CYBER RESILIENCE, TRANSPARENCY
AND MONOTONICITY UNDER ZERO-TRUST

Hideto Tomabechi drtomabechi@me.com
George Mason University* and Carnegie Mellon University***Visiting Professor, C4I and Cyber Center**Adjunct Fellow, CyLabCognitive Research Laboratories

My brief background in Computer Science areas
1985 - 1987
Yale CS, AI Lab and CogSci Proj. AI and Massively Parallel Processing
1987 - 1993
SCS, RI, CMT, LCL, Carnegie Mellon. AI, NLP, Computational Linguistics
1993 - 1998
Tokushima Univ. and Justsystems. Monotonicity and Intelligence1998 – 2014Japanese government projects, AI, Architectures, Cyber Security2008 - current
Adjunct Fellow, CyLab, Carnegie Mellon University
2014 - 2019/3
Independent Advisor to Chief of Joint Staff, Admiral Kawano, JSDF
and liaison for CMU
2GEORGE MASON UNIVERSITY

Introduction of Concepts:
Cyber- You are experts. I spare explanations.
Resilience- I spare explanations. Please ask Dr. Wells
Transparency and Monotonicity- Basic paradigm under zero-trust and quantum.

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Transparency - from Crypt-Currency experiences
Nontransparent Off-Chain Exchanges- Chinese and Japanese Exchanges
Cryptocurrency stolen
from Japanese off-chain exchanges in 2018
・500 mil USD equivalent of NEM stolenfrom(UN says by North Koreans)
・50 mil USD equivalent of Bitcoin stolen from

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Transparency vs Non-transparency in Crypto Blockchain
Crypt is a misunderstood word. "Thou shalt not encrypt".
- We hash, not encrypt- Private vs Public- Sovereign vs Public
Current resilience of blockchain comes from transparency

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What is Monotonicity
Amount of information only increases never decreases
Nakamoto type Blockchain is pseudo monotonic(using hash and digital signature)
Purely monotonic linear time algorithms exist(e.g. Tomabechi 90&91)

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Why is Monotonicity Essential for Resilient Architecture
Like accounting books, modifications are always added.
No deletion allowed.
Naturally, traces of all modifications are preserved
at data structure level
All modifications are non-destructive
and original data is recovered constant/linear time

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Some of my Monotonicity Projects
Old- mid 90's Bechi Unit atMid- 1998 -2004 Japanese government projects
for "Bullet Proof" servers
New- Crypto Asset Central Bank Foundation,advising some governments8GEORGE MASON UNIVERSITY

Monotonicity and Layered Transparency
Basic data structure for quantum proof
next generation computer architecture
Linear time monotonic algorithms
and embedded layered access models
Different levels of exposure,e.g. to law enforcement, medical, tax agency, etc.

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Still fastest -- Linear-Time Monotonic Algorithms(Tomabechi Algorithms)
Quasi-Destructive Graph Unification (Tomabechi 1990)
Quasi-Destructive Graph Unification with Structure Sharing(Tomabechi 1991)
Both are contained in my 1993 CMU Ph.D. Thesis(readable online, 🔍 "Tomabechi Ph.D Thesis")
http://maxpec.net/amazoncampaign_present/Dr_Tomabechi_treatise.pdf

Used in NLP grammar in 90s, now usable as basic datastructure (100 million times fast CPUs)
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What is Feature Structures
Set of labels and values[[label1 value1][label2 value2]]
Value can be embedded feature structures[[label1 value1][label2 [[label3 value3][label4 value4]]]
Value can be contradiction (Bottom ) or variable (Top [ ])[[label1 value1][label2 Bottom][label3 [ ]]]11GEORGE MASON UNIVERSITY

Feature Structures as Set-Theoretic Partial Functions
Everything in Universe (including concepts) are represented
as partial functions

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Combining East with WestTop “emptiness” （空）Bottom contradiction
http://tomabechi.jp/
EmptinessDrTomabechi.pdf
or🔍 "Tomabechi emptiness”

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Feature Structure as Graph Theoretic Directed Graph

Representing a third person singular feminine noun entity
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GEORGE MASON UNIVERSITYReentrant feature structure
Non-reentrant（Tokyo maybe referring to different Tokyo）[[born Tokyo][home Tokyo]]
Reentrant feature structure（Tokyo referring to same Tokyo）[[born X01 Tokyo][home X01]]
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GEORGE MASON UNIVERSITYReentrant feature structure in graph notation

Non-reentrant feature structure

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Reentrant feature structure

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A reentrant structure graph with a complex value
Using common notation found in linguistic literature

In bracketed notation

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Feature structure with cycle (directed graph with a cycle)
Example of actual English grammar rules ( using path equation notation )18

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Graph Unification on Feature Structure GraphMonotonicEfficient detection of contradictions
Non-destructive efficient data structure building

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Unification as purely monotonic operation
Simple Example of unification two graphs

abXc

Y

Zab
X

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Yc
Z
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Unification as purely monotonic operation
Simple Example of unification two graphs

ab
X

b

Y[ ]abX

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Y
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Unification with failure
Simple Example of unification two graphs

ab
X

Yb
Z

⊥ Contradiction
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Unification resulting in a cycle

Unification algorithm should not result in infinite loop even with acyclic graph input
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True monotonicity at data structure and algorithmic level
Blockchain is a pseudo monotonic
with hashing and signature
Non-Destructive Graph Unification isa true monotonic algorithm

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Unification as monotonic algorithm
1. Algorithmic guarantee of monotonicity
2. Very fast detection of contradiction
3. Non-destructive result building
4. Very efficient (linear time) complex structure building

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Monotonicity in Near Future Computations - Applicational
Under zero-trust paradigm,
we assume encryption/hashing do not work.
Resilience is achieved if monotonicity is assured.
Efficient detection andconstant/linear time (at least log N) original recovery.

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Monotonicity in Near Future Computations- Architectural (for quantum resilience)
Even linear time algorithms requirevery fast CPU for low level monotonicity
Machines are 100 million times faster than 1990
(invention of linear time algorithms)
Current CPUs allow for low level monotonic data structures
at O/S level→ My current research includes design of entire computerand network with monotonicity
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Preferred direction for monotonicity
All basic data structure for computation and network
must be monotonic
Must be embedded in low level data structure
in future operation systems
Dedicated monotonicity chips by micro code unificationor through next generation material engineering

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