2. Measures of Complexity a non--exhaustive list
Seth Lloyd
http://web.mit.edu/esd.83/www/notebook/Complexity.PDF
1. Difficulty of description. Typically measured in bits.
Information; Entropy; Algorithmic Complexity or Algorithmic Information Content; Minimum
Description Length; Fisher Information; Renyi Entropy; Code Length (prefix-free, Huffman,
Shannon- Fano, error-correcting, Hamming); Chernoff Information; Dimension; Fractal Dimension;
Lempel--Ziv Complexity.
2. Difficulty of creation. Typically measured in time, energy, dollars, etc.
Computational Complexity; Time Computational Complexity; Space Computational Complexity;
Information--Based Complexity; Logical Depth; Thermodynamic Depth; Cost; Crypticity.
3. 3. Degree of organization. This may be divided up into two quantities: a) Difficulty of describing
organizational structure, whether corporate, chemical, cellular, etc.; b) Amount of information
shared between the parts of a system as the result of this organizational structure.
a) Effective Complexity: Metric Entropy; Fractal Dimension; Excess Entropy; Stochastic
Complexity; Sophistication; Effective Measure Complexity; True Measure Complexity; Topological
epsilon-machine size; Conditional Information; Conditional Algorithmic Information Content;
Schema length; Ideal Complexity; Hierarchical Complexity; Tree subgraph diversity; Homogeneous
Complexity; Grammatical Complexity.
b) Mutual Information: Algorithmic Mutual Information; Channel Capacity; Correlation; Stored
Information; Organization.
There are a number of related concepts that are not quantitative measures of complexity per se,
but that are closely related: Long--Range Order; Self--Organization; Complex Adaptive Systems;
Edge of Chaos. 2
3. Our definition of complexity
Complex system – the one that does not fit in the sole
engineer’s head, thus collaboration of a team and
automation of a knowledge work are mandatory.
E.g.:
• Aircraft
• programming-in-the small vs.programming in the large
• VLSI – very large scale integration, more than 1000
transistors on a single chip (now transistor count is
more than 20bln. – FPGA Virtex-Ultrascale XCVU440)
• Artificial neural network – 16bln. parameters.
3
4. Sources of ideas for fighting complexity
• Software engineering / computer hardware
engineering
• Banking, insuarance, security market
• Retail industry (one of the leaders now!)
• Transport engineering (aerospace, railway,
automotive)
• Other mechanical engineering
• Civil engineering
4
5. 5
Engineering: complexity is about number of independent parts
PP&P – process, power & petroleum
PLM – product life-cycle management
From Dassault Systemes presentation
6. How to make such people?
Hunting and gathering Settled farming
7. Systems Engineering: dealing with complexity.
7
Systems Engineering (SE) is an interdisciplinary approach and means to enable the
realization of successful systems. It focuses on holistically and concurrently
understanding stakeholder needs; exploring opportunities; documenting
requirements; and synthesizing, verifying, validating, and evolving solutions while
considering the complete problem, from system concept exploration through
system disposal.
http://sebokwiki.org/wiki/Systems_Engineering_%28glossary%29
https://en.wikipedia.org/wiki/Apollo_program
Apollo landings (1969-1972)
Apollo Program
• 24 astronauts orbited Moon
• 12 astronauts walked on Moon
• 382kg of lunar soil and rocks
returned to Earth
8. System approach
in systems engineering standards and public documents
• BKCASE, Body of Knowledge and Curriculum to Advance Systems
Engineering (2015), http://www.bkcase.org/
• IEC 81346 (2009), Industrial systems, installations and equipment and
industrial products -- Structuring principles and reference designations --
Part 1: Basic rules
• ISO/IEC/IEEE 15288 (2015) Systems and software engineering - System life
cycle processes,
• ISO 15926-2 (2003), Industrial automation systems and integration --
Integration of life-cycle data for process plants including oil and gas
production facilities -- Part 2: Data model.
• ISO/IEC/IEEE 42010 (2011), Systems and software engineering -
Architecture description,
• OMG Essence (2014) – Kernel and Language for Software Engineering
Methods, specification http://www.omg.org/spec/Essence/Current
8
9. Complexity: divide and conquer
• System holonic structure
• Separation of concerns
• Abstracton (modeling-generation)
• Learning (autoencoder-decoder)
• Cognitive load management (expression
problem)
• …
9
10. System in the eyes of the beholders (stakeholders).
Theatre metaphor
Stakeholder is role vs. actor/performer, office/position, rank
System approach 2.0, based on human action
11. Holon
part-whole relationship
11
System of interest
(using system)
(system in operation environment)
(subsystem)
Subsystem
(System of interest)
(Using system)
(system in operation
environment)
Using system
(system-of-interest)
(system in operation environment)
(subsystem)
Enabling system
13. Holarhy
zoom – select
Leidraadse (2008), Guideline Systems Engineering for Public Works and Water Management, 2nd edition, http://www.leidraadse.nl/
14. There are 4 systems here:
System of
interest
Requirements
System of
interest
Constraints
(Architecture)
Using system
Stakeholder needs
14
1 2
4
Enabling system
System in
operation
environment
3
15. Generations of engineering
(modeling development for checking, simulation and generation)
15
E
f
f
e
c
t
i
v
e
n
e
s
s
Time
III generation
Model-based engineering: formal
languages («executable code»)
II generation
Contemporary («classic»)
engineering: diagrams and
drawings («pseudocode»)
I generation
«Alchemy-like engineering»:
informal texts and sketches
199018601400
IV generation
Artificial
intelligence:
formal+informal
computations
2020
16. Interdisciplinary Plurality
(on one system level, even without holarchy)
On base of Fig.3
ISO 81346-1
-Module
=Component
+Location
All specialties
• Mechanics
• Cinematics
• Electrics
• Electronics
• Control software
• Fluid dynamics
• Strength
• Temperature
• Noise
• Vibration
• …
All life cycle stages
• Inception
• Design
• Construction,
manufacturing
• Operation
• Maintenance
• Modernization
• Retirement
PLM/ALM, ERP, EAM
• Product model
• Project model
16
18. Basic system structures
ISO 81346
• =Components
• -Modules
• +Locations
• Multiple variants of representations of each system aspect.
• This is only basic system aspects, there are multiple other
system structure types!
• Rare completely separated. Usually presented in hybrid form.
18
19. Hybrid diagrams
• There are few ontology engineers, you should not expect too much
formalism.
• Most of system descriptions are hybrid (with components and
modules are mixed).
• Terminology can differ (e.g. “component” can be “functional
element” and even “module”).
19
21. Principal schema complexity
• Great metamodels (discipline)
• Modelers (collaboration)
• Model checking (formalization)
• Generate!
• Simulation
21
22. Module diagram examples (1)
22
FR160B PCB 2-Layer
USB Portable Power
Module -- - Green (3.5
x 2.6 x 1.5cm)
Model FR160B
Quantity 1
Color Green
Material PCB
Features
Input: 5V/800mA;
Output: 5V/1A; LED
lightening; With
protection board on
COB; Output current
limited protection
Application Great for DIY project
Other
ON (Press button) / OFF
(Automatically)
Packing List 1 x Module
23. Module diagram examples (2)
Intellect stack
1. Application
2. Cognitive architecture
3. Learning algorithm
4. Numerical libraries and
frameworks
5. Scientific computing
programming language
6. Hardware acceleration of
computations
23
http://www.slideshare.net/Techtsunami/cn-prt-iot-v1
http://www.w3.org/2001/12/semweb-fin/w3csw
http://ailev.livejournal.com/1210678.html
Semantic web stack
Networking Layer Comparison
24. Modules: key for complexity
• Modularity: links have a price! The more links,
the more price!
(http://arxiv.org/abs/1207.2743)
• Modules: black-boxes with functions, available
via interfaces
• Interfaces: communications. Conway law,
reverse Conway maneuver.
• Optimization: DSM
24
25. Logical and physical architectures matching
ISO 81346-1
Figure 7
25
Logical architecture
(component structure,
functional decomposition)
iteratively match with
physical architecture (module
structure, work product
decomposition).
Most complex part:
modular synthesis
26. Multiscale * beyond life cycle
<<< Inception Architecture Non-
architecture
part of design
Manufacturing Operation>>>
Using
system
IT-1 IT-2 IT-3 IT-4 IT-5
Macro IT1 IT2 IT3 IT4 IT5
Meso IT6 IT7 IT8 IT9 IT10
Micro IT11 IT12 IT13 IT14 IT15
Nano IT16 IT17 IT18 IT19 IT20
Specialization/professionalization in each cell, plus expansion to neighbors
Integration at a product level: overall table («enabling eco-system»!)
CAD/CAM/codes/PLM/CAE/ERP/EAM/…
configuration and change management!
Substance (system) levels * realization (life cycle) levels
26
27. Expression problem
• Programming-in-the small vs. programming in the large
• Granularity & modularity
• Packages (Modula)
• Object-oriented approach
• Data bases/queries
• Julia: multiple dispatch
• Functional programming – Johan van Bethem (in
https://www.illc.uva.nl/Research/Publications/Reports/PP-2005-
22.text.pdf): «much of logic is about a balance between the
expressive power of formal languages and the complexity of
performing natural tasks for them, such as model checking for
truth, consistency maintenance, or valid inference. This is the thrust
of many meta-theorems, including Gödel's and Tarski's celebrated
result about the limitations of first-order logic. The 'Golden Rule' of
logic says that gains in expressive power are lost in higher
complexity».
27
28. Practice = discipline + technology
Disciplined (competent in domain) performers
Supported with needed for a discipline tools and work products.
28
Components/alpha – how it is working
Modules/work products – how it makeable
29. Domain and endeavor:
KNOWLEDGE is an information that you can use in different projects (economy of thinking!)
• Domain/discipline = thinking (operations with abstract typed
objects). Changing every 30 years. Studied in schools and
universities.
• Technologies/way of working = tools and work products
(thinking with an exocortex). Changing in every 5 years. Trained
in workplace.
• Link between discipline and technology, discipline and real life
should be trained with a help of a teacher.
29
There is no one word from
a textbook in real life
There is no one work from
real life in a textbook
=Components,
functional elements,
Alphas
=Modules,
constructive elements,
work products
30. Project Essence Diagram: complexity of organization counts!
30
Engineering
management
Engineering
Technology
management
Using system
Technology management
and entrepreneurship
System of interest
Enabling system
31. 31
System life cycle practices drive alphas
http://arxiv.org/abs/1502.00121
Systems Engineering Essence
32. System and project life cycle (OMG Essence for systems engineering)
32
satisfied in use
represented
recognized
benefit accrued
Solution needed
viable
identified
used for
retirement
consisted
used for
operation
conceived
retired
parts
demonstrable
operational
closed
prepared
under control
concluded
initiated
formed
collaborating
seeded
foundation
established
in place
working well
principle
established
stakeholders opportunity
system
definition
system
realization
work team
way of
working
inception
development
deployment
испытания
manufacturing
retiredadjourned
ready
used for
verification
involved
satisfied for
deployment adressed
started
performingused for
production
raw materialsIn agreement
in usevalue
established
http://arxiv.org/abs/1502.00121
34. How to fight
development flow complexity?
Ideas sources:
• сomputer operating systems
• control engineering
• data communications networks
• finance and economics
• information theory
• maneuver warfare
• Manufacturing
• operations research
• probability and statistics
• queueing theory
According to Donald Reinertsen 34
35. Connectionism
• World is not symbolic! We need means to sense and process raw world
complexity!
• Non-symbolic models: distributed representations.
• Connectionism (e.g. deep learning): deal with informal implicit knowledge
processing.
• Since 2012 (GPU enabled)
35
NVIDIA® Jetson™ TX1
http://www.nvidia.com/object/embedded-systems.html
36. Avatarization of engineering software
• Learning of CAD and/or programming/configuration
• Natural language and/or programming language
• Human-computer dialog for justification of intents and constraints
• Joint human-computer idea generation and/or editing of ideas by
human
• Convenient dialog with software: avatar with name and image,
emotion recognition and usage
Company Virtual intelligent assistant
Google Google
Apple Siri
Microsoft Cortana
Facebook M
Amazon Alexa
Autodesk ???????????
36
37. 37
Thank you!
Anatoly Levenchuk,
TechInvestLab, president
INCOSE Russian chapter, research director
http://ailev.ru
ailev@asmp.msk.su
Book «Systems engineering thinking» (in Russian:
http://techinvestlab.ru/systems_engineering_thinking)