On the Analysis of Petri Nets and their Synthesis from Process Languages

Ludwik Czaja

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 37, Issue: 1, page 17-38
  • ISSN: 0988-3754

Abstract

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Processes in Place/Transition (P/T) nets are defined inductively by a peculiar numbering of place occurrences. Along with an associative sequential composition called catenation and a neutral process, a monoid of processes is obtained. The power algebra of this monoid contains all process languages with appropriate operations on them. Hence the problems of analysis and synthesis, analogous to those in the formal languages and automata theory, arise. Here, the analysis problem is: for a given P/T net with an initial marking find the set of all processes the net may evoke. The synthesis problem is: given a process language L decide if there exists a marked net whose evolutions (represented by processes) are collected in L and, in the positive case, find such net and its initial marking. The problems are posed and given a general solution.

How to cite

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Czaja, Ludwik. "On the Analysis of Petri Nets and their Synthesis from Process Languages." RAIRO - Theoretical Informatics and Applications 37.1 (2010): 17-38. <http://eudml.org/doc/92710>.

@article{Czaja2010,
abstract = { Processes in Place/Transition (P/T) nets are defined inductively by a peculiar numbering of place occurrences. Along with an associative sequential composition called catenation and a neutral process, a monoid of processes is obtained. The power algebra of this monoid contains all process languages with appropriate operations on them. Hence the problems of analysis and synthesis, analogous to those in the formal languages and automata theory, arise. Here, the analysis problem is: for a given P/T net with an initial marking find the set of all processes the net may evoke. The synthesis problem is: given a process language L decide if there exists a marked net whose evolutions (represented by processes) are collected in L and, in the positive case, find such net and its initial marking. The problems are posed and given a general solution. },
author = {Czaja, Ludwik},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Petri net; process language; analysis and synthesis of nets.; analysis and synthesis of nets},
language = {eng},
month = {3},
number = {1},
pages = {17-38},
publisher = {EDP Sciences},
title = {On the Analysis of Petri Nets and their Synthesis from Process Languages},
url = {http://eudml.org/doc/92710},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Czaja, Ludwik
TI - On the Analysis of Petri Nets and their Synthesis from Process Languages
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 1
SP - 17
EP - 38
AB - Processes in Place/Transition (P/T) nets are defined inductively by a peculiar numbering of place occurrences. Along with an associative sequential composition called catenation and a neutral process, a monoid of processes is obtained. The power algebra of this monoid contains all process languages with appropriate operations on them. Hence the problems of analysis and synthesis, analogous to those in the formal languages and automata theory, arise. Here, the analysis problem is: for a given P/T net with an initial marking find the set of all processes the net may evoke. The synthesis problem is: given a process language L decide if there exists a marked net whose evolutions (represented by processes) are collected in L and, in the positive case, find such net and its initial marking. The problems are posed and given a general solution.
LA - eng
KW - Petri net; process language; analysis and synthesis of nets.; analysis and synthesis of nets
UR - http://eudml.org/doc/92710
ER -

References

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