Strings, Languages, Automata
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Automata - Computability - Lecture Slide, Slides of Computer Science
Some concepts of Computability are Algorithmic Problems, Automata, Closure of Regular Languages, Computability, Free Languages, Machine Transforms, Magic Bullets, Minimization, Models of Computation, Nondeterministic Complexity. Important points in this lecture are: Automata, Languages,, Deterministic Finite Automata, Machine Dispenses, Dimes And Quarters, Correct Change, Java-Method Pseudocode, Over-Kill, Vending Machines, Possibilities Multiplicatively
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2012/2013
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Strings, Languages, Automata
Agenda
Today Strings Languages Deterministic Finite Automata For next time: Read up to 1. Check out ABCEZ in lecture 2-4 directory. HW 1
Vending Machine Example
Soda vend(){
int total = 0, coin; while (total != 45){ receive(coin); if ((coin==10 && total==40) ||(coin==25 && total>=25)) reject(coin); else total += coin; } return new Soda();
}
Vending Machine Example
Why was this over-kill?
Vending Machine Example
Vending Machine Example
Input: DQQD
About to put in a dime
Vending Machine Example
Input: DQQD
About to put in a quarter
Vending Machine Example
Input: DQQD
About to put in a dime
Vending Machine Example
What made this example simpler than the
Java pseudocode?
Vending Machine Example
1. Only needed two coin types “D” and
“Q” – symbols/letters in alphabet
2. Only needed 7 possible current total
amounts – states/nodes/vertices
3. Much cleaner and aesthetically
pleasing than Java lingo
Now generalize and abstractify…
Alphabets, Strings, Languages
A1: S = { D, Q }
A2:
Good: QDD, DQD, DDQ, QQQQDD, etc.
Bad: Q, D, DD, etc.
Ugly: DDD …now you’re screwed!
A3: e signifies trying to get something for
nothing (putting no money in at all).
Alphabets, Strings, Languages
DEF: The length of a string is the
number of symbols that it contains
(repetitions allowed).
Absolute values are used to denote
length.
EG: Lengths of the above good (QDD,
DQD, DDQ, QQQQDD) are: 3, 3, 3, 6
Q: What’s the length of e?
Alphabets, Strings, Languages
DEF: The concatenation of two strings is the
string resulting from putting them together
from left to right. Given strings u and v,
denote the concatenation by u v, or just
uv.
EG: ire land = ireland, QQ DD = QQDD,
DDD u is still bad, no-matter what u is!
Q1: Why the last claim?
Q2: What’s the Java equivalent of concatenation?