We propose an extension of communication structured acyclic nets (CSA-nets) based on coloured tokens. CSA-nets provide a way for representing relationships between sets of acyclic nets. Relationships between the component acyclic nets are represented, in particular, by channel places. For large CSA-nets, the number of channel places can make the model difficult to visualise and analyse. To address this, we propose to apply mechanisms found in the domain of coloured Petri nets, introducing master channel places which collapse possibly many channel places into a single node. Such places could help in the visualisation, comprehension and analysis of CSA-nets.
A complex evolving system (CES) can be viewed as a system of subsystems that are
concurrently interacting with each other. Also, such a system is often characterised by
a dynamically changing structure and features as well as intricate and large behavioural
patterns. Structured occurrence nets (SONs) [
Communication structured acyclic nets (CSA-nets) are an extension of SONs. They
have the ability to model behaviours of component subsystems using acyclic nets (rather
than occurrence nets) as well as synchronous and asynchronous communications
between component subsystems through channel places. A major application area of
CSAnets are (cyber)crime investigations that have gained a significant interest in recent years
and have already been discussed in [
What may hinder effective criminal investigations is the complexity and large
volume of information which, in turn, presents a major challenge to the investigators in
terms of both interpreting the crime and making the right decision. Bearing in mind
that accurate criminal investigation process not only helps in interpreting the crimes [
Criminal investigations are difficult to capture formally due to a high number of the various types of information, resulting from the different sources of information being involved, that need to be interpreted. As a result, criminal investigations are perceived as complicated tasks presenting a major challenge to investigators. Despite the fact that such a huge quantity of information is of high importance, its volume may distract the investigator leading to inaccurate/delayed decisions. Accurate visualisation of such complicated information would result in a better understanding of the criminal cases. In particular, it would help the investigators to detect the causality and dynamic behaviours involving the events which, in turn, would help to analyse and detect crimes.
The papers [
In this paper, we propose to improve the visualisation and analyses of CSA-nets by introducing the concept of master channel places which add folding mechanism to otherwise plain CSA-nets. We present our ideas with help of intuitive examples, leaving out their formalisation and the associated proofs. 2
Structured occurrence nets (SONs) [
In general, a CSA-net consists of several acyclic nets linked through different types
of formal relationships. They are intended to capture information about: (i) the
interaction between actual/excepted behaviors; and (ii) the collected evidence to be analysed.
CSA-nets can represent different actions of dynamic evolving systems [
A particular formal model we are using in this paper are the communication structured acyclic nets (CSA-nets), where the individual acyclic nets are linked by channel places capable of modelling both asynchronous and synchronous communication between different subsystems. In other words, the events are used to link the acyclic nets with each other through the channel . Figure 1(a) shows an example of CSA-net with two ‘horizontal’ occurrence nets (the upper one exhibiting concurrency) connected by two channel places, q1 and q2. The idea is that these places establish communication links. When the channel places are used asynchronously, the CSO-net can generate, e.g., the step sequence fdgfa; bgfe; cg. In addition, when they are used synchronously, the step sequence fdgfa; b; cgfeg can be executed. That is, there is an instantaneous transfer of tokens generated by a and b to transition c. Such a feature can, in particular, be used to model synchronous communication between the component occurrence nets.
In this paper, we are concerned with Communication Structured Acyclic Nets (CSAnets) which generalise CSO-nets by using (safe) acyclic nets (with forward and backward conflicts) instead of (conflict-free) occurrence nets. Figure 2(a) shows an example of CSA-net which, intuitively, combines two executions, one involving transitions a and c, and the other involving b, d, c and e. CSA-nets support a robust and effective structure that reduces complexity when compared to other representations, however, they lack the ability to visualise large designs at a time. More precisely, only one token can be represented in one channel place at any time. So, the idea behind this work is to improve and extend CSA-nets to be able to better visualise bigger nets, and so enhance the model visualisation and analysis. 3
In our ongoing work, we propose to allow channel places to represent more than one token at a time. Figures 1(b) and 2(b) respectively show the CSO-net of Figure 1(a) and CSA-net of Figure 2(a) where the two channel places were replaced by single place. Moreover, we added annotations on the arcs adjacent to the new places, and adjusted the execution rules. What is important to emphasize is that the annotations are sets of the original channel places (the curly brackets of sets are not shown). The execution rules follow the standard idea of Coloured Petri Nets which ensure that the tokens ‘flowing’ along the arcs match the annotations (the tokens in master channel places are simply the original channel places).
Therefore, we propose to introduce master channel places (MCPs), which introduce conciseness to CSA-net by collapsing (folding) channel places into master channel places. These master channel places allow representing more than one token and allow the component acyclic nets to communicate through a unique channel place. Inside a master channel place, there will be a set of tokens represented by a unique colours. A specific token will appear in the master channel place without conflicting with other tokens in each execution since a master channel place is colour-safe due to the fact that the original CSA-net was safe. This enhances SON visualisation contributing to a more readable and understandable model. master channel place q1 q2
q3 c15 e13 c16 e14 c17 e15
c18 c19 e16 c20 e17 e18
c22
So far we discussed an extension to coloured master channel places which do not affect the structure of the component acyclic nets. This has a positive effect on visualisation and the size of the model under investigation. However, the coloured net aspect we have introduced can be used to introduce more concise representation in the component acyclic nets as well without losing a highly intuitive acyclic net representation of the plain acyclic/occurrence nets. In particular, by the same mechanism we can collapse (fold) a set of transitions into a parameterised one. An initial idea is illustrated in Figure 5, where we use the coloured net mechanism to collapse two original transitions into a parameterised one. This uses typed channel place variables to achieve a desired effect through passing variable to collapsed transition. This process will increase comprehension and make larger systems under investigation easier to handle. 5
This paper proposed an extension of the Communication Structured Acyclic Nets
(CSAnets) based on multi-coloured tokens by introducing master channel places which
collapse many channel places into a single node. Such extension contributes positively to
a better visualisation while optimising the model size. The ongoing work is focused
on both the formalization of the proposed idea and the development of algorithms for
(semi)automatic construction and placement of master channel places, extending the
coloured net approach to the component acyclic nets without losing the intuitive
appeal of causality based representation they convey, and implementing the new type of
CSA-nets in the SONCRAFT tool [