“…As our symbolic set representation, we consider standard reduced ordered binary decision diagrams (ROBDDs, or just BDDs for short) [17]. The source of our edge-coloured graphs are the transition systems of parametrised Boolean networks (PBN) as understood in [11,60].…”
Section: Methodsmentioning
confidence: 99%
“…In [6,13] we have initially attacked the SCC decomposition problem for massive edge-coloured graphs by developing a parallel semi-symbolic algorithm for detecting terminal SCCs. The algorithm uses symbolic structures to represent sets of parameters, while the graph itself is represented explicitly.…”
Problems arising in many scientific disciplines are often modelled using edge-coloured directed graphs. These can be enormous in the number of both vertices and colours. Given such a graph, the original problem frequently translates to the detection of the graph’s strongly connected components, which is challenging at this scale.We propose a new, symbolic algorithm that computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs $$O(p\cdot n\cdot \log n)$$
O
(
p
·
n
·
log
n
)
symbolic steps, where p is the number of colours and n the number of vertices. We evaluate the algorithm using an experimental implementation based on Binary Decision Diagrams (BDDs) and large (up to $$2^{48}$$
2
48
) coloured graphs produced by models appearing in systems biology.
“…As our symbolic set representation, we consider standard reduced ordered binary decision diagrams (ROBDDs, or just BDDs for short) [17]. The source of our edge-coloured graphs are the transition systems of parametrised Boolean networks (PBN) as understood in [11,60].…”
Section: Methodsmentioning
confidence: 99%
“…In [6,13] we have initially attacked the SCC decomposition problem for massive edge-coloured graphs by developing a parallel semi-symbolic algorithm for detecting terminal SCCs. The algorithm uses symbolic structures to represent sets of parameters, while the graph itself is represented explicitly.…”
Problems arising in many scientific disciplines are often modelled using edge-coloured directed graphs. These can be enormous in the number of both vertices and colours. Given such a graph, the original problem frequently translates to the detection of the graph’s strongly connected components, which is challenging at this scale.We propose a new, symbolic algorithm that computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs $$O(p\cdot n\cdot \log n)$$
O
(
p
·
n
·
log
n
)
symbolic steps, where p is the number of colours and n the number of vertices. We evaluate the algorithm using an experimental implementation based on Binary Decision Diagrams (BDDs) and large (up to $$2^{48}$$
2
48
) coloured graphs produced by models appearing in systems biology.
“…We also give an overview of the necessary technical background needed to describe the algorithmic solution and its implementation. More details can be found in [ 4 ].…”
Section: Attractors In Parametrised Boolean Networkmentioning
confidence: 99%
“…Each attractor is classified as one of the three above-mentioned types and this information is used to incrementally build the bifurcation function , also represented symbolically using BDDs. More details about the algorithm as well as the classification procedure can be found in [ 4 ]. Fig.…”
Section: Attractor Bifurcation Analysis With Aeonmentioning
confidence: 99%
“…Such a qualitative change is called a bifurcation and the values of parameters for which it occurs are called bifurcation points . Determining (all) bifurcation points for a network, called attractor bifurcation analysis , is an important task in the analysis of BNs [ 4 ].…”
Boolean networks (BNs) provide an effective modelling tool for various phenomena from science and engineering. Any long-term behaviour of a BN eventually converges to a so-called attractor. Depending on various logical parameters, the structure and quality of attractors can undergo a significant change, known as a bifurcation. We present a tool for analysing bifurcations in asynchronous parametrised Boolean networks. To fight the state-space and parameter-space explosion problem the tool uses a parallel semi-symbolic algorithm.
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