RACSO
DFA
CFG
Operations:
Reg
,
CF
PDA
Reductions:
K
,
WP
,
CFG
,
NP
,
SAT
ANTLR:
lexical
,
syntactic
Exams
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Exercise
‹
20
›
:
{
g
∈
C
F
G
(
{
a
,
b
}
)
∣
L
(
g
)
=
{
a
,
b
}
∗
}
≤
{
G
∣
L
(
G
)
=
{
w
∈
{
a
,
b
}
∗
:
∣
w
∣
a
a
≥
1
}
}
\{g\in\mathtt{CFG}(\{a,b\})\mid\mathcal{L}(g)=\{a,b\}^*\}\quad\leq\quad\{G\mid\mathcal{L}(G)=\{w\in\{a,b\}^* : |w|_{aa}\geq 1\}\}
{
g
∈
CFG
({
a
,
b
})
∣
L
(
g
)
=
{
a
,
b
}
∗
}
≤
{
G
∣
L
(
G
)
=
{
w
∈
{
a
,
b
}
∗
:
∣
w
∣
aa
≥
1
}}
Reduce the universality problem on CFGs over
{
a
,
b
}
\{a,b\}
{
a
,
b
}
to the problem of whether a CFG generates all words over
{
a
,
b
}
\{a,b\}
{
a
,
b
}
with at least one occurrence of
a
a
aa
aa
, in order to prove that such problem is not semi-decidable (not recursively enumerable).
Authors:
Carles Creus, Guillem Godoy /
Documentation:
input g { // Write your reduction here... // output ... ; }
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