## Towards a Formal Semantics of Verilog using Duration Calculus (1998)

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Venue: | Formal Techniques for Real-Time and Fault Tolerant Systems (FTRTFT'98). LNCS |

Citations: | 8 - 2 self |

### BibTeX

@INPROCEEDINGS{Schneider98towardsa,

author = {Gerardo Schneider and Qiwen Xu},

title = {Towards a Formal Semantics of Verilog using Duration Calculus},

booktitle = {Formal Techniques for Real-Time and Fault Tolerant Systems (FTRTFT'98). LNCS},

year = {1998},

pages = {282--293},

publisher = {Springer-Verlag}

}

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### Abstract

We formalise the semantics of V \Gamma , a simple version of Verilog hardware description language using an extension of Duration Calculus. The language is simple enough for experimenting formalisation, but contains sufficient features for being practically relevant. V \Gamma programs can exhibit a rich variety of computations, and it is therefore necessary to extend Duration Calculus with several features, including Weakly Monotonic Time, infinite intervals and fixed point operators. The semantics is compositional and can be used as the formal basis of a formal theory of Verilog. Gerardo Schneider is a fellow of UNU/IIST, on leave from Catholic University of Pelotas, Brazil, where he is a lecturer. Xu Qiwen is a Research Fellow of UNU/IIST. His research interest is in Formal Techniques of Programming, including Theory for Concurrency and Real Time, Verification and Design Calculi. E-mail: qxu@iist.unu.edu Copyright c fl 1998 by UNU/IIST, Gerardo Schneider and Xu Qiwen Contents...

### Citations

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A calculus of durations
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Citation Context ...resented in Section 3. The paper is concluded with a short discussion of related work. 2 Duration Calculus of Weakly Monotonic Time with Infinite Intervals and Fixed Point Operators Duration Calculus =-=[1,4]-=-, is an extension of Interval Temporal Logic (ITL) [11] to dense time domains. The classical Duration Calculus [1], abbreviated as DC, was developed to reason about piece-wise continuous Boolean funct... |

153 |
A temporal logic for multilevel reasoning about hardware
- Moszkowski
- 1985
(Show Context)
Citation Context ...rt discussion of related work. 2 Duration Calculus of Weakly Monotonic Time with Infinite Intervals and Fixed Point Operators Duration Calculus [1,4], is an extension of Interval Temporal Logic (ITL) =-=[11]-=- to dense time domains. The classical Duration Calculus [1], abbreviated as DC, was developed to reason about piece-wise continuous Boolean functions of time (called states in literature), which model... |

87 |
Specifying message passing and time-critical systems with temporal logic, LNCS 651
- Koymans
- 1992
(Show Context)
Citation Context ...ork on synchronous languages, provides substantial simplification in verification of realtime systems. To reason about discrete events and their compositions, one needs a more involved logic. Koymans =-=[9]-=- suggested that a time point can be defined as a pair (r, n), with r denoting the real-time and n the causal order, and following the terminology in the work on synchronous languages, we call r the ma... |

34 | The Semantic Challenges of Verilog HDL
- Gordon
- 1995
(Show Context)
Citation Context ...nguage. In contrast to many attempts to formalise semantics of VHDL, another popular but reportedly less used hardware description language, there is only a little work on formal semantics of Verilog =-=[6, 13]-=-. In this paper, we give a formal semantics to a large subset of Verilog using an extension of the Duration Calculus, aiming to achieve a satisfactory level of abstraction and a more faithful modellin... |

24 |
A.P.: A formal description of hybrid systems
- Chaochen, Ji, et al.
- 1995
(Show Context)
Citation Context ...sensitive to stuttering. There has been some related work where semantics of several languages have been formalised using Duration Calculus and its appropriate extensions. He [8], Zhou, Wang and Ravn =-=[3]-=- studied semantics of HCSP in classical DC, which is sufficient because every action is assumed to take some time. Semantics of sequential real-time programs, which may contain instantaneous actions, ... |

20 |
Compositional reasoning about projected and infinite time
- Moszkowski
- 1995
(Show Context)
Citation Context ...t has the disadvantage that properties are somewhat cumbersome to express. As an alternative formulation, infinite intervals have been directly included in DC [19] following an approach by Moszkowski =-=[12]-=- for ITL. In [20], WDC is extended with infinite intervals along both macro-time and micro-time. To describe recursive computations, Pandya and Ramakrishna [16] introduced fixed point operators in DC.... |

13 | A Duration Calculus with Infinite Intervals
- Chaochen, Hung, et al.
- 1995
(Show Context)
Citation Context ...c was suggested by Liu, Ravn and Li [10]. Both DC and WDC are defined over finite intervals. However, timed systems in general and Verilog programs in particular often exhibit infinite behaviours. In =-=[2]-=-, an extension of DC was studied by Zhou, Dang and Li, where infinite behaviours are described by their finite approximations. This approach avoids284 direct interpretation of formulae over infinite ... |

12 |
Duration calculus with weakly monotonic time. This volume
- Pandya, Hung
(Show Context)
Citation Context ...Duration Calculus of Weakly Monotonic Time with Infinite Intervals and Fixed Point Operator, abbreviated as #WDCI, and it has incorporated features from several recent extensions of Duration Calculus =-=[16, 15, 17, 20]-=-. This paper is organised as follows. In Section 2, we introduce #WDCI. The semantics of V- is presented in Section 3. The paper is concluded with a short discussion of related work. 2 Duration Calcul... |

12 |
A recursive duration calculus
- Pandya, Ramakrishna
- 1995
(Show Context)
Citation Context ...Duration Calculus of Weakly Monotonic Time with Infinite Intervals and Fixed Point Operator, abbreviated as #WDCI, and it has incorporated features from several recent extensions of Duration Calculus =-=[16, 15, 17, 20]-=-. This paper is organised as follows. In Section 2, we introduce #WDCI. The semantics of V- is presented in Section 3. The paper is concluded with a short discussion of related work. 2 Duration Calcul... |

12 | Towards a Theory of Sequential Hybrid Programs
- Pandya, Hanping, et al.
- 1998
(Show Context)
Citation Context ...Duration Calculus of Weakly Monotonic Time with Infinite Intervals and Fixed Point Operator, abbreviated as #WDCI, and it has incorporated features from several recent extensions of Duration Calculus =-=[16, 15, 17, 20]-=-. This paper is organised as follows. In Section 2, we introduce #WDCI. The semantics of V- is presented in Section 3. The paper is concluded with a short discussion of related work. 2 Duration Calcul... |

9 | Duration properties of timed transition systems
- Liu, Ravn, et al.
- 1997
(Show Context)
Citation Context ... Duration Calculus, called Weakly Monotonic Time Duration Calculus, abbreviated as WDC, was formed by Pandya and Dang over such time structures [15]. A similar logic was suggested by Liu, Ravn and Li =-=[10]-=-. Both DC and WDC are defined over finite intervals. However, timed systems in general and Verilog programs in particular often exhibit infinite behaviours. In [2], an extension of DC was studied by Z... |

8 | Formal reasoning with Verilog HDL
- Pace, He
- 1988
(Show Context)
Citation Context ...nguage. In contrast to many attempts to formalise semantics of VHDL, another popular but reportedly less used hardware description language, there is only a little work on formal semantics of Verilog =-=[6, 13]-=-. In this paper, we give a formal semantics to a large subset of Verilog using an extension of the Duration Calculus, aiming to achieve a satisfactory level of abstraction and a more faithful modellin... |

6 | The quest for compositionality
- Roever
- 1985
(Show Context)
Citation Context ...tics of a compound statement as a function of the semantics of the components. The standard way to give a compositional semantics to shared variable programs, suggested first by Aczel (cited e.g., in =-=[5]-=-), is to define the semantics as a set of labelled state transition sequences, where the label records whether the transition is from the environment or from the component. This can be expressed in th... |

4 | Temporal Logic, Automata and Classical Theories: an Introduction - Dam - 1994 |

3 |
Compositional Reasoning Using Assumption - Commitment Paradigm
- Qiwen, Swarup
- 1998
(Show Context)
Citation Context |

2 |
A compositional semantics of SL
- Pandya
- 1997
(Show Context)
Citation Context ...not record the intermediate states of Verilog programs. To describe the semantics of concurrency adequately, Pandya and Dang proposed to use WDC [15] and applied to an ESTEREL-Iike language called SL =-=[14]-=-. WDC is extended with infinite intervals in [20] and applied to formalise the semantics of a toy language. Acknowledgements We would like to thank He Jifeng for introducing Verilog to us, Gordon Pace... |

2 |
Infinite duration calculus with fixed-point operators
- Wang, Xu
- 1997
(Show Context)
Citation Context ...on of formulae over infinite intervals but has the disadvantage that properties are somewhat cumbersome to express. As an alternative formulation, infinite intervals have been directly included in DC =-=[19]-=- following an approach by Moszkowski [12] for ITL. In [20], WDC is extended with infinite intervals along both macro-time and micro-time. To describe recursive computations, Pandya and Ramakrishna [16... |

1 |
From CSP to hybrid systems
- 3ifeng
(Show Context)
Citation Context ...hould probably be made insensitive to stuttering. There has been some related work where semantics of several languages have been formalised using Duration Calculus and its appropriate extensions. He =-=[8]-=-, Zhou, Wang and Ravn [3] studied semantics of HCSP in classical DC, which is sufficient because every action is assumed to take some time. Semantics of sequential real-time programs, which may contai... |