RACSO
DFA
CFG
Operations:
Reg
,
CF
PDA
Reductions:
K
,
WP
,
CFG
,
NP
,
SAT
ANTLR:
lexical
,
syntactic
Exams
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Exercise 1
›
:
{
⟨
g
1
,
g
2
⟩
∈
C
F
G
(
{
a
,
b
}
)
2
∣
L
(
g
1
)
∩
L
(
g
2
)
≠
∅
}
≤
{
⟨
G
1
,
G
2
,
G
3
⟩
∣
L
(
G
1
)
∩
L
(
G
2
)
≠
∅
∧
L
(
G
1
)
∩
L
(
G
3
)
≠
∅
∧
L
(
G
2
)
∩
L
(
G
3
)
≠
∅
}
\{\langle g_1,g_2\rangle\in\mathtt{CFG}(\{a,b\})^2\mid\mathcal{L}(g_1)\cap\mathcal{L}(g_2)\neq\emptyset\}\quad\leq\quad\{\langle G_1,G_2,G_3\rangle\mid\mathcal{L}(G_1)\cap\mathcal{L}(G_2)\neq\emptyset\;\wedge\;\mathcal{L}(G_1)\cap\mathcal{L}(G_3)\neq\emptyset\;\wedge\;\mathcal{L}(G_2)\cap\mathcal{L}(G_3)\neq\emptyset\}
{⟨
g
1
,
g
2
⟩
∈
CFG
({
a
,
b
}
)
2
∣
L
(
g
1
)
∩
L
(
g
2
)
=
∅
}
≤
{⟨
G
1
,
G
2
,
G
3
⟩
∣
L
(
G
1
)
∩
L
(
G
2
)
=
∅
∧
L
(
G
1
)
∩
L
(
G
3
)
=
∅
∧
L
(
G
2
)
∩
L
(
G
3
)
=
∅
}
Reduce the non-empty intersection problem on CFGs over
{
a
,
b
}
\{a,b\}
{
a
,
b
}
to the set of tuples of three CFGs such that each pair of such three CFGs have non-empty intersection, in order to prove that such set is undecidable (not recursive).
Authors:
Guillem Godoy /
Documentation:
input g1,g2 { // Write your reduction here... // output ... , ... , ... ; }
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