CSCI-2400 - PowerPoint PPT Presentation

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CSCI-2400

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Defined over an alphabet: Alphabets and Strings We will use small alphabets: Strings String Operations String Length Length: Examples: Length ... – PowerPoint PPT presentation

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Title: CSCI-2400


1
CSCI-2400 Models of Computation
2
Computation
memory
CPU
3
temporary memory
input memory
CPU
output memory
Program memory
4
Example
temporary memory
input memory
CPU
output memory
Program memory
compute
compute
5
temporary memory
input memory
CPU
output memory
Program memory
compute
compute
6
temporary memory
input memory
CPU
output memory
Program memory
compute
compute
7
temporary memory
input memory
CPU
Program memory
output memory
compute
compute
8
Automaton
temporary memory
Automaton
input memory
CPU
output memory
Program memory
9
Different Kinds of Automata
  • Automata are distinguished by the temporary
    memory
  • Finite Automata no temporary memory
  • Pushdown Automata stack
  • Turing Machines random access memory

10
Finite Automaton
temporary memory
input memory
Finite Automaton
output memory
Example Vending Machines
(small computing power)
11
Pushdown Automaton
Stack
Push, Pop
input memory
Pushdown Automaton
output memory
Example Compilers for Programming Languages
(medium computing power)
12
Turing Machine
Random Access Memory
input memory
Turing Machine
output memory
Examples Any Algorithm
(highest computing power)
13
Power of Automata
Finite Automata
Pushdown Automata
Turing Machine
Less power
More power
Solve more computational problems
14
Languages
15
  • A language is a set of strings
  • String A sequence of letters
  • Examples cat, dog, house,
  • Defined over an alphabet

16
Alphabets and Strings
  • We will use small alphabets
  • Strings

17
String Operations
Concatenation
18
Reverse
19
String Length
  • Length
  • Examples

20
Length of Concatenation
  • Example

21
Empty String
  • A string with no letters
  • Observations

22
Substring
  • Substring of string
  • a subsequence of consecutive characters
  • String
    Substring

23
Prefix and Suffix
  • Prefixes Suffixes

prefix
suffix
24
Another Operation
  • Example
  • Definition

25
The Operation
  • the set of all possible strings from
  • alphabet

26
The Operation
the set of all possible strings from
alphabet except
27
Languages
  • A language is any subset of
  • Example
  • Languages

28
Note that
Sets
Set size
Set size
String length
29
Another Example
  • An infinite language

30
Operations on Languages
  • The usual set operations
  • Complement

31
Reverse
  • Definition
  • Examples

32
Concatenation
  • Definition
  • Example

33
Another Operation
  • Definition
  • Special case

34
More Examples

35
Star-Closure (Kleene )
  • Definition
  • Example

36
Positive Closure
  • Definition
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