## Causality in Membrane Systems

Citations: | 6 - 0 self |

### BibTeX

@MISC{Busi_causalityin,

author = {Nadia Busi},

title = {Causality in Membrane Systems},

year = {}

}

### OpenURL

### Abstract

Summary. P systems are a biologically inspired model introduced by Gheorghe Păun with the aim of representing the structure and the functioning of the cell. P systems are usually equipped with the maximal parallelism semantics; however, since their introduction, some alternative semantics have been proposed and investigated. We propose a semantics that describes the causal dependencies occurring between the reactions of a P system. We investigate the basic properties that are satisfied by such a semantics. The notion of causality turns out to be quite relevant for biological systems, as it permits to point out which events occurring in a biological pathway are necessary for another event to happen. 1

### Citations

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Communication and Concurrency
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(Show Context)
Citation Context ...objects in v are produced. The study of causal semantics in concurrency theory is quite old. For example, the study of a causal semantics for process algebras dates back to the early nineties for CCS =-=[20]-=- (see, e.g., [13, 11, 18]), and to the mid nineties for the π-calculus [21] (see, e.g., [3, 5, 14, 15]). To the best of our knowledge, the only other works that deal with causality in bio-inspired cal... |

1017 | A calculus of mobile processes
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(Show Context)
Citation Context ...ory is quite old. For example, the study of a causal semantics for process algebras dates back to the early nineties for CCS [20] (see, e.g., [13, 11, 18]), and to the mid nineties for the π-calculus =-=[21]-=- (see, e.g., [3, 5, 14, 15]). To the best of our knowledge, the only other works that deal with causality in bio-inspired calculi with membranes and compartments are the following. In [7] a causal sem... |

409 |
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(Show Context)
Citation Context ...g in a biological pathway are necessary for another event to happen. 1 Introduction Membrane computing is a branch of natural computing, initiated by Gheorghe Păun with the definition of P systems in =-=[22, 23, 24]-=-. The aim is to provide a formal modeling of the structure and the functioning of the cell, making use especially of automata, languages and complexity theoretic tools. Membrane systems are based upon... |

360 | Computing with membranes
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(Show Context)
Citation Context ...g in a biological pathway are necessary for another event to happen. 1 Introduction Membrane computing is a branch of natural computing, initiated by Gheorghe Păun with the definition of P systems in =-=[22, 23, 24]-=-. The aim is to provide a formal modeling of the structure and the functioning of the cell, making use especially of automata, languages and complexity theoretic tools. Membrane systems are based upon... |

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(Show Context)
Citation Context ...xive and transitive closure of R. 3 P Systems We recall the definition of catalytic P systems without priorities on rules. For a thorough description of the model, motivation, and examples see, e.g., =-=[8, 12, 22, 23, 24]-=-. To this aim, we start with the definition of membrane structure: Definition 5. Given the alphabet {[, ]}, the set MS is the least set inductively defined by the following rules: • [ ] ∈ MSs176 N. Bu... |

87 | Brane calculi. interactions of biological membranes
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Citation Context ... our knowledge, the only other works that deal with causality in bio-inspired calculi with membranes and compartments are the following. In [7] a causal semantics for the Mate/Bud/Drip Brane Calculus =-=[9]-=- is proposed. In [17] a causal semantics for Beta Binders [26, 27] – based on the π-calculus semantics and on the enhanced operational semantics approach of [15] – is defined. One of the main differen... |

74 |
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Citation Context ...g in a biological pathway are necessary for another event to happen. 1 Introduction Membrane computing is a branch of natural computing, initiated by Gheorghe Păun with the definition of P systems in =-=[22, 23, 24]-=-. The aim is to provide a formal modeling of the structure and the functioning of the cell, making use especially of automata, languages and complexity theoretic tools. Membrane systems are based upon... |

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Citation Context ...produced. The study of causal semantics in concurrency theory is quite old. For example, the study of a causal semantics for process algebras dates back to the early nineties for CCS [20] (see, e.g., =-=[13, 11, 18]-=-), and to the mid nineties for the π-calculus [21] (see, e.g., [3, 5, 14, 15]). To the best of our knowledge, the only other works that deal with causality in bio-inspired calculi with membranes and c... |

65 | The origins of structural operational semantics
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(Show Context)
Citation Context ...s defined as a maximal sequence of reactions, in [1, 2, 10] no notion of reaction is provided, and the notion equivalent to the maximal parallelism computational step is defined directly by SOS rules =-=[25]-=-. A detailed comparison of the two approaches is beyond the scope of the present paper and deserves further investigation. 5 A Causal Semantics for P Systems In this section we provide a causal semant... |

65 |
P.: Beta binders for biological interactions
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(Show Context)
Citation Context ... in bio-inspired calculi with membranes and compartments are the following. In [7] a causal semantics for the Mate/Bud/Drip Brane Calculus [9] is proposed. In [17] a causal semantics for Beta Binders =-=[26, 27]-=- – based on the π-calculus semantics and on the enhanced operational semantics approach of [15] – is defined. One of the main differences between Beta Binders on one side, and Brane Calculi and P syst... |

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Citation Context ... For example, the study of a causal semantics for process algebras dates back to the early nineties for CCS [20] (see, e.g., [13, 11, 18]), and to the mid nineties for the π-calculus [21] (see, e.g., =-=[3, 5, 14, 15]-=-). To the best of our knowledge, the only other works that deal with causality in bio-inspired calculi with membranes and compartments are the following. In [7] a causal semantics for the Mate/Bud/Dri... |

29 | Causality for mobile processes
- Degano, Priami
- 1995
(Show Context)
Citation Context ... For example, the study of a causal semantics for process algebras dates back to the early nineties for CCS [20] (see, e.g., [13, 11, 18]), and to the mid nineties for the π-calculus [21] (see, e.g., =-=[3, 5, 14, 15]-=-). To the best of our knowledge, the only other works that deal with causality in bio-inspired calculi with membranes and compartments are the following. In [7] a causal semantics for the Mate/Bud/Dri... |

26 |
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Citation Context ...produced. The study of causal semantics in concurrency theory is quite old. For example, the study of a causal semantics for process algebras dates back to the early nineties for CCS [20] (see, e.g., =-=[13, 11, 18]-=-), and to the mid nineties for the π-calculus [21] (see, e.g., [3, 5, 14, 15]). To the best of our knowledge, the only other works that deal with causality in bio-inspired calculi with membranes and c... |

20 | Projective Brane Calculus - Danos, Pradalier - 2004 |

16 |
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(Show Context)
Citation Context ... For example, the study of a causal semantics for process algebras dates back to the early nineties for CCS [20] (see, e.g., [13, 11, 18]), and to the mid nineties for the π-calculus [21] (see, e.g., =-=[3, 5, 14, 15]-=-). To the best of our knowledge, the only other works that deal with causality in bio-inspired calculi with membranes and compartments are the following. In [7] a causal semantics for the Mate/Bud/Dri... |

14 |
Computing with Cells and Atoms
- Paun
- 2000
(Show Context)
Citation Context ...xive and transitive closure of R. 3 P Systems We recall the definition of catalytic P systems without priorities on rules. For a thorough description of the model, motivation, and examples see, e.g., =-=[8, 12, 22, 23, 24]-=-. To this aim, we start with the definition of membrane structure: Definition 5. Given the alphabet {[, ]}, the set MS is the least set inductively defined by the following rules: • [ ] ∈ MSs176 N. Bu... |

13 |
A rewriting logic framework for operational semantics of membrane systems
- Andrei, Ciobanu, et al.
(Show Context)
Citation Context ...e exists a partial configuration γ ′ such that γ1 ↦→ + γ ′ , γ ′ �↦→ and γ2 = heated(γ ′ ). An operational semantics for P systems with maximal parallelism semantics has been defined for P systems in =-=[1, 2, 10]-=-. The main difference w.r.t. our approach is concerned with the fact that, while in this Section a maximal parallelism computational step is defined as a maximal sequence of reactions, in [1, 2, 10] n... |

11 |
R.: A Petri net semantics for π-calculus
- Busi, Gorrieri
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(Show Context)
Citation Context |

9 |
Structural operational semantics of P Systems
- Andreai, Ciobanu, et al.
- 2006
(Show Context)
Citation Context ...e exists a partial configuration γ ′ such that γ1 ↦→ + γ ′ , γ ′ �↦→ and γ2 = heated(γ ′ ). An operational semantics for P systems with maximal parallelism semantics has been defined for P systems in =-=[1, 2, 10]-=-. The main difference w.r.t. our approach is concerned with the fact that, while in this Section a maximal parallelism computational step is defined as a maximal sequence of reactions, in [1, 2, 10] n... |

8 |
Operational patterns in beta-binders
- Priami, Quaglia
- 2005
(Show Context)
Citation Context ... in bio-inspired calculi with membranes and compartments are the following. In [7] a causal semantics for the Mate/Bud/Drip Brane Calculus [9] is proposed. In [17] a causal semantics for Beta Binders =-=[26, 27]-=- – based on the π-calculus semantics and on the enhanced operational semantics approach of [15] – is defined. One of the main differences between Beta Binders on one side, and Brane Calculi and P syst... |

5 |
Using Well–structured Transition Systems to Decide Divergence for Catalytic P Systems. Theoret
- Busi
(Show Context)
Citation Context ... for P Systems In order to compare the classical maximal parallelism semantics with the causal semantics, in this section we recall a detailed definition of the computation of a P system, proposed in =-=[4]-=-, where a maximal parallelism evolution step is represented as a (maximal) sequence of simple evolution steps, which are obtained by the application of a single evolution rule. Throughout this section... |

3 | Modeling and analysis of biological processes by mem(brane) calculi and systems - Busi, Zandron - 2006 |

3 | Molecular cell biology. W.H. Freeman and Company, 4th edition - Lodish, Berk, et al. - 1999 |

2 | Towards a Causal Semantics for Brane Calculi
- Busi
- 2007
(Show Context)
Citation Context ... π-calculus [21] (see, e.g., [3, 5, 14, 15]). To the best of our knowledge, the only other works that deal with causality in bio-inspired calculi with membranes and compartments are the following. In =-=[7]-=- a causal semantics for the Mate/Bud/Drip Brane Calculus [9] is proposed. In [17] a causal semantics for Beta Binders [26, 27] – based on the π-calculus semantics and on the enhanced operational seman... |

2 |
Causality and Concurrency in Beta-binders TR-012006 The Microsoft Research
- Guerriero, Priami
- 2006
(Show Context)
Citation Context ...only other works that deal with causality in bio-inspired calculi with membranes and compartments are the following. In [7] a causal semantics for the Mate/Bud/Drip Brane Calculus [9] is proposed. In =-=[17]-=- a causal semantics for Beta Binders [26, 27] – based on the π-calculus semantics and on the enhanced operational semantics approach of [15] – is defined. One of the main differences between Beta Bind... |

2 |
Proof Systems for cause based equivalences
- Kiehn
- 1993
(Show Context)
Citation Context ...produced. The study of causal semantics in concurrency theory is quite old. For example, the study of a causal semantics for process algebras dates back to the early nineties for CCS [20] (see, e.g., =-=[13, 11, 18]-=-), and to the mid nineties for the π-calculus [21] (see, e.g., [3, 5, 14, 15]). To the best of our knowledge, the only other works that deal with causality in bio-inspired calculi with membranes and c... |

1 |
Operational semantics and rewriting logic in membrane computing
- Andrei, Ciobanu, et al.
- 2005
(Show Context)
Citation Context ...e exists a partial configuration γ ′ such that γ1 ↦→ + γ ′ , γ ′ �↦→ and γ2 = heated(γ ′ ). An operational semantics for P systems with maximal parallelism semantics has been defined for P systems in =-=[1, 2, 10]-=-. The main difference w.r.t. our approach is concerned with the fact that, while in this Section a maximal parallelism computational step is defined as a maximal sequence of reactions, in [1, 2, 10] n... |