A Methodology for System Complexity Analysis Based on the DIKWP



A Methodology for System Complexity Analysis Based on the DIKWP

通用人工智能AGI测评DIKWP实验室

2025-10-30

A Methodology for System Complexity Analysis Based on the DIKWP Model (Simplified Version)

—A Case Study of Artificial Consciousness and Cognitive Intelligent Systems

Yucong Duan

International Standardization Committee of Networked DIKWP for Artificial Intelligence Evaluation(DIKWP-SC)

World Artificial Consciousness CIC(WAC)

World Conference on Artificial Consciousness(WCAC)

(Email: duanyucong@hotmail.com)

introduction

The continuous development of artificial intelligence and cognitive systems is driving the innovation of the paradigm of algorithm complexity analysis. Traditional algorithm complexity studies (such as time complexity O(n), spatial complexity O(n^2), etc.) mainly serve procedural or functional computing modes, emphasizing single-dimensional metrics such as input-output, process control, and resource consumption. However, with the emergence of Artificial Consciousness, Semantic Intelligence, and Cognitive Modeling, more and more algorithms are described as complex systems with multi-layered structures, semantic drives, and cognitive flows. The DIKWP model proposed by Professor Duan Yucong (Data, Information, Knowledge, Wisdom, andPurpose) is a model of cognitive computing and semantic intelligence.

This paper systematically demonstrates how to carry out hierarchical, holographic, and semantic-oriented complexity analysis for DIKWP-structured algorithms and systems, so as to provide a scientific quantitative basis and cutting-edge methodology for the theoretical modeling, algorithm design and engineering implementation of artificial consciousness systems.

1. Review of DIKWP model and cognition of algorithm structure

1.1 Introduction to the DIKWP model

The DIKWP model is a cognitive and semantic continuum that breaks down any complex problem and system into five levels:

D (Data): Raw facts, signals, and environmental inputs

I (Information): Structured content, features, and events extracted and filtered from data

K (Knowledge): Knowledge base, empirical rules, pattern models, and associative inference

W (Wisdom): Global decision-making, dynamic planning, value ranking, and strategy generation

P (Purpose): Goal Intent, Task Driven, Ultimate Constraint, Feedback Regulation

DIKWP not only describes the generation path of knowledge and intelligence, but can also be regarded as the semantic basis for the "self-explanatory" and "self-optimized" of any cognitive system.

1.2 Paradigm shift described by the DIKWP algorithm

The algorithm described by DIKWP is no longer a single input-processing-output link, but a multi-layer circular system with purpose as the core, knowledge and wisdom as the mediator, and data and information as the basis. Each layer has independent computing and processing, and constantly interacts with other layers to form semantic flows, information loops, and policy feedback.

Therefore, in order to analyze the complexity of such algorithms, it is necessary to move out of the traditional framework of "single-level and single-path flow" and move to a new system of "multi-layer structure, inter-layer interaction, and cognitive flow".

2. Theoretical Basis of DIKWP Complexity Analysis

2.1 Limitations of traditional complexity analysis

Traditional complexity theory is mainly measured by the number of steps executed by the algorithm, the space required, and the depth of the call stack, but these methods cannot accurately describe the cognitive intelligence system:

The pressure of multi-source heterogeneous input on information extraction and fusion

Knowledge reasoning, multi-branching and uncertainty of rule links

The search space and decision-making depth of intelligent strategic planning

The number of iterations of the purpose to dynamically adjust with global feedback

Information flow and semantic loss between layers

Therefore, it is necessary to expand the semantic dimension and structural depth of complexity analysis.

2.2 The five-layer principle of DIKWP complexity analysis

Embedding complexity analysis into a DIKWP model breaks down the complexity of a system or algorithm into five dimensions:

Level	Complexity connotation	Measure what and how	Instance metrics
D	Data scale and collection cost	Number of input data points, number of signal channels, sampling frequency	O(N)、O(M × N)
I	Complexity of information extraction and processing	Feature engineering, event extraction, data structuring	O(F(N))、O(N N)
K	Knowledge Reasoning and Model Computing	The number of rule matches, the size of the knowledge base, and the number of inference steps	O(R × K)、O(depth)
W	Intelligent decision-making and overall planning	Decision tree width, state space size, policy adjustment	O(S)、O(G)
P	Closed-loop complexity of purpose scheduling and feedback	The number of purpose switches, the level of target evolution, and the depth of feedback	O(T × L)

3. Detailed explanation of hierarchical complexity analysis methods

3.1 Layer D (Data Complexity) in detail

The core question: How much raw data does the system need to process? How much pressure is there on computing/communication/storage for data acquisition, sampling, and perception ?

Typical Indicators:

Number of data points (e.g., total number of camera pixels, number of sensor samples)

Number of data types (e.g., multimodal: visual, sound, text, etc.)

Sample rate per unit time

Complexity Formula:

C D = O ( N )

where N is the total number of data points.

Example: If the camera captures 30 frames per second at 640×480 pixels per frame, the original input complexity of the D layer is:

O ( 30 × 640 × 480 ) =O ( 9 , 216 , 000 ) 每秒

3.2 Layer I (Information Complexity) in detail

Core question: How to efficiently extract useful information from raw data? What is the computational cost of feature extraction and structuring operations?

Typical Indicators:

Feature dimension F (e.g., image features, number of speech MFCCs).

Dealing with algorithm complexity (e.g O ( N ) ., , O ( N log N ) ).

Depth of information fusion (e.g., multi-channel fusion, event combination)

Complexity Formula:

C I = O ( F ( N ) )

where F is the number of features and N is the number of basic data points.

Example:

Image Edge Detection:; O ( W × H )

Speech Signal Transformation: etc. O ( M log M )

3.3 Layer K (Knowledge Complexity) in detail

Core question: How deep and extensive is the retrieval of the knowledge base, rule reasoning, and model invocation? What is the length and branch complexity of the inference path?

Typical Indicators:

The size of the knowledge base (number of rules R, entity/relationship K).

Inference path depth (maximum number of recursive layers, graph traversal depth)

Knowledge matching complexity (e.g O ( R × K ) ., , O ( log K ) ).

Complexity Formula:

C K = O ( R × K )

where R is the number of rules and K is the number of knowledge elements.

Example: The expert system inference chain traverses N rules, and the knowledge graph depth-first search path complexity is O ( log K ) .

3.4 Layer W (Intelligent Complexity) in detail

Core question: The space and depth of global planning, dynamic strategy and multi-objective decision-making? How expensive is the state space explosion and planning tree search?

Typical Indicators:

Status space size S (e.g., map resolution, total number of feasible steps).

Strategy adjustment round G (e.g., game tree branching, reinforcement learning iteration).

Complexity of search algorithms (e.g., A*, Monte Carlo trees, etc.)

Complexity Formula:

C W = O ( S ) 或 O ( S × G )

Example: Route planning uses the A* algorithm, and if the map is 1000 × 1000, the state space size is O ( 10 6 ) .

3.5 P-layer (purpose complexity) in detail

Core Questions: What is the complexity of system purpose changes, target switching, and task feedback? What is the overhead of global scheduling and multi-target coupling?

Typical Indicators:

The number of purpose switches T (e.g., multi-objective dynamic scheduling).

Purpose level L (e.g., compound task, task decomposition tree depth).

Number of feedback adjustment cycles

Complexity Formula:

C P = O ( T × L )

where T is the number of switches, and L is the level/influence area involved each time.

Example: If the assistant responds to 10 purpose changes per second in a multitasking scenario with an purpose tree depth of 3, then:

C P = O ( 10 × 3 ) = O ( 30 )

4. Coupling of interlayer interaction and global complexity

4.1 Interlayer-dependent link effects

In the DIKWP structure, complexity is not simply added to the layers, but reflects a significant interlayer dependency and coupling relationship, such as:

The quality of information extraction (layer I) directly affects the number of effective branches of knowledge reasoning (layer K).

The depth of strategic planning of the intelligence layer is closely related to the size of the knowledge base.

The switching frequency and feedback speed of the purpose layer (P-layer) are limited by the complexity of the decision-making link of the W/K layer.

This multi-layer interaction leads to a dynamic coupling relationship in the overall complexity, which needs to be jointly modeled.

4.2 Combined expression of overall complexity

The most common expression is a linear superposition model:

C DIKWP = C D + C I + C K + C W + C P

When there is a strong dependency or feedback coupling relationship between layers, it can also be expressed in a product model or nested combination:

C DIKWP = O ( ( C D + C I ) × ( C K + C W ) × C P )

Thereinto:

( C D + C I ) Represents data and information processing loads;

( C K + C W ) It represents the pressure of knowledge reasoning and strategy generation;

C P Indicates the feedback complexity of the purpose layer in system scheduling.

If there are multiple feedback paths of W→I or P→K, it may lead to dynamic complexity inflation in the operation of the system, that is, the overall complexity is amplified due to cyclic dependence.

5. Case study and visualization development

5.1 Case 1: The robot looks for the target object

Take a robot performing the task of "visual recognition + path navigation + target confirmation" as an example, and estimate the complexity of each DIKWP level of the robot.

DIKWP Analysis:

Level	Main operations	Parameters/scale	Complexity expression
D	Camera image acquisition + point cloud perception	N = 10 6	O ( 10 6 )
I	Feature Extraction / Object Detection (Deep Neural Networks).	F = 100 , N = 10 6	O ( F ⋅ N ) =O ( 10 8 )
K	The target model is matched, and the inference chain is traversed	, R = 1000 chain length = 10	O ( 10 ⋅ 1000 ) =O ( 10 4 )
W	Path planning (map 100 × 100), A* algorithm	S = 10 4	O ( 10 4 )
P	Purpose switching frequency 3 times/sec, purpose level 2	T = 3 , L = 2	O ( 3 ⋅ 2 ) =O ( 6 )

Global Complexity Sum:

C DIKWP = O ( 10 6 ) + O ( 10 8 ) + O ( 10 4 ) + O ( 10 4 ) + O ( 6 ) ≈ O ( 10 8 )

Conclusion: Layer I (feature processing) is the biggest computational bottleneck, and algorithm optimization or model pruning strategy should be considered.

5.2 Case 2: Intelligent medical diagnosis system

Suppose the system is an intelligent consultation robot based on electronic medical records, and its DIKWP hierarchy is as follows:

Layer D: original medical record text, real-time physiological sensing data, and doctor's voice input;

Layer I: information extraction (such as named entity recognition, keyword matching);

Layer K: Medical Knowledge Reasoning (Symptoms → Diseases → Chain of Treatment Rules);

Layer W: diagnosis and treatment path planning, drug/surgical plan deduction;

P-layer: Dynamically adjust goals and wellness plans based on patient feedback.

Layer complexity analysis:

Level	Complexity expression	illustrate
D	O ( N )	N is the number of electronic medical record/sensor data records
I	O ( F ( N ) )	Text mining, feature structuring processing
K	O ( R ⋅ K )	The size of the rule base and the length of the inference chain
W	O ( S )	Treatment plan space and optimization of the number of rounds
P	O ( T ⋅ L )	Dynamic health feedback loop depth

Diagnostic Bottleneck Analysis:

If the K-tier medical knowledge base is too large (million rules), it will become the main performance bottleneck;

If Layer I NLP is inefficient, it will slow down the downstream process;

If the P-layer feedback delay is high, the user experience will be reduced, and an efficient intent-behavior closed loop needs to be introduced.

6. The engineering significance of DIKWP complexity analysis

6.1 Hierarchical optimization guidance for cognitive system design

It can be clarified which cognitive layer is attributed to the system performance bottleneck (e.g., W-layer search, K-layer inference)

Support hierarchical heterogeneous hardware allocation (e.g., D/I layer available GPU, K layer available knowledge inference chip, etc.)

For the high-complexity layer, algorithm optimization, model pruning, and caching mechanism can be prioritized

6.2 Semantic interpretability of intelligent behavior is improved

The complexity of each layer can be interpreted as the "difficulty" of the cognitive process, which supports the transparency and controllability of the system

Users/developers can use the complexity distribution map to understand the causes of resource consumption and latency of AI systems

6.3 Dynamic scheduling and resource allocation of intelligent systems

In multi-task/multi-agent collaboration scenarios, computing power and communication resources can be dynamically allocated to the DIKWP layer that needs it most

P-layer complexity can be used to design a "task scheduler" for intelligent systems, which intelligently queues and switches according to priority

7. Discipline frontiers and future prospects

7.1 Trends in interdisciplinary integration

The cross-innovation of computational complexity theory and cognitive science has promoted the development of multi-layer complexity measurement system

In the future, the DIKWP model can be combined with complex network theory, multi-agent system, brain-inspired computing, etc., to achieve system-level complexity simulation and tuning

7.2 Complexity Driven by Artificial Consciousness and Self-Explanatory Intelligence

The DIKWP complexity analysis method provides a theoretical basis for the self-monitoring and dynamic adjustment of cognitive load of artificial consciousness system

It supports the design of self-supervision and adaptive feedback mechanism for the whole link of "intent-knowledge-behavior-data".

It helps to realize the full semantic interpretation and automatic optimization of "why is it slow, where is it difficult, and how to tune" of the AI system

7.3 Trends in tooling and automation

In the future, a DIKWP complexity analysis toolbox can be developed to automatically monitor and visualize the complexity of each layer of the cognitive system in real time

Supports interconnection with the automatic scheduling platform to implement intelligent resource scheduling and algorithm fine-tuning (AutoML for DIKWP)

8. Summary and outlook

This paper proposes and demonstrates in detail the algorithm complexity analysis method based on the DIKWP model, which expands the paradigm of traditional complexity analysis with cognitive structure and semantic flow as the center, and provides a scientific, hierarchical and multi-dimensional quantitative analysis framework for the design, evaluation and optimization of artificial consciousness and cognitive intelligence systems.

Through case analysis and engineering scenario mapping, the great value and application prospects of DIKWP complexity analysis in practical applications, system design, performance bottleneck location, intelligent behavior interpretation, and future AI adaptive systems are demonstrated.

In the future, with the rapid development of cognitive intelligence, artificial consciousness and adaptive systems, the complexity analysis method based on the DIKWP model will become one of the core methodologies of cognitive science, artificial intelligence, systems engineering and other multidisciplinary disciplines, which will not only improve the intelligence, interpretability and self-evolution ability of AI systems, but also promote a deeper understanding of the nature of cognition and intelligence.