![](bga.png)
C or I.
Propagation: From C (, or I), it is only possible to
perform CD (, or IJ). Both of these transitions connect
a node of the context to a node of an input strand .
After the transition CD (, or IJ), if the white node in
state 2 is not the last node of the first strand, we will
obtain either C or I, and, hence, we will repeat the
same step. Else we can only obtain the transition DE
(, or JK), to obtain a E (, or K).
Input Strand Interconnection: When the last
node of the last input strand is connected to the last
node of the context, all the input strands are correctly
docked (because the direction of the docking is from
the left to the right, and the last node of the context is
its right most node).
Initialization: By the transition DE (, or JK), we
will get E (, or K).
Propagation: From E (, or K), it is only possible
to perform the transition EF (, or KL). Both of these
transitions change the state of the black node to the
state d (JK also connect the white node in e to the
black node in c). After the transition EF (, or KL),
if the black node in 2 is not the first node of the first
strand, we will obtain either E or F, and we can only
repeat the same step. Else we can only perform the
transition FG (, or LM), and we will obtain G (, or
M).
Undocking: This stage undocks the output strand
and the stimulus by breaking the connections between
the nodes in the first strand and the nodes in the sec-
ond strand from right to the left.
Initialization: By the transition FG (, or LM), we
will get G (, or M).
Propagation: From G, we can only perform the
transition GH (if the black node in 3 is not a sepa-
rator). From M, if the grey node in 2 is a stimulus
separator or an input separator, we can perform either
the transition MN or MO. Therefore we can perform
either the transition GH, MN or MO. If the white node
in 3 is not the last node of the first strand, we will ob-
tain either G or M, and will repeat the same step.
Reinitialization: When the undocking stage is
terminated, we have a pair of a context and a output
strand, or a triple of a context, an output strand and a
stimulus. They must be reinitialized to be able to par-
ticipate in another reaction. This is done by the rules
from 16 to 18 for the context and by the rules from 19
to 22 for the stimulus and the output strand.
6 CONCLUSIONS
This paper has proposed a framework based on the
RNA replication mechanism to design the third level
of our formal modeling. With this framework, it is
possible to implement any reactions of a catalytic re-
action network by using nucleotide smart objects in
a generic way. In order to prove the validity of such
an implementation, we have introduced a global state
transition diagram that resumes the graph rewriting
rules. The NSOs in the same strand need not to be in
the same place. They may exist at different locations
in a physical environment and be connected through
the Internet. This modeling opens a new vista for new
application scenarios of proximity-based federation
of smart objects. With this new approach based on the
RNA replication mechanism, and with the representa-
tion of the interactions among smart objects based on
catalytic reaction networks, we will become able to
consider, to describe, and to implement new innova-
tive scenarios beyond the current scope of stereotyped
applications of ubiquitous, pervasive, and/or mobile
computing.
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FORMALIZATION OF AN RNA-INSPIRED MIDDLEWARE FOR COMPLEX SMART OBJECT FEDERATION
SCENARIOS
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