RECAP

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RECAP

• CSE 318

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Final Exam

• Cumulative
• Regular languages, automata 20
• Context-free languages, pushdown automata 20
• Turing machines, decidable, recognizable,
  nondecidable languages 40
• (remaining 20 flexibility)

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Two Key Questions

• What is computation?
• Non-deterministic computation
• What kinds of problems we can solve with
  computation?
• limits of computation

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Computation
trans1
trans2
transn
conf1
conf2
.
confn
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Examples
Finite automata
(q,0,p)
(p,0,f)
(s,1,q)
(s,100)
(f,e)
(p,0)
(q,00)
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Nondetermistic Computation

• Theoretical (i.e., artificial) construct that
  facilitates
• Proving properties of computation
• Writing algorithms in a simplified form

trans1
conf2
conf1
Trans1
Conf2
.
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Configuration
A configuration indicate the current state of the
computation
Configuration
Machine
Finite automata
Pushdown automata
Turing machines
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Transitions
A transition indicates how the configurations are
transformed
Transition
Machine
Finite automata
(state, symbol, state)
Pushdown automata
((state, symbol, pop), (state,push))
Turing machines
((state, symbol, symbol), (state, ?/?))
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Notion of Acceptance
Acceptance indicates what kinds of configurations
are considered successful computations
Configuration
Machine
Acceptance if
f accepting state, w e
(f,w)
Finite automata
f accepting state, w e
Pushdown automata
(f,w,?)
f accepting state
(f, w)
Turing machines
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Machines versus Classes of Languages
Machine
Expressiveness Finite Automata
Pushdown Automata Turing Machines
Regular Languages
Context-free Languages
Decidable languages
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Machine vs. n-stack NFA
Machine
n-stack NFA Finite Automata Pushdown
Automata Turing Machines
NFA 0 stacks
NFA 1 stack
NFA 2 stacks
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Computation and Countability

• Surprisingly deep connection
• If a language L can be enumerated then it is
  recognizable
• To recognize if w is in L
• Print next string in L
• If w w then accept
• else goto 1
• And the other way around!

w
Enumerator of L
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Problems that Can be Solved with Computation
Church-Turing Thesis
Algorithms Turing machines
Therefore, C, C, Prolog, Lisp, Small talk, and
Java programs can be simulated byTuring machines
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Classes of Languages
(HALT)
Turing machines Pushdown Automata Finite
Automata
(ww w ??)
(Palindrome)
Regular languages
(ab)