## Undecidable Verification Problems for Programs with Unreliable Channels (1994)

Venue: | Information and Computation |

Citations: | 58 - 11 self |

### BibTeX

@ARTICLE{Abdulla94undecidableverification,

author = {Parosh Aziz Abdulla and Bengt Jonsson},

title = {Undecidable Verification Problems for Programs with Unreliable Channels},

journal = {Information and Computation},

year = {1994},

volume = {130},

pages = {316--327}

}

### Years of Citing Articles

### OpenURL

### Abstract

We consider the verification of a particular class of infinite-state systems, namely systems consisting of finite-state processes that communicate via unbounded lossy FIFO channels. This class is able to model e.g. link protocols such as the Alternating Bit Protocol and HDLC. In an earlier paper, we showed that the problems of checking reachability, safety properties, and eventuality properties are decidable for this class of systems. In this paper, we show that the following problems are undecidable, namely ffl The model checking problem in propositional temporal logics such as Propositional Linear Time Temporal Logic (PTL) and Computation Tree Logic (CTL). ffl The problem of deciding eventuality properties with fair channels: do all computations eventually reach a given set of states if the unreliable channels satisfy fairness assumptions. The results are obtained through a reduction from a variant of Post's Correspondence Problem. This research report is a revised and extended ...

### Citations

1506 |
The Temporal Logic of Reactive and Concurrent Systems - Specification
- Manna, Pnueli
- 1992
(Show Context)
Citation Context ...d p 62 f(s 0 ) for any s 0 6= s. The formula OE is defined as 32:p. 2 5.2 Hierarchy of Decidable Problems in PTL Relating to the hierarchy of properties expressible in PTL defined by Manna and Pnueli =-=[MP92]-=-, the following can be concluded about lossy channel systems. Safety properties (2p), eventuality properties or guarantee propertiess(3p) and obligation properties (2ps3q) are decidable . Response pro... |

1184 | Automatic verification of finite-state concurrent systems using temporal logic specifications
- Clarke, Emerson, et al.
- 1986
(Show Context)
Citation Context ...ication of finite-state systems, for which efficient algorithmic verification methods have been developed and successfully applied to e.g. communication protocols and hardware structures ([BCM + 90], =-=[CES86]-=-, [Hol91], [VW86], etc.). For infinite-state systems, e.g. systems that operate on data from unbounded domains, algorithmic verification is more difficult. In general, verification of infinite-state s... |

769 |
Design and Validation of Computer Protocols
- Holzmann
- 1991
(Show Context)
Citation Context ...f finite-state systems, for which efficient algorithmic verification methods have been developed and successfully applied to e.g. communication protocols and hardware structures ([BCM + 90], [CES86], =-=[Hol91]-=-, [VW86], etc.). For infinite-state systems, e.g. systems that operate on data from unbounded domains, algorithmic verification is more difficult. In general, verification of infinite-state systems re... |

586 |
An automata-theoretic approach to automatic program verification
- Vardi, Wolper
(Show Context)
Citation Context ...state systems, for which efficient algorithmic verification methods have been developed and successfully applied to e.g. communication protocols and hardware structures ([BCM + 90], [CES86], [Hol91], =-=[VW86]-=-, etc.). For infinite-state systems, e.g. systems that operate on data from unbounded domains, algorithmic verification is more difficult. In general, verification of infinite-state systems requires a... |

360 | Model-checking for realtime systems - Alur, Courcoubetis, et al. - 1990 |

273 |
Ordering by divisibility in abstract algebras
- Higman
- 1952
(Show Context)
Citation Context ...n's theorem) Let M be a finite set. There is no infinite sequence w 1 w 2 w 3 \Delta \Delta \Delta of strings in M , such that w i 6�� w j for all i ! j. The proof of the theorem can be found e.g.=-= in [Hig52]-=- and [Cou91]. It is straightforward to generalize the theorem to sequences fl 1 fl 2 fl 3 \Delta \Delta \Delta of global states. 4.2 The Recurrent State Problem (RSP) For a lossy channel system L, a c... |

239 |
P.: On communicating finite-state machines
- Brand, Zafiropulo
- 1983
(Show Context)
Citation Context ...ult was quite surprising in view of the fact that all nontrivial verification problems are undecidable for the class of finite-state systems that communicate via unbounded perfect FIFO channels (e.g. =-=[BZ83]-=-). Lossy channel systems can model many interesting systems, e.g. link protocols such as the Alternating Bit Protocol [BSW69] and HDLC [ISO79]. The HDLC protocol is intended to provide reliable full-d... |

175 | B.: Verifying programs with unreliable channels
- Abdulla, Jonsson
- 1993
(Show Context)
Citation Context ...f finite-state systems that communicate via unbounded but lossy FIFO channels (called lossy channel systems), and proved that several interesting verification problems are decidable for these systems =-=[AJ93]-=-. This result was quite surprising in view of the fact that all nontrivial verification problems are undecidable for the class of finite-state systems that communicate via unbounded perfect FIFO chann... |

163 | A note on reliable full-duplex transmission over half-duplex links
- Bartlett, Scantlebury, et al.
- 1969
(Show Context)
Citation Context ...te-state systems that communicate via unbounded perfect FIFO channels (e.g. [BZ83]). Lossy channel systems can model many interesting systems, e.g. link protocols such as the Alternating Bit Protocol =-=[BSW69]-=- and HDLC [ISO79]. The HDLC protocol is intended to provide reliable full-duplex data transfer between protocol entities, using an error-prone physical communication channel. The protocol includes pro... |

155 | Parallel program schemata - Karp, Miller - 1969 |

129 | Reasoning about systems with many processes - German, Sistla - 1992 |

117 |
Expressing interesting properties of programs in propositional temporal logic
- Wolper
- 1986
(Show Context)
Citation Context ...fication procedure for reasoning about a certain set of temporal properties over systems with FIFO channels. The method is not powerful enough to reason about arbitrary finite state processes. Wolper =-=[Wol86]-=- shows that by using an assumption of data-independence, the problem of proving that a data-independent systems satisfies the specification of a perfect FIFO channel can be transformed into a verifica... |

92 | C.: Bisimulation equivalence is decidable for all context-free processes - Christensen, Hüttel, et al. - 1995 |

78 | Model checking for context-free processes - Burkart, Steffen |

67 | Ccs + time = an interleaving model for real time systems - Yi - 1991 |

64 | Decidability of bisimulation equivalences for parallel timer processes - Čerāns - 1993 |

53 | Bisimulation equivalence is decidable for basic parallel processes - Christensen, Hirshfeld, et al. - 1993 |

50 | Avoiding the state explosion problem in temporal logic model checking - Clarke, Grumberg - 1987 |

39 | Time-abstracted bisimulation: Implicit specifications and decidability - Larsen, Yi - 1997 |

38 |
Decidability of a temporal logic problem for petri nets
- Jančar
- 1990
(Show Context)
Citation Context ... operate on clocks [ACD90, C92, LY93], data-independent systems [JP93, Wol86], systems with many identical processes [CG87, GS92, SG90], context-free processes ([BS92, CHS92, CHM93]), and Petri nets (=-=[Jan90]-=-). Recently, the authors of this paper considered the class of finite-state systems that communicate via unbounded but lossy FIFO channels (called lossy channel systems), and proved that several inter... |

36 | Deciding bisimulation equivalence for a class of nonfinite-state programs - Jonsson, Parrow - 1993 |

32 |
Protocol description and analysis based on a state transition model with channel expressions
- Pachl
- 1987
(Show Context)
Citation Context ...e.g. channel alphabets of size one [KM69, RY86], bounded channel languages [GGLR87, CF87], and others [Fin88]). These classes are restrictive and do not cover e.g. the Alternating Bit Protocol. Pachl =-=[Pac87]-=- shows that the reachability problem is decidable if the set of reachable states of the system for each control state consists of a set of channel contents that constitute a recognizable language (a l... |

30 |
Decidability of the termination problem for completely specified protocols
- Finkel
- 1994
(Show Context)
Citation Context ...ransformation to the reachability problem. ffl Eventuality properties: Do all computations of a system eventually reach a given set of states. This result has also been proven independently by Finkel =-=[Fin94]-=-. In this paper, we investigate the decidability of more general verification problems for the same class of systems. It might be expected that the techniques used for proving decidability of the prev... |

26 |
S.: Data flow analysis of communicating finite state machines
- Peng, Puroshothaman
- 1991
(Show Context)
Citation Context ...nite union of cartesian products of regular languages). Algorithms that are not decision procedures, and which may or may not succeed for a given system, have been developed by Purushothaman and Peng =-=[PP91]-=- and by Brand and Joyner [BZ83]. Sistla and Zuck [SZ91] present a verification procedure for reasoning about a certain set of temporal properties over systems with FIFO channels. The method is not pow... |

17 | Network grammars, communication behaviours and automatic veri - Stadler, Grumberg - 1989 |

13 | On deadlock detection in systems of communicating finite state machines - Gouda, Gurari, et al. - 1987 |

9 |
A new class of analyzable CFSMs with unbounded FIFO channels
- Finkel
- 1988
(Show Context)
Citation Context ... tape of a Turing Machine [BZ83]. Decidability results have been obtained for limited subclasses (e.g. channel alphabets of size one [KM69, RY86], bounded channel languages [GGLR87, CF87], and others =-=[Fin88]-=-). These classes are restrictive and do not cover e.g. the Alternating Bit Protocol. Pachl [Pac87] shows that the reachability problem is decidable if the set of reachable states of the system for eac... |

8 | Boundedness, empty channel detection, and synchronization for communicating finite automata - Rosier, Yen - 1986 |

8 |
Automatic Temporal Verification of Buffer Systems
- Sistla, Zuck
- 1991
(Show Context)
Citation Context ... Algorithms that are not decision procedures, and which may or may not succeed for a given system, have been developed by Purushothaman and Peng [PP91] and by Brand and Joyner [BZ83]. Sistla and Zuck =-=[SZ91]-=- present a verification procedure for reasoning about a certain set of temporal properties over systems with FIFO channels. The method is not powerful enough to reason about arbitrary finite state pro... |

7 |
On constructing obstruction sets of words
- Courcelle
- 1991
(Show Context)
Citation Context ... Let M be a finite set. There is no infinite sequence w 1 w 2 w 3 \Delta \Delta \Delta of strings in M , such that w i 6�� w j for all i ! j. The proof of the theorem can be found e.g. in [Hig52] =-=and [Cou91]. -=-It is straightforward to generalize the theorem to sequences fl 1 fl 2 fl 3 \Delta \Delta \Delta of global states. 4.2 The Recurrent State Problem (RSP) For a lossy channel system L, a computation �... |

7 |
On Some Variants of Post’s Correspondence Problem
- Ruohonen
(Show Context)
Citation Context ...fairness property for lossy channel systems. The undecidability of RSP is shown through a reduction from a variant of the Post's Correspondence Problem called the Cyclic Post's Correspondence Problem =-=[Ruo83]-=-. As far as we are aware, this is the first application of the Cyclic Post's Correspondence Problem to prove the undecidabilty of a property for infinite traces. The fact that RSP corresponds to one p... |

6 | Simulation of linear FIFO nets having a structured set of terminal markings - Choquet, Finkel - 1987 |

4 |
communications -- HDLC procedures -- elements of procedures
- Data
- 1979
(Show Context)
Citation Context ...that communicate via unbounded perfect FIFO channels (e.g. [BZ83]). Lossy channel systems can model many interesting systems, e.g. link protocols such as the Alternating Bit Protocol [BSW69] and HDLC =-=[ISO79]-=-. The HDLC protocol is intended to provide reliable full-duplex data transfer between protocol entities, using an error-prone physical communication channel. The protocol includes procedures both for ... |