1. AUTOMATON, AND COMPUTATION?
Preliminaries
WHAT ARE
FORMAL LANGUAGE,
AUTOMATON, AND COMPUTATION?
・ History
・ Basic Terminology & Notations
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Preliminaries

2. History (1) Automata
A math model for the study of the network of nerves in the brain
W.S.Mculloch & W.Pitt
1943
Sequential circuit design
D.A.Huffman, G.H.Mealy, E.F.Moore
1950’s
“Automata Studies”
C.E.Shannon & J.McCarthy eds.
1956
Finite automata (S.C.Kleene)
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Preliminaries

3. History (2) Formal Grammars and Languages
A math model for studying linguistics qualitatively
Generative grammar
N.Chomsky
1950’s (1956, 1959)
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4. History (3) Algorithm 23 math problems by D.Hilbert
1900
Hilbert’s tenth problem
Definitions of algorithm
A.M.Turing: Turing machine
S.C.Kleene: Recursive function
A.Church:  definable function
E.L.Post: Post system
All in the year 1936
Church’s thesis
Algorithm = Turing machine
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5. History (4) Close Relations Among Them
Four types of formal grammars and their relation to automata
Finite automata  Regular sets
Pushdown automata  Context-free languages  BNF (ALGOL 60)
Linear bounded automata  Context-sensitive languages
Turing machines  Recursively enumerable sets
Phrase-structure Grammars = Turing machines
As definitions of algorithms
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6. History (5) And Then ··· Ａｐｐｌｉｃａｔｉｏｎs Computational Complexity Theory
Compiler design
Automatic translation of natural languages
And more
Computational Complexity Theory
Discovery of NP-complete problems
S.C.Cook, 1972
New models of computation
Quantum computation
D.Deutsch, 1985
DNA-based computation
T.Head, 1987; L.Adleman, 1994
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7. Basic Terminology & Notations
alphabet a finite set of symbols (letters)
Σ = {a1, …, an}
word over Σ
a finite sequence of symbols in Σ
length of a word
|a1a2…an| = n where each ai is in Σ
Both ε and λ denote the empty word
Σ* is the set of all words over Σ
language
a subset of Σ * for some alphabet Σ
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8. Operations on Words Concatenation (product) n-th power of a word w
associative: x•(y•z) = (x•y) •z
n-th power of a word w
w0 = ε, wn+1 = w•wn
reversal (mirror image)
(a1a2…an)R = an…a2a1 if each ai is in Σ
prefix, suffix, subword
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9. Operations on Languages
Let L, L’ be languages over Σ.
product L•L’ = {w•w’ | wL, w’L’}
n-th power L0 = {ε}, Ln = Ln-1•L if n>0
reversal LR = {wR | wL}
Kleene closure L* = n0Ln
positive closure L+ = n>0Ln
Abbreviations:
{w}*, {w}+  w*, w+
L•L’, w•w’  LL’, ww’
L{w}L’  LwL’
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10. Schedule and Textbooks
The schedule is subject to change according to the understanding of the course attendant
Jan
Feb
Mar
Formal Languages & Automata
Models of Computation
Complexity Theory
Recommended Textbooks
・ J.E.Hopcroft & J.D.Ullman, Introduction to Automata Theory, Languages, and Computation, 2nd ed, Addison-Wesley, 2000
・ D.C.Kozen, Automata and Computability, Springer, 1997
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