## Verifying Timing Properties of Concurrent Algorithms (1994)

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Citations: | 16 - 6 self |

### BibTeX

@MISC{Luchangco94verifyingtiming,

author = {Victor Luchangco and Ekrem Söylemez and Stephen Garland and Nancy Lynch},

title = { Verifying Timing Properties of Concurrent Algorithms},

year = {1994}

}

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### Abstract

This paper presents a method for computer-aided verification of timing properties of real-time systems. A timed automaton model, along with invariant assertion and simulation techniques for proving properties of real-time systems, is formalized within the Larch Shared Language. This framework is then used to prove time bounds for two sample algorithms -- a simple counter and Fischer's mutual exclusion protocol. The proofs are checked using the Larch Prover.

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Citation Context ..., 4]; the primary di erences are that both tools now support full rst-order logic, and that LP now has features for reasoning about linear inequalities [17] similar to those in the Boyer-Moore prover =-=[2, 3]-=- and in PVS [19]. 2.3. Machine-Readable De nitions Figure 2 contains an LSL de nition of the untimed part of automaton C k. This formal de nition mimics the de nition given in Figure 1. It builds upon... |

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Citation Context ..., 4]; the primary di erences are that both tools now support full rst-order logic, and that LP now has features for reasoning about linear inequalities [17] similar to those in the Boyer-Moore prover =-=[2, 3]-=- and in PVS [19]. 2.3. Machine-Readable De nitions Figure 2 contains an LSL de nition of the untimed part of automaton C k. This formal de nition mimics the de nition given in Figure 1. It builds upon... |

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Citation Context ...c. 3. Fischer's Mutual Exclusion Algorithm In this section, we use timed automata to model Fischer's well-known timing-based mutual exclusion algorithm, which uses a single shared read-write register =-=[7]-=-. We use 1Two periods .. in this proof script mark the end of a multiline LP command; they do not indicate any elision of the script. 2While the length of this proof suggests room for improvementinLP,... |

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Citation Context ...ilities. Later, we use the Larch Prover (LP), which provides assistance for reasoning in rst-order logic. The versions of these tools used for this paper are enhancements of the versions described in =-=[5, 4]-=-; the primary di erences are that both tools now support full rst-order logic, and that LP now has features for reasoning about linear inequalities [17] similar to those in the Boyer-Moore prover [2, ... |

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Citation Context ...stems has the same attractions as for untimed systems. Furthermore, it is capable of proving performance as well as correctness properties. Examples of proofs done by hand using this method appear in =-=[11, 10, 20, 6, 9]-=-. Just as in the untimed case, the timed proofs are amenable to automation. Speci cally, the notions of timed automata, invariant assertions, and simulation mappings are formalized using the Larch Sha... |

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Citation Context ...method has been extended to proofs of correctness and timing properties for timing-based systems [11, 13, 10]. The extended method is based on the timed automaton model of Merritt, Modugno and Tuttle =-=[15]-=-. Both the speci cation and implementation are described as timed automata, which include timing conditions in their states. The implementation's conditions represent timing assumptions, and the speci... |

63 | Forward and backward simulations for timingbased systems
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Citation Context ...omated, for example, using HOL [8], Isabelle [16], and the Larch Prover [21]. Recently, the simulation method has been extended to proofs of correctness and timing properties for timing-based systems =-=[11, 13, 10]-=-. The extended method is based on the timed automaton model of Merritt, Modugno and Tuttle [15]. Both the speci cation and implementation are described as timed automata, which include timing conditio... |

38 |
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Citation Context ...rastructure is used to specify, verify, and analyze two sample algorithms|a simple counter [11] and Fischer's mutual exclusion protocol. Fischer's algorithm has been veri ed many times by many people =-=[1, 18, 19]-=-, including some with machine assistance [19]. But in addition to the usual correctness property ofmutual exclusion, we prove a more di cult timing property|an upper bound on the time from when some p... |

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Citation Context ...rastructure is used to specify, verify, and analyze two sample algorithms|a simple counter [11] and Fischer's mutual exclusion protocol. Fischer's algorithm has been veri ed many times by many people =-=[1, 18, 19]-=-, including some with machine assistance [19]. But in addition to the usual correctness property ofmutual exclusion, we prove a more di cult timing property|an upper bound on the time from when some p... |

23 |
Larch: Languages and Tools for Formal Speci cation
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Citation Context ...the untimed case, the timed proofs are amenable to automation. Speci cally, the notions of timed automata, invariant assertions, and simulation mappings are formalized using the Larch Shared Language =-=[5]-=-, and this formal infrastructure is used to specify, verify, and analyze two sample algorithms|a simple counter [11] and Fischer's mutual exclusion protocol. Fischer's algorithm has been veri ed many ... |

21 | Simulation techniques for proving properties of real-time systems
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Citation Context ...omated, for example, using HOL [8], Isabelle [16], and the Larch Prover [21]. Recently, the simulation method has been extended to proofs of correctness and timing properties for timing-based systems =-=[11, 13, 10]-=-. The extended method is based on the timed automaton model of Merritt, Modugno and Tuttle [15]. Both the speci cation and implementation are described as timed automata, which include timing conditio... |

19 | Verification of a multiprocessor cache protocol using simulation relations and higher-order logic - LOEWENSTEIN, DILL - 1990 |

13 |
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Citation Context ...omated, for example, using HOL [8], Isabelle [16], and the Larch Prover [21]. Recently, the simulation method has been extended to proofs of correctness and timing properties for timing-based systems =-=[11, 13, 10]-=-. The extended method is based on the timed automaton model of Merritt, Modugno and Tuttle [15]. Both the speci cation and implementation are described as timed automata, which include timing conditio... |

4 |
Using simulation techiniques to prove timing properties
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Citation Context ...stems has the same attractions as for untimed systems. Furthermore, it is capable of proving performance as well as correctness properties. Examples of proofs done by hand using this method appear in =-=[11, 10, 20, 6, 9]-=-. Just as in the untimed case, the timed proofs are amenable to automation. Speci cally, the notions of timed automata, invariant assertions, and simulation mappings are formalized using the Larch Sha... |

4 |
Veri cation of Real-Time Systems Using PVS
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Citation Context ...rastructure is used to specify, verify, and analyze two sample algorithms|a simple counter [11] and Fischer's mutual exclusion protocol. Fischer's algorithm has been veri ed many times by many people =-=[1, 18, 19]-=-, including some with machine assistance [19]. But in addition to the usual correctness property ofmutual exclusion, we prove a more di cult timing property|an upper bound on the time from when some p... |

4 | Lynch and Frits Vaandrager. Forward and backward simulations: I. untimed systems - Nancy - 1995 |

4 | editors, Stepwise Refinement of Distributed Systems - Bakker, Rozenberg - 1989 |

3 |
Veri cation of a multiprocessor cache protocol using simulation relations
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Citation Context ...rved is an exercise in equational deduction. Such deductions are natural candidates for partial automation. Proofs of this sort for untimed systems have already been automated, for example, using HOL =-=[8]-=-, Isabelle [16], and the Larch Prover [21]. Recently, the simulation method has been extended to proofs of correctness and timing properties for timing-based systems [11, 13, 10]. The extended method ... |

3 | Formal verification of data type refinement - Nipkow - 1989 |

3 | Correctness of Protocols in Distributed Systems - Sgaard-Andersen - 1993 |

3 | Electrical Engineering and Computer Science - thesis, MIT - 1994 |

2 |
Formal veri cation of data type re nement | theory and practice
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Citation Context ...rcise in equational deduction. Such deductions are natural candidates for partial automation. Proofs of this sort for untimed systems have already been automated, for example, using HOL [8], Isabelle =-=[16]-=-, and the Larch Prover [21]. Recently, the simulation method has been extended to proofs of correctness and timing properties for timing-based systems [11, 13, 10]. The extended method is based on the... |

2 |
Incorporating specialized theories in a general purpose theorem prover
- Pogosyants
- 1994
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Citation Context ...are enhancements of the versions described in [5, 4]; the primary di erences are that both tools now support full rst-order logic, and that LP now has features for reasoning about linear inequalities =-=[17]-=- similar to those in the Boyer-Moore prover [2, 3] and in PVS [19]. 2.3. Machine-Readable De nitions Figure 2 contains an LSL de nition of the untimed part of automaton C k. This formal de nition mimi... |

2 |
rgen S gaard-Andersen. Correctness of Protocols in Distributed Systems
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Citation Context ...stems has the same attractions as for untimed systems. Furthermore, it is capable of proving performance as well as correctness properties. Examples of proofs done by hand using this method appear in =-=[11, 10, 20, 6, 9]-=-. Just as in the untimed case, the timed proofs are amenable to automation. Speci cally, the notions of timed automata, invariant assertions, and simulation mappings are formalized using the Larch Sha... |

1 |
Anya Pogosyants. Computer-assisted simulation proofs
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Citation Context ...on. Such deductions are natural candidates for partial automation. Proofs of this sort for untimed systems have already been automated, for example, using HOL [8], Isabelle [16], and the Larch Prover =-=[21]-=-. Recently, the simulation method has been extended to proofs of correctness and timing properties for timing-based systems [11, 13, 10]. The extended method is based on the timed automaton model of M... |

1 | Anya Pogosyants. Computer-assisted simulation proofs - S��gaard-Andersen, Garland, et al. - 1993 |