cs3102: Theory of Computation Class 7: Context-Free Languages Spring 2010 University of Virginia David Evans Menu • Nondeterministic PDAs • Reviewing Machine Models of Computing • Linguistic Models of Computing DPDA Recap: DFA/ε + Stack ε q 1 q 2 a, ε → + b, + → ε q 0 b, + → ε ε, ε → $ q 3 ε, $ → ε Processing: aabb State Stack q 0 Input aabb $ q 1 aabb +$ q 1 aabb ++$ q 1 aabb +$ q 2 aabb $ q 2 aabb ε q 3 aabb ε, $ → ε Adding Nondeterminism DFA NFA a a a Regular Languages Regular Languages Configuration: one state Configuration: set of states What does it mean to add nondeterminism to a DPDA? Adding Nondeterminism to DPDA DPDA NPDA a, h p → h t Languages recognized: ? Configuration: one state + one stack a, h p → h t a, h p → h t Adding Nondeterminism to DPDA DPDA NPDA a, h p → h t Languages recognized: ? Configuration: one state + one stack a, h p → h t a, h p → h t Languages recognized: ? + ? Configuration: set of <state, stack> pairs
7
Embed
Class 7: Context-Free Languages - Computer Scienceevans/cs3102-s10/classes/class7/class7.pdf · Class 7: Context-Free Languages Spring 2010 University of Virginia David Evans Menu
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
cs3102: Theory of Computation
Class 7:
Context-Free Languages
Spring 2010
University of Virginia
David Evans
Menu
• Nondeterministic PDAs
• Reviewing Machine Models of Computing
• Linguistic Models of Computing
DPDA Recap: DFA/ε + Stack
ε
q1 q2
a, ε→ +
b, +→ ε
q0b, +→ ε
ε, ε→ $
q3
ε, $ → ε
Processing: aabb
State
Stack
q0
Input aabb
$
q1
aabb
+$
q1
aabb
++$
q1
aabb
+$
q2
aabb
$
q2
aabb
ε
q3
aabb
ε, $ → ε
Adding Nondeterminism
DFA NFA
aa
a
Regular Languages Regular Languages
Configuration: one state Configuration: set of states
What does it mean to add nondeterminism to a DPDA?