## Bisimulation and other undecidable equivalences for lossy channel systems (2001)

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Venue: | In Proc. of TACS’01, volume 2215 of LNCS |

Citations: | 5 - 0 self |

### BibTeX

@INPROCEEDINGS{Schnoebelen01bisimulationand,

author = {Ph. Schnoebelen},

title = {Bisimulation and other undecidable equivalences for lossy channel systems},

booktitle = {In Proc. of TACS’01, volume 2215 of LNCS},

year = {2001},

pages = {385--399},

publisher = {Springer}

}

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### Abstract

Abstract. Lossy channel systems are systems of finite state automata that communicate via unreliable unbounded fifo channels. Today the main open question in the theory of lossy channel systems is whether bisimulation is decidable. We show that bisimulation, simulation, and in fact all relations between bisimulation and trace inclusion are undecidable for lossy channel systems (and for lossy vector addition systems). 1

### Citations

315 | The Linear Time – Branching Time Spectrum
- Glabbeek
- 2001
(Show Context)
Citation Context ...erties of the chosen equivalence (e.g. the equivalence is a congruence). It is widely admitted that all interesting behavioral equivalences sit in van Glabbeek’s branching time – linear time spectrum =-=[Gla01]-=-, with bisimulation as the strongest equivalence, and trace equivalence as the weakest. For partially analyzable infinite-state systems, bisimulation is sometimes decidable [HJ99,Jan00] and sometimes ... |

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

248 | Hertzmann A. Style Machines - Brand - 2000 |

187 | Verifying programs with unreliable channels
- Abdulla, Jonsson
- 1993
(Show Context)
Citation Context ...nkel showed that termination is decidable for lossy systems [Fin94]. Abdulla and Jonsson showed the decidability of reachability, safety properties over traces, and eventuality properties over states =-=[AJ96b]-=-. These are fundamental results, with many practical applications in automated protocol verification. One should not believe that lossy channel systems are trivial models where everything is decidable... |

81 | Verification on infinite structures - Burkart, Caucal, et al. - 2000 |

76 | B.: On-the-fly analysis of systems with unbounded, lossy fifo channels - Abdulla, Bouajjani, et al. - 1998 |

70 |
Unreliable channels are easier to verify than perfect channels
- Cece, Finkel, et al.
- 1996
(Show Context)
Citation Context ... protocol), the classical model assumed perfect channels [Boc78,BZ81]. Therefore it is really ironic, and somewhat paradoxical, that lossy channels are “easier to analyze than perfect ones!”, quoting =-=[CFP95]-=-. Finkel showed that termination is decidable for lossy systems [Fin94]. Abdulla and Jonsson showed the decidability of reachability, safety properties over traces, and eventuality properties over sta... |

67 | Infinite results - Moller - 1996 |

67 |
Computability of recursive functions
- Shepherdson, Sturgis
- 1963
(Show Context)
Citation Context ...s can be used to simulate the tape of a Turing machine on a single fifo channel as soon as |Σ| ≥ 2 [BZ81, p. 31], and (2) extended rules allow one to simulate a Turing machine on a 2-counters machine =-=[SS63]-=-. For our purposes we introduce the following problem, a variant of the halting problem that makes the reduction in section 4 smoother: Non-empty Reachability. Instance: An extended channel system S w... |

59 | Undecidable verification problems for programs with unreliable channels
- Abdulla, Jonsson
- 1996
(Show Context)
Citation Context ... and Jonsson proved that recurrent reachability properties are undecidable, so that model-checking problems for (branching-time or linear-time) temporal logic is undecidable for lossy channel systems =-=[AJ96a]-=-, and Mayr showed that boundedness is undecidable [May00]. Also, systems where the channels are unreliable but fair (do not lose all messages all the time) cannot be analyzed [AJ96a], and one cannot s... |

49 | Deciding BisimulationLike Equivalences with Finite-State Processes
- Jančar, Kučera, et al.
- 2001
(Show Context)
Citation Context ...lla and Kindahl [AK95] studied equivalence problems between a lossy channel system and a finite state system, but such problems are less general than checking equivalence between two infinite systems =-=[JKM01]-=- and the decidability results of [AK95] cannot be used for the general case. Our contribution. In this paper we show that all equivalences in the branching time – linear time spectrum are undecidable ... |

48 | Undecidable problems in unreliable computations
- Mayr
- 2003
(Show Context)
Citation Context ...s are undecidable, so that model-checking problems for (branching-time or linear-time) temporal logic is undecidable for lossy channel systems [AJ96a], and Mayr showed that boundedness is undecidable =-=[May00]-=-. Also, systems where the channels are unreliable but fair (do not lose all messages all the time) cannot be analyzed [AJ96a], and one cannot say whether systems are correct with probability 1 when me... |

46 | Undecidability of bisimilarity for Petri nets and some related problems
- Jančar
- 1995
(Show Context)
Citation Context ...th bisimulation as the strongest equivalence, and trace equivalence as the weakest. For partially analyzable infinite-state systems, bisimulation is sometimes decidable [HJ99,Jan00] and sometimes not =-=[Jan95]-=-, and other equivalences are usually at least as hard as bisimulation. Surveys can be found in [Mol96,JM99,BCMS01]. Bisimulation between lossy channel systems. Today, the main open question in the the... |

45 | Model-checking lossy vector addition systems
- Bouajjani, Mayr
- 1999
(Show Context)
Citation Context ... is more discriminating than trace inclusion and less than bisimulation. The proof even shows undecidability for lossy vector addition systems, a weaker model that one uses when channels are not fifo =-=[BM99]-=-. Plan of the paper. Section 2 recalls basic notions (words, transition systems, behavioral equivalences). We define channel systems (extended, standard, and lossy) in section 3. The main results, giv... |

42 | Verifying lossy channel systems has nonprimitive recursive complexity
- Schnoebelen
(Show Context)
Citation Context ...protocol verification. One should not believe that lossy channel systems are trivial models where everything is decidable. First the main decidable problems do not have primitive recursive complexity =-=[Sch01]-=-, and secondly many problems are undecidable: Abdulla and Jonsson proved that recurrent reachability properties are undecidable, so that model-checking problems for (branching-time or linear-time) tem... |

39 | Symbolic Verification of Lossy Channel Systems: Application to the Bounded Retransmission Protocol - Abdulla, Annichini, et al. - 1999 |

32 |
Decidability of the termination problem for completely speci protocols
- Finkel
- 1994
(Show Context)
Citation Context ...Therefore it is really ironic, and somewhat paradoxical, that lossy channels are “easier to analyze than perfect ones!”, quoting [CFP95]. Finkel showed that termination is decidable for lossy systems =-=[Fin94]-=-. Abdulla and Jonsson showed the decidability of reachability, safety properties over traces, and eventuality properties over states [AJ96b]. These are fundamental results, with many practical applica... |

31 | Bisimulation equivalence is decidable for normed process algebra - Hirshfeld, Jerrum - 1999 |

29 |
Data flow analysis of communicating finite state machines
- Peng, Puroshothaman
- 1991
(Show Context)
Citation Context ...od for them can be general and fully algorithmic. For example, existing methods only check sufficient but not necessary conditions for correctness (e.g. [JJ93]), or only terminate in some cases (e.g. =-=[PP91]-=-), or only deal with channel systems of a certain type (e.g. [CF97]). c1?c p2 p3sLossy channels. A few years ago, Finkel, Abdulla and Jonsson independently identified lossy channel systems as a very p... |

26 |
Testing for Unboundedness of FIFO Channels
- Jéron, Jard
- 1993
(Show Context)
Citation Context ...s are Turing powerful, and no verification method for them can be general and fully algorithmic. For example, existing methods only check sufficient but not necessary conditions for correctness (e.g. =-=[JJ93]-=-), or only terminate in some cases (e.g. [PP91]), or only deal with channel systems of a certain type (e.g. [CF97]). c1?c p2 p3sLossy channels. A few years ago, Finkel, Abdulla and Jonsson independent... |

19 | Reasoning about probabilistic lossy channel systems
- Abdulla, Baier, et al.
- 2000
(Show Context)
Citation Context ...fair (do not lose all messages all the time) cannot be analyzed [AJ96a], and one cannot say whether systems are correct with probability 1 when messages are lost with low (less than 1 2 ) probability =-=[ABPJ00]-=-. Hence lossy channel systems are an example of a partially analyzable infinite-state system model (along with Petri nets, pushdown systems, . . . ) that has important practical applications [AKP97,AB... |

15 | Decidability of Bisimilarity for One-Counter Processes
- Jančar
- 2000
(Show Context)
Citation Context ...(as soon as we have one channel or two counters) and the classic-lossy semantics (as soon as we have two counters). Note that with only one counter, bisimulation is decidable even for perfect systems =-=[Jan00]-=-. The proof does not apply to systems with one single channel under the classiclossy semantics, and this is the main direction we see for future work. Another case where the proof does not apply is wh... |

11 | Programs with Quasi-Stable Channels are Effectively
- Cece, Finkel
(Show Context)
Citation Context ...ting methods only check sufficient but not necessary conditions for correctness (e.g. [JJ93]), or only terminate in some cases (e.g. [PP91]), or only deal with channel systems of a certain type (e.g. =-=[CF97]-=-). c1?c p2 p3sLossy channels. A few years ago, Finkel, Abdulla and Jonsson independently identified lossy channel systems as a very promising class of channel systems. With lossy systems, one assumes ... |

11 | On-the- analysis of systems with unbounded lossy Fifo-channels - Abdulla, Bouajjani, et al. |

10 | Finite State Description of Communication Protocols - Bochmann - 1978 |

8 |
Decidability of simulation and bisimulation between lossy channel systems and finite state systems
- Abdulla, Kindahl
(Show Context)
Citation Context ...s. Today, the main open question in the theory of lossy channel systems is the decidability of bisimulation, andsother equivalences. In this direction, almost nothing is known 1 . Abdulla and Kindahl =-=[AK95]-=- studied equivalence problems between a lossy channel system and a finite state system, but such problems are less general than checking equivalence between two infinite systems [JKM01] and the decida... |

7 |
Modular specification of process algebras
- Glabbeek, Vaandrager
- 1993
(Show Context)
Citation Context ...hingtime notions of behavior, where the timing of non-deterministic choices is important. The consequence is that two configurations can be bisimilar under one lossy semantics and not under the other =-=[GV93]-=-. Because of this, we consider both semantics and prove undecidability of bisimulation under each one. Definition 3.4 (Two Lossy Semantics). With a channel system S = 〈Q, Σ, C, Γ, ∆〉 we associate two ... |

6 | Techniques for decidability and undecidability of bisimilarity - Jancar, Moller - 1999 |

6 | Towards Analysing and Synthesizing Protocols - Zafiropulo, West, et al. - 1980 |

5 | Lossy counter machines - Mayr - 1998 |

5 | Symbolic Veri of Lossy Channel Systems: Application to the Bounded Retransmission Protocol - Abdulla, Annichini, et al. - 1999 |

5 | Veri on in structures - Burkart, Caucal, et al. - 2001 |

4 |
Programs with quasi-stable channels are eectively recognizable
- Cece, Finkel
- 1997
(Show Context)
Citation Context ...xisting methods only check sucient but not necessary conditions for correctness (e.g. [JJ93]), or only terminate in some cases (e.g. [PP91]), or only deal with channel systems of a certain type (e.g. =-=[CF97-=-]). 2 Ph. Schnoebelen Lossy channels. A few years ago, Finkel, Abdulla and Jonsson independently identied lossy channel systems as a very promising class of channel systems. With lossy systems, one as... |

3 |
Undecidable veri problems for programs with unreliable channels
- Abdulla, Jonsson
- 1996
(Show Context)
Citation Context ... and Jonsson proved that recurrent reachability properties are undecidable, so that model-checking problems for (branching-time or linear-time) temporal logic is undecidable for lossy channel systems =-=[AJ96a]-=-, and Mayr showed that boundedness is undecidable [May00]. Also, systems where the channels are unreliable but fair (do not lose all messages all the time) cannot be analyzed [AJ96a], and one cannot s... |

2 | An improved search strategy for lossy channel systems - Abdulla, Kindahl, et al. - 1997 |

1 |
Modular speci of process algebras
- Glabbeek, Vaandrager
- 1993
(Show Context)
Citation Context ...chingtime notions of behavior, where the timing of non-deterministic choices is important. The consequence is that two congurations can be bisimilar under one lossy semantics and not under the other [=-=GV-=-93]. Because of this, we consider both semantics and prove undecidability of bisimulation under each one. Denition 3.4 (Two Lossy Semantics). With a channel system S = hQ; ; C; ; i we associate two la... |

1 |
Testing for unboundedness of channels
- Jeron, Jard
- 1993
(Show Context)
Citation Context ...stems are Turing powerful, and no verication method for them can be general and fully algorithmic. For example, existing methods only check sucient but not necessary conditions for correctness (e.g. [=-=JJ93]-=-), or only terminate in some cases (e.g. [PP91]), or only deal with channel systems of a certain type (e.g. [CF97]). 2 Ph. Schnoebelen Lossy channels. A few years ago, Finkel, Abdulla and Jonsson inde... |

1 |
Data analysis of communicating nite state machines
- Peng, Iyer
- 1991
(Show Context)
Citation Context ...ethod for them can be general and fully algorithmic. For example, existing methods only check sucient but not necessary conditions for correctness (e.g. [JJ93]), or only terminate in some cases (e.g. =-=[PP91-=-]), or only deal with channel systems of a certain type (e.g. [CF97]). 2 Ph. Schnoebelen Lossy channels. A few years ago, Finkel, Abdulla and Jonsson independently identied lossy channel systems as a ... |