## Homotopy and Concurrency (1994)

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Venue: | Bulletin of the EATCS |

Citations: | 27 - 2 self |

### BibTeX

@ARTICLE{Gunawardena94homotopyand,

author = {Jeremy Gunawardena},

title = {Homotopy and Concurrency},

journal = {Bulletin of the EATCS},

year = {1994},

volume = {54},

pages = {184--193}

}

### Years of Citing Articles

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### Abstract

In this paper we give a homotopy theoretic proof of a well-known result in database engineering: that 2-phase locking is safe. The proof gives an immediate intuitive reason for why the 2-phase locking condition implies safety. We point out a number of interesting open questions regarding the interplay between homotopy and concurrency. Keywords: Homotopy theory, serializability, 2-phase locking, concurrency theory 1 Introduction What has homotopy got to do with concurrency? At first sight it seems unlikely that there should be any relationship between these two subjects. After all, homotopy theory is about continuous objects while concurrency typically deals with discrete structures. In this paper I will try to show that, on the contrary, there may be a very natural relationship between the two. Instead of making a lot of abstract statements about homotopy and concurrency I would like to work through the proof of a theorem which all database engineers learn at their Mother's knee: th...

### Citations

1604 |
Concurrency control and recovery in database systems
- BERNSTEIN, HADZILACOS, et al.
- 1987
(Show Context)
Citation Context ...ait for the deadlock to occur and roll back the execution (ie: to run time backwards). Deadlock detection and recovery are important issues for database engineers but they do not concern us here; see =-=[1]-=- for more information. Why does 2PL work? It is at this point that ideas from topology become useful. Consider two paths of a transaction system which are homotopic. To make this precise, think of a p... |

1520 | Impossibility of distributed consensus with one faulty process
- FISCHER, LYNCH, et al.
- 1985
(Show Context)
Citation Context ...otios Zaharoglu, [16], Elizabeth Borowsky and Eli Gafni, [2], Maurice Herlihy and Nir Shavit, [10, 11, 12], have found important generalisations of the classical Fischer, Lynch and Patterson Theorem, =-=[7]-=-, using arguments from combinatorial and algebraic topology. Serious discussion of these contributions would exceed my brief here. This paper is an appetizer; the main course awaits those who are temp... |

180 |
Atomic transactions
- LYNCH, MERRIT, et al.
- 1993
(Show Context)
Citation Context ...ribed above. Nowadays one must contend with distributed databases, nested transactions, multiple versions, replication, recovery from aborts, etc. The recent book by Lynch, Merritt, Weihl and Fekete, =-=[14]-=-, gives an account of the modern approach which is based on the Atomicity Theorem, [14, Theorem 5.24], a substantial generalisation of the classical Serializability Theorem. Is there a homotopy theore... |

146 |
Generalized FLP impossibility result for t-resilient asynchronous computations
- Boroswsky, Gafni
- 1993
(Show Context)
Citation Context ...f "higher dimensional automata" as a semantic framework for true concurrency. In a different direction, Soma Chaudhuri, [4], Michael Saks and Fotios Zaharoglu, [16], Elizabeth Borowsky and E=-=li Gafni, [2]-=-, Maurice Herlihy and Nir Shavit, [10, 11, 12], have found important generalisations of the classical Fischer, Lynch and Patterson Theorem, [7], using arguments from combinatorial and algebraic topolo... |

131 | Modeling concurrency with geometry, in
- Pratt
- 1991
(Show Context)
Citation Context ...ple of the potential relationship between homotopy and concurrency. In recent years a number of people have used ideas from homotopy theory and algebraic topology to study concurrency. Vaughan Pratt, =-=[15], Rob van -=-Glabbeek, [17], Eric Goubault and Thomas Jensen, [8, 9], have developed a theory of "higher dimensional automata" as a semantic framework for true concurrency. In a different direction, Soma... |

102 | More Choices allow more faults: Set consensus problems in totally asynchronous systems
- Chaudhuri
- 1993
(Show Context)
Citation Context ...abbeek, [17], Eric Goubault and Thomas Jensen, [8, 9], have developed a theory of "higher dimensional automata" as a semantic framework for true concurrency. In a different direction, Soma C=-=haudhuri, [4]-=-, Michael Saks and Fotios Zaharoglu, [16], Elizabeth Borowsky and Eli Gafni, [2], Maurice Herlihy and Nir Shavit, [10, 11, 12], have found important generalisations of the classical Fischer, Lynch and... |

96 | The Asynchronous Computability Theorem for t-Resilient Tasks
- Herlihy, Shavit
- 1993
(Show Context)
Citation Context ...semantic framework for true concurrency. In a different direction, Soma Chaudhuri, [4], Michael Saks and Fotios Zaharoglu, [16], Elizabeth Borowsky and Eli Gafni, [2], Maurice Herlihy and Nir Shavit, =-=[10, 11, 12]-=-, have found important generalisations of the classical Fischer, Lynch and Patterson Theorem, [7], using arguments from combinatorial and algebraic topology. Serious discussion of these contributions ... |

94 | System deadlocks
- Coffman, Elphick, et al.
- 1971
(Show Context)
Citation Context ...iolating one of the forbidden boxes or running time backwards. This corresponds to a deadlock. This geometric way of representing the behaviour of semaphore programmes seems to have first appeared in =-=[5] where it -=-is attributed, without reference, to Djikstra. It is sometimes referred to as a "progress graph". The problem of detecting deadlocks in such systems has generated some elegant work which exp... |

43 | Homology of higher dimensional automata
- Goubault, Jensen
- 1992
(Show Context)
Citation Context ...ncy. In recent years a number of people have used ideas from homotopy theory and algebraic topology to study concurrency. Vaughan Pratt, [15], Rob van Glabbeek, [17], Eric Goubault and Thomas Jensen, =-=[8, 9], have dev-=-eloped a theory of "higher dimensional automata" as a semantic framework for true concurrency. In a different direction, Soma Chaudhuri, [4], Michael Saks and Fotios Zaharoglu, [16], Elizabe... |

38 | A Simple Constructive Computability Theorem for Wait-Free Computation
- Herlihy, Shavit
- 1994
(Show Context)
Citation Context ...semantic framework for true concurrency. In a different direction, Soma Chaudhuri, [4], Michael Saks and Fotios Zaharoglu, [16], Elizabeth Borowsky and Eli Gafni, [2], Maurice Herlihy and Nir Shavit, =-=[10, 11, 12]-=-, have found important generalisations of the classical Fischer, Lynch and Patterson Theorem, [7], using arguments from combinatorial and algebraic topology. Serious discussion of these contributions ... |

22 |
Bisimulation semantics for higher dimensional automata
- Glabbeek
- 1991
(Show Context)
Citation Context ...ationship between homotopy and concurrency. In recent years a number of people have used ideas from homotopy theory and algebraic topology to study concurrency. Vaughan Pratt, [15], Rob van Glabbeek, =-=[17], Eric Gou-=-bault and Thomas Jensen, [8, 9], have developed a theory of "higher dimensional automata" as a semantic framework for true concurrency. In a different direction, Soma Chaudhuri, [4], Michael... |

16 |
A fast algorithm for testing for safety and detecting deadlocks in locked transaction systems
- Lipski, Papadimitriou
- 1981
(Show Context)
Citation Context ...e characterisation of safety in dimension 2 was later used by Lipski and Papadimitriou to give an elegant O(n log n log log n) algorithm for checking safety in two transaction systems with n records, =-=[13]-=-. The paper by Yannakakis, Papadimitriou and Kung contains much more. They give a characterisation of safety in any dimension and use this to prove not only that 2PL is safe (in any dimension) but als... |

14 |
The geometry of semaphore programs
- Carson, Reynolds
- 1987
(Show Context)
Citation Context ... as a "progress graph". The problem of detecting deadlocks in such systems has generated some elegant work which exploits the underlying geometry; see, for instance, the paper by Carson and =-=Reynolds, [3]-=-. Semaphore programmes are more subtle than one might think at first sight, especially when there are more than two transactions. An useful example to think about is the following T 1 = PxPyP zV xPwV ... |

7 | Experimentation and proof in mathematics - Epstein, Levy - 1995 |

6 |
Partial Order Methods for Temporal Verification
- Wolper, Godefroid
- 1993
(Show Context)
Citation Context ... put it another way, the holes in the space arise from mutual exclusion.) Commutativity has appeared in various guises in concurrency. To give just one example, Valmari, Godefroid, Wolper and others, =-=[18]-=-, have used it to circumvent the state explosion problem. Commutativity is applied at each state, or locally, as a topologist would say, to show that certain paths need not be searched (because they a... |

5 |
Locking policies: Safety and freedom from deadlock
- Yannakakis, Papadimitriou, et al.
- 1979
(Show Context)
Citation Context ...t homotopy of paths implies equivalence (in the sense that of having the same effect on the database) was first pointed out by Yannakakis, Papadimitriou and Kung, but only for systems in dimension 2, =-=[19] and [13, -=-Theorem 1]. They also gave a characterisation of safety in dimension 2 by requiring that a "convex closure" 1 of the forbidden regions be connected, [19, Theorem 3]. This characterisation do... |

4 | Co-operating sequential processes - Djikstra - 1968 |

2 |
A tutorial on algebriac topology and distributed computation. Draft available from herlihy@crl.dec.com
- Herlihy
- 1994
(Show Context)
Citation Context ...semantic framework for true concurrency. In a different direction, Soma Chaudhuri, [4], Michael Saks and Fotios Zaharoglu, [16], Elizabeth Borowsky and Eli Gafni, [2], Maurice Herlihy and Nir Shavit, =-=[10, 11, 12]-=-, have found important generalisations of the classical Fischer, Lynch and Patterson Theorem, [7], using arguments from combinatorial and algebraic topology. Serious discussion of these contributions ... |

2 |
free k-set agreement is impossible: the topology of public knowledge
- Wait
- 1993
(Show Context)
Citation Context ...ensen, [8, 9], have developed a theory of "higher dimensional automata" as a semantic framework for true concurrency. In a different direction, Soma Chaudhuri, [4], Michael Saks and Fotios Z=-=aharoglu, [16]-=-, Elizabeth Borowsky and Eli Gafni, [2], Maurice Herlihy and Nir Shavit, [10, 11, 12], have found important generalisations of the classical Fischer, Lynch and Patterson Theorem, [7], using arguments ... |

1 | Concurrency without homotopy - Parrow - 1995 |