On the complexity of occurrence and convergence problems in reaction systems

Formenti, Enrico; Manzoni, Luca; Porreca, Antonio E.

doi:10.1007/s11047-014-9456-3

Cited by 23 publications

(21 citation statements)

References 5 publications

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“…This paper pursues the seminal results in [8,16,15,11,4] about the dynamical behavior of RS. The purpose is to cover a broad range of questions involving cycles, attractors and reachability, providing in this way a reference list for them.…”

Section: Introductionmentioning

confidence: 86%

Complexity of the dynamics of reaction systems

Dennunzio

Formenti

Manzoni

et al. 2019

Information and Computation

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Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena that complements the more traditional approaches, for instance those based on differential equations. A comprehensive list of decision problems about the dynamical behavior of reaction systems (such as cycles and fixed/periodic points, attractors, and reachability) is provided along with the corresponding computational complexity, which ranges from tractable problems to PSPACE-complete problems.$ This paper collects, in a more extended/generalized version, both results presented at CiE 2014 conference [10] and the ones presented at DCFS 2014 conference [9]. It also contains a considerable number of further results.

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Section: Introductionmentioning

confidence: 86%

Complexity of the dynamics of reaction systems

Dennunzio

Formenti

Manzoni

et al. 2019

Information and Computation

Self Cite

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“…We have earlier, [14], presented another form of a similar construction. Names of reactions have been used as elements of the background set also in [5]. Our result shows that if one starts with a sequence (or cycle)…”

Section: Names Of Reactions As Elements Of the Background Setmentioning

confidence: 96%

“…Apart from various applications, reaction systems as such have been objected to many theoretical studies, [2,5,9,10,11,12,13]. The arising problems are mathematically very interesting, since the model is simple and clean.…”

Section: Introductionmentioning

confidence: 99%

Two-Step Simulations of Reaction Systems by Minimal Ones

Salomaa¹

2015

Acta Cybern

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Reaction systems were introduced by Ehrenfeucht and Rozenberg with biochemical applications in mind. The model is suitable for the study of subset functions, that is, functions from the set of all subsets of a finite set into itself. In this study the number of resources of a reaction system is essential for questions concerning generative capacity. While all functions (with a couple of trivial exceptions) from the set of subsets of a finite set S into itself can be defined if the number of resources is unrestricted, only a specific subclass of such functions is defined by minimal reaction systems, that is, the number of resources is smallest possible. On the other hand, minimal reaction systems constitute a very elegant model. In this paper we simulate arbitrary reaction systems by minimal ones in two derivation steps. Various techniques for doing this consist of taking names of reactions or names of subsets as elements of the background set. In this way also subset functions not at all definable by reaction systems can be generated. We follow the original definition of reaction systems, where both reactant and inhibitor sets are assumed to be nonempty

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“…The research on minimal systems is by now rich and broader than what we could cover in this section. Typical research topics in this area are: simulation of state sequences [43]; functions defined by minimal reaction systems [41]; computational complexity of various problems in such systems [40], [25]; normal forms [32]; connections to Boolean lattices [31].…”

Section: Corollary 3 ([13]mentioning

confidence: 99%

Reaction Systems: A Model of Computation Inspired by the Functioning of the Living Cell

Ehrenfeucht¹,

Petre²,

Rozenberg³

2017

The Role of Theory in Computer Science

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Reaction systems is a model of computation inspired by the functioning of the living cell. It formalizes the interactions between biochemical reactions which form the basic mechanism (the skeleton) underlying this functioning. This paper is a tutorial style introduction to reaction systems-it introduces the basic notions and reviews a number of research directions which are motivated either by biological considerations or by the need of understanding the basic formal processes (computations) underlying the dynamic behavior of reaction systems.

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On the complexity of occurrence and convergence problems in reaction systems

Cited by 23 publications

References 5 publications

Complexity of the dynamics of reaction systems

Complexity of the dynamics of reaction systems

Two-Step Simulations of Reaction Systems by Minimal Ones

Reaction Systems: A Model of Computation Inspired by the Functioning of the Living Cell

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