Database Reference
In-Depth Information
By convention, each turn-on/turn-off of the M UC determines a corresponding
turn-on/turn-off of the RDB machine M RC .
Let us now introduce the operator of concurrent (“parallel”, that is, time-shared)
composition of application programs P
P( 2 )
(where P( 2 ) is obtained from P( 2 ) by incrementing each address in its instructions
by the integer N +
=
P( 1 )
|
P( 2 ) such that P
=
P( 1 )
1, where N is the biggest address in P( 1 ) ), in the time-shared
mode of the concurrent multiple-user universal machine M UC , by the following
definition:
Definition 45
A concurrent execution of a program P
=
P( 1 )
|···|
P(n) on a ma-
chine M UC is a computation system CS
=
(TrS, In S , Out S , Stop S ) , where TrS
=
(S PU ,
P ) is a deterministic transition system with:
1. The set of configurations (obtained during the concurrent execution of programs):
S PU ={
(i, st, ID T )
|
i is the address of some instruction of the program P(m)
=
Pr(ID T ), 1
m n, executed during the transaction ID T
1 , st
S U is the
state of M UC before the execution of this i th instruction
}
.
P is a function defined for any time-shared window during the execu-
tion of a program P(m) in the state st
2. The
S U such that there is a transaction ID T
with Pr(ID T )
=
P(m) (if P(m) /
∈{
Pr(i)
|
1
i
K
}
,for K
=
min
{
k
1
|∀
j
k, Pr(j)
, then in this time-window the execution of this program P(m)
just begins and we set Pr(K)
=
P
}
=
P(m) and ID T =
K ), as follows:
2.1. ((i, st, ID T ),(j,λIn EU (z)(st), ID T ))
∈→ P if (i, In EU ,j)
Pr(ID T ) is ex-
ecuted in this time-window, where z
INP is the input value taken by M UC
in this current state st
S U and λ is the abstraction operator (currying) of
λ -calculus such that λIn EU (z)(st)
I EU (z, st) .
=
∈→ P ,if (i,f,j)
2.2. ((i, st, ID T ),(j,f (st), ID T ))
Pr(ID T ) is executed in
this time-window and f/
.
If there is no instruction with the address j (we reached the end of
this program) then ((j,f (st), ID T ),(j,f (st), ID T ))
∈{
COMMIT , ROLLBACK
}
∈→ P , and this time-
window is closed by imposing Pr(ID T )
=
P
.
2.3.
(i, st, ID T ), j,f(st), ID T ∈→ P
j,f(st),ID T , k,Out U f(st) ,ID T ∈→ P ,
if (i,f,j),(j, Out U ,k)
Pr(ID T ) are executed in this time-window and
f
∈{
COMMIT , ROLLBACK
}
. Set Pr(K)
=
Pr(ID T ) with K
=
min
{
k
1
|∀
j
k, Pr(j)
=
P }
, and after that set Pr(ID T )
=
P and ID T =
K .
2.4. ((i, st, ID T ),(j, st, ID T ))
∈→ P ,if (i,t,j,k)
Pr(ID T ) is executed in this
time-window and t(sk)
=
1,
2.5. ((i, st, ID T ),(k, st, ID T ))
∈→ P ,if (i,t,j,k)
Pr(ID T ) is executed in this
time-window and t(sk) =
0.
3. In S (x) = ( 0 , In U (x), 1 ) .
4. Out S (i, st, ID T )
=
Out U (st) .
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