## Constructing Exponential-size Deterministic Zielonka Automata (2006)

Venue: | IN "ICALP", VOL. LNCS 4052 |

Citations: | 4 - 1 self |

### BibTeX

@INPROCEEDINGS{Genest06constructingexponential-size,

author = {Blaise Genest and Anca Muscholl},

title = {Constructing Exponential-size Deterministic Zielonka Automata},

booktitle = {IN "ICALP", VOL. LNCS 4052},

year = {2006},

pages = {565--576},

publisher = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

The well-known algorithm of Zielonka describes how to transform automatically a sequential automaton into a deterministic asynchronous trace automaton. In this paper, we improve the construction of deterministic asynchronous automata from finite state automaton. Our construction improves the well-known construction in that the size of the asynchronous automaton is simply exponential in both the size of the sequential automaton and the number of processes. In contrast, Zielonka’s algorithm gives an asynchronous automaton that is doubly exponential in the number of processes (and simply exponential in the size of the automaton).

### Citations

246 | On communicating finite-state machines - Brand, Zafiropulo - 1983 |

192 | editors. The Book of Traces - Diekert, Rozenberg - 1995 |

126 |
Concurrent program schemes and their interpretations
- Mazurkiewicz
- 1977
(Show Context)
Citation Context ... (trace) automata. These are basically (deterministic) local automata that exchange information using shared (state) variables. The underlying mathematical theory is the theory of Mazurkiewicz traces =-=[10]-=-, which has brought a large number of beautiful results in the theory of automata and logics (see [5] for a survey). The basic idea of trace theory is to model actions in a concurrent system by explic... |

47 |
Notes on finite asynchronous automata
- Zielonka
- 1987
(Show Context)
Citation Context ...n a concurrent system by explicitly providing an independence relation between actions that do not share any resource. A fundamental and difficult result for Mazurkiewicz traces is Zielonka’s theorem =-=[16]-=-, which states that (diamond) finite state automata can be effectively transformed into deterministic asynchronous automata. This result is all the more fundamental since it has been used for several ... |

32 | Towards a theory of regular MSC languages
- Henriksen, Mukund, et al.
- 1999
(Show Context)
Citation Context ...ronous automata. This result is all the more fundamental since it has been used for several other closely related problems, as synthesis of communicating automata, with bounded communication channels =-=[13,7,8]-=-, or existentially-bounded channels [6] or causal memory [1]. The main drawback of Zielonka’s theorem is that it yields an asynchronous automaton of doubly exponential size in the size of the alphabet... |

27 |
Synthesizing distributed finite-state systems from MSCs
- Mukund, Kumar, et al.
- 2000
(Show Context)
Citation Context ...ronous automata. This result is all the more fundamental since it has been used for several other closely related problems, as synthesis of communicating automata, with bounded communication channels =-=[13,7,8]-=-, or existentially-bounded channels [6] or causal memory [1]. The main drawback of Zielonka’s theorem is that it yields an asynchronous automaton of doubly exponential size in the size of the alphabet... |

23 |
Regular sets of infinite message sequence charts
- Kuske
(Show Context)
Citation Context ...ronous automata. This result is all the more fundamental since it has been used for several other closely related problems, as synthesis of communicating automata, with bounded communication channels =-=[13,7,8]-=-, or existentially-bounded channels [6] or causal memory [1]. The main drawback of Zielonka’s theorem is that it yields an asynchronous automaton of doubly exponential size in the size of the alphabet... |

18 | Beyond message sequence graphs - Madhusudan, Meenakshi - 2001 |

15 | Synthesis of distributed algorithms using asynchronous automata - Stefanescu, Esparza, et al. - 2003 |

10 | Bounded MSC communication - Lohrey, Muscholl - 2004 |

7 | Causal closure for MSC languages
- Adsul, Mukund, et al.
- 2005
(Show Context)
Citation Context ... has been used for several other closely related problems, as synthesis of communicating automata, with bounded communication channels [13,7,8], or existentially-bounded channels [6] or causal memory =-=[1]-=-. The main drawback of Zielonka’s theorem is that it yields an asynchronous automaton of doubly exponential size in the size of the alphabet [16,4]. Thespaper [14] gives a more direct proof of Zielonk... |

7 |
A Kleene theorem and model checking for a class of communicating automata
- Genest, Kuske, et al.
(Show Context)
Citation Context ... fundamental since it has been used for several other closely related problems, as synthesis of communicating automata, with bounded communication channels [13,7,8], or existentially-bounded channels =-=[6]-=- or causal memory [1]. The main drawback of Zielonka’s theorem is that it yields an asynchronous automaton of doubly exponential size in the size of the alphabet [16,4]. Thespaper [14] gives a more di... |

6 | Keeping Track of the Latest Gossip in a Distributed System
- Mukund, Sohoni
- 1997
(Show Context)
Citation Context ...bounded channels [6] or causal memory [1]. The main drawback of Zielonka’s theorem is that it yields an asynchronous automaton of doubly exponential size in the size of the alphabet [16,4]. Thespaper =-=[14]-=- gives a more direct proof of Zielonka’s theorem, with a complexity which is doubly exponential in the number of processes (instead of the size of the alphabet). Similarly, [7] synthesizes bounded com... |

3 | Unfolding Synthesis of Asynchronous Automata
- Baudru, Morin
- 2006
(Show Context)
Citation Context ...xity of other works [12,15] using Zielonka’s theorem or its variant for communicating processes [1,13,7] to produce a distributed automaton with local final states or without deadlock. Very recently, =-=[2]-=- proposed a construction of non-deterministic asynchronous automata of size |A| 2|Σ| while we produce a deterministic one. Their complexity is thus polynomial in |A| but still doubly exponential in Σ,... |

2 |
From global specification to local implementations
- Mukund
- 2002
(Show Context)
Citation Context ..., this construction is tight, since the determinization of sequential automata requires exponential size. Related work. There were several attempts to simplify Zielonka’s construction as described in =-=[16,12]-=-. In some special cases the construction can be indeed simplified (see e.g . [5] Ch. 8), but the complexity is still exponential (the starting point there is a monoid homomorphism in place of an autom... |