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High undecidability of weak bisimilarity for Petri nets (1994)  (Make Corrections)  (3 citations)
Petr Jancar
TAPSOFT



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Abstract: It is shown that the problem whether two labelled place/transition Petri nets (with initial markings) are weakly bisimilar is highly undecidable { it resides at least at level ! of the hyperarithmetical hierarchy; on the other hand it belongs to  1 1 (the rst level of the analytical hierarchy). It contrasts with  0 1 -completeness of the same problem for trace (language) equivalence. Relations to similar problems for the process algebra BPP (Basic Parallel Processes) are also discussed. ... (Update)

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.... Petri nets, we easily get 0 1 completeness of this problem (the problem whether two Petri nets are non bisimilar is 0 1 complete) [18] shows that the problem for weak bisimilarity is much more complicated from this point of view it is beyond the arithmetical...

...de nitions and claims the results. The relevant proofs are given in Section 3. A preliminary version of the paper appeared as the report [13]. The report is self contained since it includes an appendix describing a needed construction of [12] Here we only refer to [12]...

Cited by:   More
Weak Bisimilarity and Regularity of BPA is EXPTIME-hard - Mayr (2002)   (Correct)
High undecidability of weak bisimilarity for Petri nets - Jancar (1994)   (Correct)
Undecidability of Bisimilarity for Petri Nets and Some Related.. - Jancar (1995)   (Correct)

Active bibliography (related documents):   More   All
0.4:   Decidability of Bisimulation Equivalence for Normed Pushdown.. - Stirling (1996)   (Correct)
0.2:   Nested Semantics over Finite Trees are Equationally Hard - Aceto, Fokkink, van.. (2003)   (Correct)
0.2:   Decidability Questions for Bisimilarity of Petri Nets and Some.. - Jancar (1994)   (Correct)

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0.7:   Strong Bisimilarity Can Be Opened - Andersen, Hüttel, Jensen (2002)   (Correct)
0.6:   Petri Nets and Regular Processes - Esparza, Jancar, Moller (1999)   (Correct)
0.5:   Hereditary History Preserving Bisimilarity Is Undecidable - Jurdzinski, Nielsen, Srba   (Correct)

Related documents from co-citation:   More   All
3:   Communication and Concurrency (context) - Milner - 1989
2:   Undecidable equivalences for Basic Parallel processes (context) - uttel - 1993
2:   Computation: Finite and Innite Machines (context) - Minsky - 1967

BibTeX entry:   (Update)

P. Jancar, High undecidability of weak bisimilarity for Petri nets, Techn. rep. ECS-LFCS-94-298, Univ. of Edinburgh, UK, August 1994 (to appear in Proc. TAPSOFT/CAAP '95, Lecture Notes in Computer Science). http://citeseer.ist.psu.edu/jancar94high.html   More

@inproceedings{ jancar95high,
    author = "Petr Jancar",
    title = "High Undecidability of Weak Bisimilarity for Petri Nets",
    booktitle = "{TAPSOFT}",
    pages = "349-363",
    year = "1995",
    url = "citeseer.ist.psu.edu/jancar94high.html" }
Citations (may not include all citations):
1933   Communication and Concurrency (context) - Milner - 1989
108   Petri Net Theory and the Modelling of Systems (context) - Peterson - 1981
103   An algorithm for the general Petri net reachability problem (context) - Mayr - 1984
102   Bisimulation equivalence is decidable for all context-free p.. - Christensen, uttel et al. - 1992
51   Handbook of Mathematical Logic (context) - Barwise - 1989
39   A polynomial algorithm for deciding bisimilarity of normed c.. - Hirshfeld, Jerrum et al. - 1994
29   Petri nets and the equivalence problem (context) - Hirshfeld - 1994
23   the reachability problem for 5-dimensional vector addition s.. (context) - Hopcroft, Pansiot - 1979
21   branching time spectrum (context) - van Glabbeek, time - 1990
20   Bisimulation equivalence is decidable for all Basic Parallel.. (context) - Christensen, Hirshfeld et al. - 1993
18   A polynomial-time algorithm for deciding bisimulation equiva.. - Hirshfeld, Jerrum et al. - 1994
13   Computation: Finite and Innite Machines (context) - Minsky - 1967
9   the decidability of non-interleaving process equivalences - Kiehn, Hennessy - 1994
7   Decision problems for Petri nets and vector addition systems (context) - Hack - 1975
7   the uniform word problem for commutative context-free gramma.. (context) - Esparza
5   Decidability questions for bisimilarity of Petri nets and so.. (context) - Jan - 1994
4   Undecidable equivalences for Basic Parallel processes (context) - uttel - 1993
3   High undecidability of weak bisimilarity for Petri nets - Jan - 1994
2   Lecture notes to the Summerschool in logical methods in conc.. (context) - Stirling, temporal et al. - 1993

Documents on the same site (http://www.cs.vsb.cz/~jan59/):   More
Boundedness of Reset P/T Nets - Dufourd, Jancar, Schnoebelen (1999)   (Correct)
Simulation of One-Counter Nets via Colouring - Jancar, Moller (1999)   (Correct)
On Monotonic Automata with a Restart Operation - Jancar, Mraz, Platek, Vogel (1999)   (Correct)

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