On the nature and
future of
ToC
ToC
Avi Wigderson
Institute for Advanced Study
‫המקדש ניתנה הנבואה לשוטים‬-‫מיום שחרב בית‬
Since the destruction of the Temple prophecy was given to fools
Det er vanskeligt at spaa, især naar det gælder Fremtiden
It is difficult to make predictions, especially about the future
About my 2 cents
40 years in the field: my views evolved
Not so much… past plenaries:
Depth through Breadth STOC ’04
The art of Reduction
FCRC ‘07
Position paper with Oded Goldreich:
ToC: a scientific perspective ‘96
- The arguments got far stronger
- The world is changing much faster
Computer
Science
Independent
major
academic
discipline
Mathematics
Statistics
Social
Science
Theory of
Computation
Optimization
Biology
Economics
Information
& Coding
Physics
Computer
Science
Mathematics
Statistics
Social
Science
Optimization
Biology
Economics
Information
& Coding
Physics
Ptolemy's geocentric model
Transportation
Emotions
Medicine
Food
ML
Decisions
Technology
Law
Science
Recreation
Medicine
Transportation
Emotions
Food
Computer
Science
ML
& Technology
Decisions
Technology
Law
Science
Recreation
Medicine
transportation
Emotions
Food
Computer
Science
& Technology
Decisions
Technology
Law
Science
recreation
Transportation
Medicine
Emotions
Food
Computer
Science
Science
&
Technology
Decisions
Technology
Law
Science
Recreation
Computer
Science
Mathematics
Statistics
Social
Science
Theory of
Computation
Optimization
Biology
Economics
Information
& Coding
Physics
Computer
Science
Mathematics
Statistics
Social
Science
Must grow!
ToC
Optimization
Biology
Economics
Information
& Coding
Physics
Proof by exhaustion:
Laundry lists
Beginnings:
The dual life of ToC
CS&E
MATH
Young
Impatient
Old
Patient
Practice
Utility
Study computer
systems!
Modeling
challenges
ToC
Aesthetics
Abstraction
Rigorously!
Freely!
Complexity
zoo
ToC & CS: Great theories
-
Turing machine (toc  cs)
Cellular automata (life, replication, tolerance)
Automata (Non-deterministic,Probabilistic)
Formal languages (programming, compilation)
Verification (model def & checking)
Data bases (relational, hierarchical,…)
Complexity (NP, completeness, reductions)
Efficient algs & data structures
Cryptography (Internet, e-commerce)
Distributed sytems (asynchrony, atomicity)
Randomness (algs, PRGs, weak sources)
Learning (Perceptrons, PAC,…)
ToC & CS: great theories
- Turing machine (toc  cs)
Automata (Non-deterministic,Probabilistic)
Cellular automata (life, replication, tolerance)
Formal languages (programming, compilation)
Verificaion (model def & checking)
Data bases (relational, …)
Complexity (NP, completeness, reductions)
Efficient algs & data structures
Cryptography (Internet, e-commerce)
Distributed sytems (asynchrony, atomicity)
Randomness (algs, PRGs, weak sources)
Learning (Perceptrons, PAC,…)
-
Parallel algs (NC, networks)
Space comp. (NL=coNL, SL=L,…)
Networks (Sorting, comm, expanders,…)
Quantum computing (crypto,info,physics)
Online algs (competitive analysis)
Approx algs (PCP, hardness, hierarchies,…)
Sublinear algs (Property testing, local decoding)
Differential Privacy (Adaptive science,…)
Learn Why & How these theories developed
Turing Award for ToC work
-
Turing machine
Cellular Automata
Automata
Formal languages
Verificaion
Data bases
Complexity
Algorithms
Cryptography
Randomness
Distributed systems
Learning
Crypto revolutions
Mind games!
- Public-key crypto
Predated
- RSA
& enabled
- Formal foundations
the Internet
- Zero Knowledge proof for every theorem
& e-commerce
- Oblivious computation for every function
- Completeness theorems for protocols
- Universal composability (Internet setting)
- Constant-depth crypto
- Non-Black-Box crypto
- PIR/Delegation (interactive proofs for clouds)
- Homomorphic encryption
- Indistinguishability Obfuscation (?)
Circuit comp, Learning, Pseudorandomnes,PCP,……
Other ZK appearances
Physical ZK proofs:
- Child education
- Nuclear disarmament
- Anonymous DNA testing
Practical ZK proofs:
- Anonymous cash: Bitcoin, Z-cash,…
- Public ledgers …
Science- Quantum SZK proofs:
- Black-hole firewall paradox,…
ToC & Math
Logic
Users
Collaborators
Suppliers
Combinatorics
Theory of
Computation
Algebra
Number
theory
Geometry
Lattice
theory
Algebraic
Geometry
Analysis
-
ToC  Math
Isoperimetric inequalities
Stability (inverse) theorems
Metric embeddings
Explicit constructions
Structure vs. randomness thms
Exponential sum estimates
(Un)Definability results
Statistical sample bounds
Lots of new questions & collaborations
with practically all math areas!
An integral part of understanding computation!
Two recent breakthroughs
Kadison-Singer (open 65 years)
Linear solvers, spectral sparsifiers,
Insistence on prob O(nlogn)  det O(n)
Hyperbolic polynomials, approx permanent
Free probability, Electrical networks,…
Explicit Ramsey graphs (open 70 years)
Voting, influence, pseudorandomness,
circuit complexity, extractors, finding
entropy, sum-product theorem,…
Two more
Efficient characterization of primes (200 y)
Taylor-made prob alg, derandomization,
polynomials, PIT, number theory estimates
Reverse Minkowaski inequality (100 years)
Lattices, Integer programming, Additive
combinatorics, Convex geometry, Crypto,
Brownian motion,…
Two more
First-order variable hierarchy strict (20yrs)
Constant depth circuits, random
restrictions, sensitivity, cliques in G(n,p)
Operator scaling algorithm (20 years)
PIT, matrix scaling, perfect matching, non
commutative fields, commutative invariant
theory, quantum information theory,
Brascamp-Lieb ineuqalities,…
Million $$ questions
(7 Clay millennium problems)
The Riemann hypothesis (150 years)
About pseudorandom walks
Navier-Stokes equations (250 years)
About Turing universality of water (?)
P=NP? (50 years)
Also about computational complexity
Nearby fields
Foundational discoveries
Use interactivity of ToC
Optimization
(ORSA/TIMS 3000 attn.)
PCP thm (prog testing, game th, coding th)
Harness of approx (analysis Bool fns, long/
short codes, univ approx algs, dichotomies)
LP/SDP hierarchies (rand rest, Fourier,…)
Extended formulations (exp. lower bds!
non-negative rank, quantum comm. Comp.)
Continuous algs flows, spectral, descents
interior pt, ellipsoid, scaling,…
Algorithmic Game Theory Opt. aspects of
auctions, mechanism design, equilibria,…
Coding Theory
(ISIT 700 attn)
Local decoding (PCP, hardness, prog/prop
testing, geometry, Kakeya, PIT, alg comp)
List decoding (Optimal bounds! ECCs,
Crypto, extractors, PCPs,…)
LDCP (linear time enc/dec! expanders,
Tornado, Fountain, belief propagation,…)
RS/RM/BCH (Wt. enumeration, capacity
achieving, influence, threshold, add. comb )
Information Theory
Statistics
Numerical analysis
Control theory
………
Natural & Social
Sciences
Computation
Church-Turing Thesis
ToC Methodology!
Turing machine can emulate any computation!
info process:
Computation: every evolution by a
sequence of simple, local steps, of
bits in computers
computers in a network
neurons in the brain atoms in matter
cells in living tissue
bacteria in Petri dish
prices in a market
individuals in populations
deductions in a proof proteins in a cell
qbits in entanglement friends on Facebook…
Understanding Computation
great challenge &
responsibility
Models
Algorithms
ToC Methodology!
Resources
Efficiency
Computation: every evolution by a
Upper bds
sequence of simple, local steps, of
Lower bds
Reductions
Completeness
bits
in computersQuantum
computers in a network
Abstraction
neurons in the brain atoms in matter
Play
cells in living tissue
bacteria in Petri dish
prices in a market
individuals in populations
hyperboli
deductions in a proof proteins in ac cell
ToC  Sciences
Scientific revolution: fundamental, new
- Questions
- Methodology
- Definitions
- Principles
- Results
- Connections
- Insights
- Standards …
Sciences are conservative! (decades-centuries)
Heliocentric model, Evolution, Bacteria, General
Relativity, Quantum mechanics, Quasi-periodic
crystals…
Early Successes:
NP-completeness 1000s of papers, by scientists,
in science journals!
“P  NP” as a law of nature: Intractability as a
modeling guide, like 2nd law of thermodynamics
Biology
Morphogenesis, Self-Replication, Tolerance
Genome, Comput. biology, Phylogenetics
Natural algs / Influence systems
Neurobiology: Circuits of the Mind,…
Evolution as (a learning) algorithm
Sex is an algorithm
Initial, Formal, Predictive !
Physics
ToC & Stat Phys
1-dim Cellular Automata with eternal memory
under constant noise rate
MCMC rigorous analysis, conductance, expanders,
approximating the permanent,…
Spatial & temporal equivalences of Statistical
Physics systems
Threshold phenomena (spin, K-sat) rigorous!
(PCP, Approximation, Game Theory, Stability in
Comb., Message passing, Belief prop, Coding Th)
Quantum mechanics
Factoring algorithm  Billions of $$
Fundamental questions about QM
BQP = Adiabatic
Recent stuff I heard
at IAS Physics talks:
Hamiltonian dynamics, completeness
- Circuits
- Quantum circuits
Area Law & entanglement - P, NP, BQP, SZK
- Quantum state
Black hole firewall paradox complexity?
AdS/CFT correspondence
Do these belong in
Quantum
Economics
Complexity of equilibria (hardness)
Algorithmic Game Theory (& optimization)
Auctions, Mechanism design
Price of anarchy
2008 crash (information asymmetry
arising from computational intractability)
Social Sciences
Six degrees of separation
Markets, crowds and networks
Internet, WWW, Social, Financial nets
Processes in nets
(epidemics, gossip, influence,…)
Dynamics of nets
(growth, individual, aggregate…)
Differential privacy
(policy, law, health…)
Philosophy
collusion
coordination
conflict
creativity
entropy
equilibrium
evolution
game
induction
intelligence
interaction
lnowledge
language
learning
Novel, formal
ontology
prediction meanings & uses
privacy
-Add comp comp
process
-Stir well
proof
randomness -Put in oven
secret
simultaneity
strategy
synchrony
truth
verification
What our small community has achieved
in a short period is comparable to the
greatest scientific revolutions of all time!
What went right?
What has changed?
How should we act?
Our
Our
Our
Our
science & mission
community
education
politics
What kind of science is ToC?
Mathematical?
Technological?
Natural?
Social?
Experimantal?
Philosophical?
(all answers correct)
Independent academic discipline!
Mission: understand computation in all forms
Computer
Science
Mathematics
Statistics
Social
Science
Must grow!
Must grow-up!
ToC
Optimization
Biology
Economics
Information
& Coding
Physics
We have grown, organically
Mathematics
Computer
Science
Statistics
Logic
AGT
Learning
Crypto
Theoretical
Core ToC
Theoretical
Computer
Comp.
Comp.
Computer
Science
Structure,
Insights,
Science
Interconnectivity,…
Quantum
Computing
Economics
Randomnes
s
Communication
Complexity
Property
testing
Verification
Social
Science
Distributed
Lower
bounds
Biology
Physics
Must preserve common goals, language, confs,…
Community: Culture & People
-
key to past+future success
Open-minded
Collegial
Democratic
Driven
Diverse
Cohesive
Online dating profile examples
Educational
Agile
Smart
Chair Dean/Funding/ ask:
- Self confidence ?
- Is your work practical?
- Does it explain reality?
Answer: My science is!
Education,
confidence & independence
College: ToC major! Teach our science and
its history, as happened, in full glory, e.g.
Algs 101
Complexity/logic 101
Algs@science 101
Data reps
Modeling principles
Modeling principles
Graph algs
Circuit comp
Comp & math
Approx algs
Communication comp
Comp & biology
Parallel algs
Crypto
Comp & physics
Dist algs
Learning
Comp & economics
Prob algs
Semantics
Comp & Soc. Sci
Sublinear algs Verification
Comp & Philosophy
Heuristics
Formal languages
……
Interactive, cross-fertilizing ideas across all I,II,III,…
Great achievements by other sciences I,II,III,…
Education: Basic knowledge
K-12, teaching colleges: ToC principles
Save CS ed. from programming-oriented ed
- Write books
- Design curricula
- Give popular lectures
“Computers cannot solve every problem!”
“Algs create industries & cure disease”
“Turing = Einstein, but far more influential”
“Mult harder than Add? Prove it!”
“World economy rests on comp. assumption”
Politics (growing-up)
CATCS: ToC growth & health requires
(besides great research!!), also
funding, positions, education, advocacy…
Education: PR, popular lectures, papers
Advocacy: Congress, NSF, universities
Service: Chairs, deans, NSF officers,…
Do what you do best!
Internal competition* on resources:
Do what you like best and promote it!
*Vast resources flow to CS
Thank you!