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decidability
XDict
可決定性; 可判定性
PyDict
可決定性; 可判定性
Taiwan
MOE
computer
dictionary
(
moecomp
)
decidability
半可決策性
The
Free
On
-
line
Dictionary
of
Computing
(
foldoc
)
A
property
of
sets
for
which
one
can
determine
whether
something
is
a
member
or
not
in
a
{
finite
}
number
of
computational
steps
.
Decidability
is
an
important
concept
in
{
computability
theory
}.
A
set
(
e
.
g
. "
all
numbers
with
a
5
in
them
")
is
said
to
be
"
decidable
"
if
I
can
write
a
program
(
usually
for
a
{
Turing
Machine
})
to
determine
whether
a
number
is
in
the
set
and
the
program
will
always
terminate
with
an
answer
YES
or
NO
after
a
finite
number
of
steps
.
Most
sets
you
can
describe
easily
are
decidable
,
but
there
are
infinitely
many
sets
so
most
sets
are
undecidable
,
assuming
any
finite
limit
on
the
size
(
number
of
instructions
or
number
of
states
)
of
our
programs
.
I
.
e
.
how
ever
big
you
allow
your
program
to
be
there
will
always
be
sets
which
need
a
bigger
program
to
decide
membership
.
One
example
of
an
undecidable
set
comes
from
the
{
halting
problem
}.
It
turns
out
that
you
can
encode
every
program
as
a
number
:
encode
every
symbol
in
the
program
as
a
number
(
001
,
002
, ...)
and
then
string
all
the
symbol
codes
together
.
Then
you
can
create
an
undecidable
set
by
defining
it
as
the
set
of
all
numbers
that
represent
a
program
that
terminates
in
a
finite
number
of
steps
.
A
set
can
also
be
"
semi
-
decidable
" -
there
is
an
{
algorithm
}
that
is
guaranteed
to
return
YES
if
the
number
is
in
the
set
,
but
if
the
number
is
not
in
the
set
,
it
may
either
return
NO
or
run
for
ever
.
The
{
halting
problem
}'
s
set
described
above
is
semi
-
decidable
.
You
decode
the
given
number
and
run
the
resulting
program
.
If
it
terminates
the
answer
is
YES
.
If
it
never
terminates
,
then
neither
will
the
decision
algorithm
.
(
1995
-
01
-
13
)
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