## Forward and Backward Simulations Part I: Untimed Systems (1995)

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Venue: | Information and Computation |

Citations: | 134 - 18 self |

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@ARTICLE{Lynch95forwardand,

author = {Nancy Lynch and Frits Vaandrager},

title = {Forward and Backward Simulations Part I: Untimed Systems},

journal = {Information and Computation},

year = {1995},

volume = {121},

pages = {214--233}

}

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### Abstract

A unified, comprehensive presentation of simulation techniques for verification of concurrent systems is given, in terms of a simple untimed automaton model. In particular, (1) refinements, (2) forward and backward simulations, (3) hybrid forward-backward and backward-forward simulations, and (4) history and prophecy relations are defined. History and prophecy relations are abstract versions of the history and prophecy variables of Abadi and Lamport, as well as the auxiliary variables of Owicki and Gries. Relationships between the different types of simulations, as well as soundness and completeness results, are stated and proved. Finally, it is shown how invariants can be incorporated into all the simulations. Even though many results are presented here for the first time, this paper can also be read as a survey (in a simple setting) of the research literature on simulation techniques. The development for untimed automata is designed to support a similar development for timed automata...

### Citations

438 | The existence of refinement mappings
- Abadi, Lamport
- 1991
(Show Context)
Citation Context ...ckward and backward-forward simulations. We also define history relations and prophecy relations, which are abstract versions of the history and prophecy variables, respectively, of Abadi and Lamport =-=[1]-=-. We prove implication relationships among the different types of simulations, as well as soundness and completeness theorems. Finally, we show how invariants can be incorporated into all of the simul... |

413 |
Proof of correctness of data representations
- Hoare
- 1972
(Show Context)
Citation Context ...imulations in proving correctness has been well demonstrated. Abstraction mappings, which are essentially refinement mappings, comprise a basic proof method for implementations of abstract data types =-=[6, 18]-=-. Typical examples of forward simulation proofs appear in [20]. Backward simulations have been much less widely used. Abadi and Lamport [1] demonstrate the usefulness of prophecy variables (and hence ... |

388 |
Defining liveness
- Alpern, Schneider
- 1985
(Show Context)
Citation Context ...ta refinement of [7]. The present paper provides complete proof methods for trace inclusion between automata with finite invisible nondeterminism. Such automata express the class of safety properties =-=[2]-=-. For simplicity, we have not considered liveness properties here. Simulation techniques that deal with liveness are for instance described in [21, 22, 1, 8]. The results of [1, 8] are more general th... |

55 | Refinement calculus, part I: Sequential nondeterministic programs
- Back, Wright
(Show Context)
Citation Context ...terminism. We preferred not to use this notion since it fails to reduce reasoning about entire executions to reasoning about individual states and transitions. 7. This paper is related to the work of =-=[17, 18, 3, 7, 48]-=- on data refinement. In [17], an operation is a binary relation over some universal set \Sigma. A data type is a triple (AI ; AO ; AF ), where AI and AF are the initialization and finalization operati... |

48 |
Algebraic Theory of Automata
- Ginzburg
- 1969
(Show Context)
Citation Context ...simulation we consider is a refinement, which is a functional simulation similar to those studied in [16] and very similar to a homomorphism between automata in the sense of classical automata theory =-=[4]-=-. A refinement from an automaton A to another automaton B is a function from states of A to states of B such that (a) the image of every start state of A is a start state of B, and (b) every step of A... |

38 | The existence of re nement mappings - Abadi, Lamport - 1991 |

32 |
Simulations between specifications of distributed systems
- Jonsson
- 1991
(Show Context)
Citation Context ...d to a single state of A. Forward simulations are similar to the the simulations of [27, 8], the possibilities mappings of [19, 21], the downward simulations of [7, 12, 5], the forward simulations of =-=[11]-=-, and the history measures of [14]. The correspondence conditions (a) and (b) above are generalized so that (a) every start state of A has some image that is a start state of B, and (b) every step of ... |

30 |
Compositional Verification of Distributed Systems
- Jonsson
- 1987
(Show Context)
Citation Context ...ions and backward simulations, which are generalizations of refinements that allow a set of states of B to correspond to a single state of A. Forward simulations are similar to the the simulations of =-=[27, 8]-=-, the possibilities mappings of [19, 21], the downward simulations of [7, 12, 5], the forward simulations of [11], and the history measures of [14]. The correspondence conditions (a) and (b) above are... |

25 | De ning liveness - Alpern, Schneider - 1985 |

19 |
Process simulation and refinement
- He
- 1989
(Show Context)
Citation Context ...allow a set of states of B to correspond to a single state of A. Forward simulations are similar to the the simulations of [27, 8], the possibilities mappings of [19, 21], the downward simulations of =-=[7, 12, 5]-=-, the forward simulations of [11], and the history measures of [14]. The correspondence conditions (a) and (b) above are generalized so that (a) every start state of A has some image that is a start s... |

19 |
Prespecification in data refinement
- Hoare, He, et al.
- 1987
(Show Context)
Citation Context ...allow a set of states of B to correspond to a single state of A. Forward simulations are similar to the the simulations of [27, 8], the possibilities mappings of [19, 21], the downward simulations of =-=[7, 12, 5]-=-, the forward simulations of [11], and the history measures of [14]. The correspondence conditions (a) and (b) above are generalized so that (a) every start state of A has some image that is a start s... |

17 |
On decomposing and refining specifications of distributed systems
- Jonsson
- 1990
(Show Context)
Citation Context ..., we give soundness and partial completeness results. Backward simulations occurred first in [7] under the name of upward simulations and were used later in the setting of CSP in [12, 5]. In [24] and =-=[10]-=-, where they are called prophecy mappings and backwards simulations, respectively, it is observed that they are closely related to the prophecy variables first defined in [1]. In the case of a backwar... |

14 |
Modular verification of asynchronous networks
- Jonsson
- 1987
(Show Context)
Citation Context ...e Lemma 4.8 to show that if f and f 0 are forward simulations from A to B and from B to C, respectively, f 0 ffi f is a forward simulation from A to C. Theorem 4.10 (Soundness of forward simulations, =-=[21, 9, 30]-=-) AsF B ) A T B. Proof: Versions of this proof appears in the cited papers. The proof is similar to that of Theorem 4.4. Theorem 4.11 (Partial completeness of forward simulations) Suppose B is determi... |

5 | Re nement calculus, part I: Sequential nondeterministic programs - Back, Wright - 1989 |

2 |
Foundations of compositional program refinement (first version
- Gerth
(Show Context)
Citation Context ... Schneider who call them invariants in [13] and ND measures in [14]. They also occur in the work of Jonsson [11] under the name subset simulations, and are related to the failure simulations of Gerth =-=[3]-=-. Forward-backward simulations combine in a single relation both a forward and a backward simulation. Below we present simple proofs of their soundness and completeness by making this connection expli... |