrix includes determining a number of inputs and outputs of the system and determining a frequency of each input for each output.

14. The process for measuring a complexity of a system of claim 13, wherein creating the contingency matrix includes dividing each frequency by a summation of the frequencies.

15. The process for measuring a complexity of a system of claim 12, wherein α

=1.