3
Proof:
LFP = PTIME
LFP + <
΅
PTIME
[why ?]
To show
PTIME
΅
LFP + <
Let M = (Q,
S
,
D
,
d
, q
0
, Q
a
, Q
r
) be a PTIME
Turing machine
Input: Enc(
A
) = 01
n
Enc(R
1
A
) Enc(R
m
A
)
Output: accept or reject
Need: formula
f
s.t.
A
²
f
iff T accepts
A