ANGLUIN'S ALGORITHM FOR LEARNING REGULAR SETS Ullas Aparanji - - PowerPoint PPT Presentation

▶
angluin s algorithm for learning regular sets
SMART_READER_LITE
LIVE PREVIEW

ANGLUIN'S ALGORITHM FOR LEARNING REGULAR SETS Ullas Aparanji - - PowerPoint PPT Presentation

Jan 23, 2023 153 likes •573 views

ANGLUIN'S ALGORITHM FOR LEARNING REGULAR SETS Ullas Aparanji DISCLAIMER The speaker takes no responsibility for any mental, psychological, emotional or spiritual mutilation or damage caused as a result of this talk. Construct a DFA to

slide-1
SLIDE 1

ANGLUIN'S ALGORITHM FOR LEARNING REGULAR SETS

Ullas Aparanji

slide-2
SLIDE 2

DISCLAIMER

  • The speaker takes no responsibility for any

mental, psychological, emotional or spiritual mutilation or damage caused as a result of this talk.

slide-3
SLIDE 3
slide-4
SLIDE 4

Construct a DFA to accept all strings

  • ver {a,b} which have an even

number of a's and an even number

  • f b's
slide-5
SLIDE 5

THE END

slide-6
SLIDE 6

L* Algorithm

  • Learns a DFA
  • Teacher
  • Oracle
  • Membership queries
  • Equivalence queries
  • Minimally Adequate Teacher
slide-7
SLIDE 7
slide-8
SLIDE 8

NOTATIONS

  • U: Unknown language to be learnt
  • A: Alphabet
slide-9
SLIDE 9

OBSERVATION TABLE

  • S: Non-empty finite prefix-closed set of strings
  • E: Non-empty finite suffix-closed set of strings
  • T: Mapping from finite set of strings to {0,1}
  • T(u) = 1 iff u belongs to U
slide-10
SLIDE 10

Which of these sets are prefix- closed?

  • {1110, 10, 1}
  • {011, 0, λ, 11, 01}
  • {110, 1, 0, λ, 11}
  • {0, λ, 10, 010}
slide-11
SLIDE 11

Which of these sets are suffix- closed?

  • {1110, 10, 1}
  • {011, 0, λ, 11, 01}
  • {110, 1, 0, λ, 11}
  • {0, λ, 10, 010}
slide-12
SLIDE 12
slide-13
SLIDE 13

OBSERVATION TABLE

  • Rows: Elements of S U S.A
  • Columns: Elements of E
  • Entry in row s and column e contains T(s.e)
  • Initially S = E = { λ }
  • row(s) denotes row of the table corresponding

to s

slide-14
SLIDE 14

What is row(a)? row(λ)?

slide-15
SLIDE 15

TWO CRUCIAL PROPERTIES

  • CLOSED: An observation table is closed if for

all t belonging to S.A, there exists an s belonging to S such that row(t) = row(s)

  • CONSISTENT: An observation table is

consistent if whenever s1, s2 (both belonging to S) satisfy row(s1) = row(s2), then for all a belonging to A, row(s1.a) = row(s2.a)

slide-16
SLIDE 16

Is this closed?

λ a aa aaa λ 1 a b 1

slide-17
SLIDE 17

Is this closed?

λ a λ 1 a 1 aa ab aaa 1 aab

slide-18
SLIDE 18

Is this closed?

λ a λ 1 a 1 1 aa ab aaa 1 aab

slide-19
SLIDE 19

Is this closed?

λ a λ 1 a aa ab aaa aab

slide-20
SLIDE 20

Is this consistent?

λ a aa aaa λ 1 a b 1

slide-21
SLIDE 21

Is this consistent?

λ a λ 1 a 1 aa ab aaa 1 aab

slide-22
SLIDE 22

Is this consistent?

λ a λ 1 a 1 1 aa ab aaa 1 aab

slide-23
SLIDE 23

Is this consistent?

λ a λ 1 a aa ab aaa aab

slide-24
SLIDE 24

Is this closed? Is it consistent?

slide-25
SLIDE 25

The DFA

  • Construct a DFA M(S, E, T) corresponding to

closed and consistent table.

  • Alphabet A
  • State set Q
  • Initial state q0
  • Accepting state set F
  • Transition function δ
slide-26
SLIDE 26
slide-27
SLIDE 27
slide-28
SLIDE 28
slide-29
SLIDE 29
slide-30
SLIDE 30
slide-31
SLIDE 31

Assume counterexample = bb

slide-32
SLIDE 32
slide-33
SLIDE 33
slide-34
SLIDE 34

Let counterexample = abb

slide-35
SLIDE 35
slide-36
SLIDE 36
slide-37
SLIDE 37
slide-38
SLIDE 38

Construct DFA that accepts all binary strings divisible by 3

slide-39
SLIDE 39

THE END

slide-40
SLIDE 40
  • Angluin, Dana. "Learning regular sets from

queries and counterexamples." Information and computation 75.2 (1987): 87-106.