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## Encoding higher level extensions of petri nets in answer set programming”, arXiv preprint arXiv:1306.3548 (2013)

Citations: | 2 - 2 self |

### Citations

2127 |
Petri nets: Properties, analysis and applications
- Murata
- 1989
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Citation Context ...ersome, hence inconvenient. other techniques, such as process algebra, temporal logics, and mathematical equations when one considers the restrictions on Petri Nets imposed by mathematical techniques =-=[11]-=-, the cumbersomeness of encoding in pi-calculus even for small models [12], or the lack of applicability to higher level Petri Net extensions. Previous work on Petri Net to ASP translation has been li... |

1842 | The stable model semantics for logic programming
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...thways. We start with a brief background on ASP, multisets, and Petri Nets. 2 Fundamentals Answer Set Programming (ASP) is a declarative logic programming language based on the Stable Model Semantics =-=[15]-=-. Code presented in this paper follows the Clingo [16] syntax. The reader is referred to [16,17] for the syntax and semantics of Answer Set Programs. A multiset A over a domain set D is a pair 〈D,m〉, ... |

713 | Knowledge Representation, Reasoning and Declarative Problem Solving
- Baral
(Show Context)
Citation Context ...swer Set Programming (ASP) is a declarative logic programming language based on the Stable Model Semantics [15]. Code presented in this paper follows the Clingo [16] syntax. The reader is referred to =-=[16,17]-=- for the syntax and semantics of Answer Set Programs. A multiset A over a domain set D is a pair 〈D,m〉, where m : D → N is a function giving the multiplicity of d ∈ D in A. Given two multsets A = 〈D,m... |

498 |
Kommunikation mit Automaten
- Petri
- 1962
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Citation Context ... In order to answer such questions, we have to model pathways, add interventions / extensions to them based on the question, simulate them, and reason with the simulation results. We found Petri Nets =-=[1]-=- to be a suitable formalism for modeling biological pathways, as their graphical representation is very close to the biological pathways, and they can be extended to add necessary assumptions and inte... |

172 | Coloured Petri nets and CPN tools for modeling and validation of concurrent systems
- Jensen, Kristensen, et al.
(Show Context)
Citation Context ...r nadh and 2 tokens of h. Similar notation is used to specify marking on places, when not present, the place is assumed to be empty of tokens. Numerous Petri Net modeling and simulation systems exist =-=[5,6,7,8]-=-, but we did not find them to be suitable for our application, either due to limited adaptability outside their intended application domain, limited extendibility, or ease of extendibility. In additio... |

98 | Potassco: The Potsdam Answer Set Solving Collection
- Gebser, Kaminski, et al.
- 2011
(Show Context)
Citation Context ...sets, and Petri Nets. 2 Fundamentals Answer Set Programming (ASP) is a declarative logic programming language based on the Stable Model Semantics [15]. Code presented in this paper follows the Clingo =-=[16]-=- syntax. The reader is referred to [16,17] for the syntax and semantics of Answer Set Programs. A multiset A over a domain set D is a pair 〈D,m〉, where m : D → N is a function giving the multiplicity ... |

71 |
Quantitative modeling of biochemical networks.
- Hofestadt, Thelen
- 1998
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Citation Context ...ical environment with pathway representation similar to standard biological pathways. It also only supports one possible evolution. Petri Nets have been previously used to analyze biological pathways =-=[22,23,24]-=-, but most of this analysis has been limited to dynamic and structural properties of the Petri Net model. [25] took a different approach, where they surveyed the Petri Net implementations and came up ... |

61 |
Answer set programming at a glance.
- Brewka, Niemela, et al.
- 2011
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Citation Context ...ative programming language with numerous competitive solvers [9]. It has been effectively used in various domains, such as spacecrafts, work flows, natural language processing, and biological systems =-=[10]-=-. The suitability of ASP to analyze Petri Nets is further reinforced over 3 Though a Petri Net with colored tokens can be converted into a regular Petri Net without colored tokens, they are usually to... |

52 | Bounded LTL model checking with stable models. Theory and Practice of Logic Programming
- Heljanko, Niemelä
- 2003
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Citation Context ...s [12], or the lack of applicability to higher level Petri Net extensions. Previous work on Petri Net to ASP translation has been limited to specific classes of Petri Nets, such as regular Petri Nets =-=[13]-=- and Simple Logic Petri Nets (SLPN) [14], focusing on analyzing their properties. Neither used colored tokens. Please see our previous work [2] for more details. Though our focus in the current work i... |

46 | The first answer set programming system competition, in:
- Gebser, Liu, et al.
- 2007
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Citation Context ...eatures, such as intuitive encoding, easy extendibility, and strong reasoning capability in Answer Set Programming (ASP), which is a declarative programming language with numerous competitive solvers =-=[9]-=-. It has been effectively used in various domains, such as spacecrafts, work flows, natural language processing, and biological systems [10]. The suitability of ASP to analyze Petri Nets is further re... |

43 |
Analysis of Asynchronous Concurrent Systems by Petri Nets
- Ramchandani
- 1974
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Citation Context ..., j) : p ∈ P, c/q ∈Mj(p), 0 ≤ j ≤ k} = {holds(p, q, c, ts) : holds(p, q, c, ts) ∈ A} 5 Extension - Timed Transitions Biological processes vary in time required for them to complete. Timed transitions =-=[21]-=- model this variation of duration. The timed transitions can be reentrant or non-reentrant12. We extend our encoding to allow reentrant timed transitions. q [2]stqse/2 q' t3 e/2 e/2 cytc [2]stcytcse/2... |

43 |
Application of petri net based analysis techniques to signal transduction pathways
- Sackmann, Heiner, et al.
- 2006
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Citation Context ...ical environment with pathway representation similar to standard biological pathways. It also only supports one possible evolution. Petri Nets have been previously used to analyze biological pathways =-=[22,23,24]-=-, but most of this analysis has been limited to dynamic and structural properties of the Petri Net model. [25] took a different approach, where they surveyed the Petri Net implementations and came up ... |

39 |
Using Petri net tools to study properties and dynamics of biological systems
- Peleg
- 2005
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Citation Context ...ible evolution. Petri Nets have been previously used to analyze biological pathways [22,23,24], but most of this analysis has been limited to dynamic and structural properties of the Petri Net model. =-=[25]-=- took a different approach, where they surveyed the Petri Net implementations and came up with questions answerable by each. Contrary to the previous work, we focus on real world biological questions ... |

35 |
Some decision problems related to the reachability problem for Petri nets
- Araki, Kasami
- 1976
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Citation Context ... W (p, t) to mean W (〈p, t〉). We use similar simpler notation for QW . 5 The reset arc is involved here because we use a modified execution semantics of reset arcs compared to the standard definition =-=[19]-=-. Even though both capture similar operation, our definition allows us to model elimination of all quantity of a substance as soon as it is produced, even in a maximal firing set semantics. Our semant... |

29 | Pi calculus versus petri nets: Let us eat” humble pie” rather than further inflate the” pi hype”.
- Aalst
- 2005
(Show Context)
Citation Context ...poral logics, and mathematical equations when one considers the restrictions on Petri Nets imposed by mathematical techniques [11], the cumbersomeness of encoding in pi-calculus even for small models =-=[12]-=-, or the lack of applicability to higher level Petri Net extensions. Previous work on Petri Net to ASP translation has been limited to specific classes of Petri Nets, such as regular Petri Nets [13] a... |

26 |
Petri net semantics of priority systems.
- Best, Koutny
- 1992
(Show Context)
Citation Context ...ily encoded by making small code changes. 4 Extension - Priority Transitions Priority transitions enable ordering of Petri Net transitions, favoring high priority transitions over lower priority ones =-=[20]-=-. In a biological context, this is used to model primary (or dominant) vs. secondary pathways / processes in a biological system. This prioritization may be due to an intervention (such as prioritizin... |

12 |
Snoopy e a unifying Petri net tool
- Heiner, Herajy, et al.
- 2012
(Show Context)
Citation Context ...r nadh and 2 tokens of h. Similar notation is used to specify marking on places, when not present, the place is assumed to be empty of tokens. Numerous Petri Net modeling and simulation systems exist =-=[5,6,7,8]-=-, but we did not find them to be suitable for our application, either due to limited adaptability outside their intended application domain, limited extendibility, or ease of extendibility. In additio... |

9 |
Cell Illustrator 4.0: A computational platform for systems biology
- Nagasaki
- 2010
(Show Context)
Citation Context ...r nadh and 2 tokens of h. Similar notation is used to specify marking on places, when not present, the place is assumed to be empty of tokens. Numerous Petri Net modeling and simulation systems exist =-=[5,6,7,8]-=-, but we did not find them to be suitable for our application, either due to limited adaptability outside their intended application domain, limited extendibility, or ease of extendibility. In additio... |

9 |
H and Miyano S: Structural modeling and analysis of signaling pathways based on Petri nets
- Li, Suzuki, et al.
(Show Context)
Citation Context ...ical environment with pathway representation similar to standard biological pathways. It also only supports one possible evolution. Petri Nets have been previously used to analyze biological pathways =-=[22,23,24]-=-, but most of this analysis has been limited to dynamic and structural properties of the Petri Net model. [25] took a different approach, where they surveyed the Petri Net implementations and came up ... |

4 |
Mathematics of Multisets, in Multiset processing: Mathematical, computer science and molecular computing points of view, Calude
- Syropoulos
(Show Context)
Citation Context ... ⊗ n to represent ∀d ∈ D,m(d) ⊗ n, where n ∈ N, ⊗ ∈ {<,>,≤,≥,=, 6=}. We use the notation d/n ∈ A to represent that d appears n-times in A; we drop A when clear from context. The reader is referred to =-=[18]-=- for details. A basic Petri Net [1] is a bipartite graph of a finite set of place nodes P = {p1, . . . , pn}, and transition nodes T = {t1, . . . , tm} connected through directed arcs E = E+ ∪ E−. An ... |

3 | K.: Encoding Petri nets in Answer Set Programming for simulation based reasoning. http://arxiv.org/abs/1306.3542
- Anwar, Baral, et al.
- 2013
(Show Context)
Citation Context ...phical representation is very close to the biological pathways, and they can be extended to add necessary assumptions and interventions relevant to the questions as shown in our prequel to this paper =-=[2]-=-. Looking through the pathways, we found that certain aspects of biological pathways, such as multiple locations and substance types (perhaps connected to these locations) cannot be represented by reg... |

2 | Model Checking with Logic Based Petri Nets. Technical report ifi-07-02, Insitut für Informatik, Technische Universität Clausthal JuliusAlbert Str
- Behrens, Dix
- 2007
(Show Context)
Citation Context ...higher level Petri Net extensions. Previous work on Petri Net to ASP translation has been limited to specific classes of Petri Nets, such as regular Petri Nets [13] and Simple Logic Petri Nets (SLPN) =-=[14]-=-, focusing on analyzing their properties. Neither used colored tokens. Please see our previous work [2] for more details. Though our focus in the current work is on biological questions, our approach ... |

1 |
et al.: A note on colored Petri nets
- Peterson
- 1980
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Citation Context ...n Figure 1), regular (uncolored) tokens do not provide sufficient fidelity to represent various token types needed as input to a transition. As a result, we have to use Petri Nets with colored tokens =-=[4]-=- to model such biological pathways3. In contrast to our previous work, the place nodes in this Petri Net model represent locations rather than substances. Even electron-carrier (substances) q, cytc ar... |

1 |
M.: Renew–the reference net workshop. Petri Net Newsletter 56
- Kummer, Wienberg, et al.
- 1999
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