Summary: Introductio To Computational Complexity
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2 Finite state automata
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2.2 Deterministic finite automate (DFA's)
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DFA definition with the 5-tuple M
(Q, Σ, delta, q_0, F) -
Transition function (syntax)
Delta : Q x Σ → Q -
3 Turing machines
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3.3 A better approach to identfiy (even) palindromes
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Quadruatic (worst-case) runtime
Ntot = n^2/2 + 5n/2 scales q uadratically in the length n of bitstring to be processed --> iterative checking procedure -
3.4.5 History
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Who is Alan Turing (1912 - 1954)
An English mathematician and computer scientist --> father of both AI and theoretical copmuter sicence. -
4 Decision problems and languages
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4.1 Three points of view on computational challenges
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The most elementary building blocks of information
Symbols taken from an alphabet -
Two very important/usefull languages
The empty lanague, language of all strings -
3 ways to describe the same underlaying concept
Decision problems, boolean functions and languages -
6 Time-bounded computations
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Difference between computability and computational complexity
Computability focuses on what can be computed, while computational complexity studies the resources required for computation (how expensive) -
6.1 Motvation : multiplication vs factorization
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Gradeschool multiplication algortihm
Multiply each digit of the second number by each digit of the first number and then add the results. -
Factorization as cryptographic primitive
The key idea is that users create a public key based on two large prime numbers and an axiliary value that they publish The prime numbers are being kept a secret --> can only be decoded by someone who knows them
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