Deterministic Finite State Acceptors

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Deterministic Finite State Acceptors

• Reading 2.1

2
Automata
Input Tape
a b b a
a b
Tape Head (moves -gt)
Current State
0 1
3
Features of Automata

• May or may not have a storage mechanism
• Control Unit tells current state
• Transition function governs current state
• One transition is a move
• Can be transducers or accepters
• Can be deterministic or non-deterministic

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Formal Notation

• Automaton A Q,S, q0, F, d
• Q is finite set of states
• S is tape alphabet
• q0 is initial state
• F is a subset of Q, set of final states
• d Transition function
• d QX S Q

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DFAs

• Type of automaton
• Deterministic No probability involved
• Finite Refers to the number of states, not the
  language it represents
• Accepter At end, output is yes or no only

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Transition Graphs
0
0
1
0
q2
q1
qo
1
1
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The Transition Function

• d Q X S -gt Q
• Table notation or function notation
• Many paths followed d
• For word w and letter a,
• d(q,wa) d(d(q,w),a) d(q, ?) q
• From previous example,
• - d(qo,1)
• - d(q0,100)

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Trap States

• Slightly altered automaton
• What is d(q0,110)?
• Transition not defined goes to invisible trap
  state - not accepted, no way out

0
1
0
q2
q1
qo
1
1
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Languages and DFAs

• DFAs define a language
• Deterministic one outarc for every member of
  the input alphabet
• Regular Language Language accepted by a DFA.

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Write DFAs that accept

• All strings on a,b that start with abba
• L w ? a,b w mod 3 0
• All strings on a,b that have less than three
  as
• L ab2wb3 w ? a,b
• All strings on a,b that contain abba
• All strings on a,b with an even number of as.