4
EF v.s. Pebble Games
•
Ehrenfeucht-Fraisse:
•
k pebbles
•
k rounds
•
•
Main Theorem:
•
Duplicator wins (A,B)
iff A, B agree on all
formulas in FO[k]
•
Pebble games
•
k pebbles
•
n (or
w
) rounds
•
•
Main Theorem
•
Duplicator wins for n
(or
w
) rounds iff A, B
agree on all L
w
1
,
w
[n]
(or L
k
1
,
w
) formulas