Showing papers by "Grzegorz Rozenberg published in 2012"

Minimal reaction systems

Abstract: Reaction systems are a formal model for processes inspired by the functioning of the living cell. These processes are determined by the iteration of the state transition functions of reaction systems, also called rs functions. In this paper we provide mathematical characterisations of rs functions implemented/defined by "minimal reaction systems", i.e., reaction systems with reactions using the minimal number of reactants, or the minimal number of inhibitors, or the minimal number of resources (i.e., reactants and inhibitors together).

Computational Nature of Gene Assembly in Ciliates

Abstract: reduction graphs be ARG. It turns out that there are graphs in ARG that are not (isomorphic to) reduction graphs. To obtain a characterization we need one more property of reduction graphs: the ability to linearly order the vertices to resemble its (in general not unique) underlying legal string, as done in Fig. 11. To make this linear order of vertices explicit, we introduce a third set of edges, called merge edges , to the reduction graph as done in Fig. 14. s 2 2 7 7 4 4 7 7 3 3 5 5 3 3 4 4 2 2 6 6 5 5 6 6 t Fig. 14. Merge edges are added to the reduction graph of Fig. 11. Now, when is a set of edges M for G ∈ ARG a set of merge edges? Like desire edges, they have the properties that (1) the edges connect vertices with a common label and (2) each vertex except s and t is connected to exactly one merge edge. Moreover, M and the set E2 are disjoint – no desire edge is parallel to a merge edge. Finally, the reality edges and merge edges must allow for a path from s to t passing each vertex once. This last requirement is equivalent to the fact that the reality and merge edges induce a connected graph. If it is possible to add a set of merge edges to the graph, then it is not difficult to see that the graph is isomorphic to a reduction graph Ru. Indeed, we can identify such a u for this reduction graph by simply considering the alternating path from s to t over the reality and merge edges. The orientation (positiveness or negativeness) of each pointer is determined by the crossing or non crossing of the desire edges (exactly as we defined the notion of reduction graph). To characterize reduction graphs we need the notion of a pointer-component graph. Given an abstract reduction graph, a pointer-component graph describes how the labels of that abstract reduction graph are distributed among its connected components. Definition 5.14. Let G ∈ ARG. The pointer-component graph of G, denoted by PCG, is a multigraph (ζ, E, e), where ζ is the set of connected components of G, E = dom(G) and e is, for e ∈ E, defined by e(e) = {C ∈ ζ | C contains vertices labelled by e}. The pointer-component graph of G = Ru of Fig. 12 is given in Fig. 15. We have ζ = {C1, C2, C3, R} where R is the linear component and the other elements are cyclic components of Ru. It is shown in [7] that, surprisingly, G ∈ ARG has a set of merge edges precisely when the pointer-component graph PCG is a connected graph. In other words: Theorem 5.15 ([7]). An abstract reduction graph G is isomorphic to a reduction graph iff PCG is a connected graph. Computational nature of gene assembly in ciliates 21

Stability and chaos in reaction systems

Abstract: Reaction systems are an abstract model of biochemical reactions in the living cell within a framework of finite (though often large) discrete dynamical systems. In this setting, this paper provides an analytical and experimental study of stability. The notion of stability is defined in terms of the way in which small perturbations to the initial state of a system are likely to change the system's eventual behavior. At the stable end of the spectrum, there is likely to be no change; but at the unstable end, small perturbations take the system into a state that is probabilistically the same as a randomly selected state, similar to chaotic behavior in continuous dynamical systems.

Representing reaction systems by trees

Abstract: Reaction systems formally model the functioning of the living cell. By representing sets of reactions by trees, we obtain a useful tool to investigate the state spaces of reaction systems. In particular, we give an upper bound on the fraction of inactive states within a subspace of the state space. This subspace represents partial knowledge of the (unknown) state under consideration.

Membrane Systems and Petri Net Synthesis

Abstract: Automated synthesis from behavioural specifications is an attractive and powerful way of constructing concurrent systems. Here we focus on the problem of synthesising a membrane system from a behavioural specification given in the form of a transition system which specifies the desired state space of the system to be constructed. We demonstrate how a Petri net solution to this problem, based on the notion of region of a transition system, yields a method of automated synthesis of membrane systems from state spaces.

Membrane Systems and Petri Net Synthesis

Abstract: Automated synthesis from behavioural specifications is an attractive and powerful way of constructing concurrent systems. Here we focus on the problem of synthesising a membrane system from a behavioural specification given in the form of a transition system which specifies the desired state space of the system to be constructed. We demonstrate how a Petri net solution to this problem, based on the notion of region of a transition system, yields a method of automated synthesis of membrane systems from state spaces.

Membrane Systems and Petri Net Synthesis (Invited Paper)

Abstract: Automated synthesis from behavioural specifications is an a ttractive and powerful way of constructing concurrent systems. Here we focus on the problem of synthesising a membrane system from a behavioural specification given in the form of a transition s ystem which specifies the desired state space of the system to be constructed. We demonstrate how a Petri net solution to this problem, based on the notion of region of a transition system, yields a method of automated synthesis of membrane systems from state spaces.

Relevance of Entities in Reaction Systems

Abstract: Reaction systems are a model for the investigation of processes carried out by biochemical reactions in living cells. A reaction system consists of a set of reactions which transform a current system’s state (a set of entities) into the successor state. In this paper we investigate which entities are actually relevant from the point of view of generating dynamic processes through such state transformations.

A formal framework for processes inspired by the functioning of living cells

Abstract: Natural Computing is concerned with both human-designed computing inspired by nature and computing taking place in nature. The former research strand investigates computational techniques, models of computation and computational devices inspired by nature. The latter research strand investigates, in terms of information processing, processes taking place in nature.

Membrane Systems and Petri Net Synthesis

Abstract: Automated synthesis from behavioural specifications is an attractive and powerful way of constructing concurrent systems. Here we focus on the problem of synthesising a membrane system from a behavioural specification given in the form of a transition system which specifies the desired state space of the system to be constructed. We demonstrate how a Petri net solution to this problem, based on the notion of region of a transition system, yields a method of automated synthesis of membrane systems from state spaces.