Kolmogorov Complexity Estimation via Phrase Partitioning

Solution Overview

Problem

The estimation of Kolmogorov Complexity for a finite string is inefficient due to the time and resource-intensive nature of the Lempel/Ziv 78 compression algorithm, which requires encoding, compression, and inverse compression ratio calculations.

Innovation Solution

A data transmission system that estimates Kolmogorov Complexity by partitioning the string into unique phrases, determining the number of phrases, and using the formula C≡N^2*L to calculate a normalized complexity estimate, allowing or rejecting data transmission based on whether this estimate falls within a predetermined complexity band.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If the LZ78 compression algorithm is used to estimate Kolmogorov Complexity, then the estimation accuracy is improved, but the computational time and resource consumption increase significantly

Engineering Contradiction:

ImproveKolmogorov Complexity estimation accuracyVSAvoidcomputational time

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The patent extracts only the essential component needed for complexity estimation from the full LZ78 algorithm. Instead of implementing the complete compression process with encoding and decoding, it extracts solely the partitioning mechanism that divides the string into phrases, discarding the time-consuming compression and decompression steps while retaining the core capability to measure complexity through phrase count.

Inventive Principle:

Principle #2Taking out (Extraction)

Solution Approach 2:

The patent performs only the necessary portion of the LZ78 algorithm (partitioning) without completing the full compression process. By performing partial action - just the partitioning step rather than the entire encode-compress-decode cycle - the system achieves sufficient complexity estimation accuracy without the excessive time and resource consumption of the complete algorithm.

Inventive Principle:

Principle #16Partial or excessive action

2Measurement precision

If the LZ78 compression algorithm is used to estimate Kolmogorov Complexity, then the estimation accuracy is improved, but the resource consumption increases

Engineering Contradiction:

ImproveKolmogorov Complexity estimation accuracyVSAvoidresource consumption

Core Design Contradiction:

Measurement precisionVSUse of energy by moving object

Solution Approach 1:

The patent extracts only the essential component needed for complexity estimation from the full LZ78 algorithm. Instead of implementing the complete compression process with encoding and decoding, it extracts solely the partitioning mechanism that divides the string into phrases, discarding the time-consuming compression and decompression steps while retaining the core capability to measure complexity through phrase count.

Inventive Principle:

Principle #2Taking out (Extraction)

Solution Approach 2:

The patent performs only the necessary portion of the LZ78 algorithm (partitioning) without completing the full compression process. By performing partial action - just the partitioning step rather than the entire encode-compress-decode cycle - the system achieves sufficient complexity estimation accuracy without the excessive time and resource consumption of the complete algorithm.

Inventive Principle:

Principle #16Partial or excessive action

3Measurement precision

If the complete LZ78 compression process is performed, then the complexity estimation is more accurate, but the processing efficiency decreases

Engineering Contradiction:

Improvecomplexity estimation accuracyVSAvoidprocessing efficiency

Core Design Contradiction:

Measurement precisionVSProductivity

Solution Approach 1:

The patent extracts only the essential component needed for complexity estimation from the full LZ78 algorithm. Instead of implementing the complete compression process with encoding and decoding, it extracts solely the partitioning mechanism that divides the string into phrases, discarding the time-consuming compression and decompression steps while retaining the core capability to measure complexity through phrase count.

Inventive Principle:

Principle #2Taking out (Extraction)

Solution Approach 2:

The patent performs only the necessary portion of the LZ78 algorithm (partitioning) without completing the full compression process. By performing partial action - just the partitioning step rather than the entire encode-compress-decode cycle - the system achieves sufficient complexity estimation accuracy without the excessive time and resource consumption of the complete algorithm.

Inventive Principle:

Principle #16Partial or excessive action

Data Source

PatentUS7313817B2Data transmission system utilizing efficient complexity estimation of the kolmogorov complexity for data transmission

Publication Date: 2007.12.25 LEIDOS INNOVATIONS TECHNOLOGY INC

AI summary

A system, method and program storage device tangibly embodying a program of instructions for determining whether to allow transmission of data from a source destined for a destination over a network, comprising: acquiring a string of a predetermined length in bits (L) from the data; partitioning the acquired string into a partition of phrases, each of the phrases in the partition being unique and having one or more bits; determining a number of phrases (N) in the partition; estimating a normalized complexity (C) for the Kolmogorov Complexity in the acquired string viaC≡N2⁢L;and evaluating whether to allow transmission of the data based on a comparison of whether the normalized complexity estimate (C) is within a predetermined normal complexity estimate band.