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## A Decision Procedure for an Extensional Theory of Arrays (2001)

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Venue: | In 16th IEEE Symposium on Logic in Computer Science |

Citations: | 84 - 15 self |

### Citations

655 | PVS: A prototype verification system.
- Owre, Rushby, et al.
- 1992
(Show Context)
Citation Context ... A decision procedure for a theory of arrays is of interest for applications in formal verification and program analysis. Such a procedure is also of value for theorem-provers. The PVS theorem-prover =-=[11]-=- has an undocumented decision procedure for a theory of arrays [12], and HOL has some automatic support for a theory of arrays via a library for finite partial functions [3]. Two kinds of array theori... |

455 | Simplification by cooperating decision procedures,
- Nelson, Oppen
- 1979
(Show Context)
Citation Context ...eory with just 1-dimensional arrays. Equations between array terms are allowed. They prove that determining the invalidity of an equation in their theory of arrays is NP-complete. Nelson and Oppen In =-=[10]-=-, Nelson and Oppen describe an extensional theory of arrays. Their theory allows multidimensional arrays. They do not present their satisfiability procedure for the extensional theory, but in [9], Nel... |

359 |
The Classical Decision Problem.
- Borger, Gradel, et al.
- 1997
(Show Context)
Citation Context ... 0 n ), where f 0 ; i 0 1 ; : : : ; i 0 n are the translations of f; i 1 ; : : : ; i n . The undecidability results for classical first order logic with just function symbols and equality (see, e.g., =-=[5]-=-) can then be applied to show that even quite restricted quantified fragments of the extensional theory of arrays are undecidable. A decision procedure for Arr may be useful even for applications whic... |

190 | Towards a mathematical science of computation.
- McCarthy
- 1962
(Show Context)
Citation Context ...es that are strictly weaker than Arr, either because they restrict the form of formulas in the theory (e.g., to just equations), disallow equations between arrays, or are non-extensional. McCarthy In =-=[8]-=-, McCarthy introduces the function symbols read and write and gives an informal semantics for an extensional theory of arrays based on them. Collins and Syme Collins and Syme present in HOL a theory o... |

127 |
Techniques for Program Verification.
- Nelson
- 1980
(Show Context)
Citation Context ... In [10], Nelson and Oppen describe an extensional theory of arrays. Their theory allows multidimensional arrays. They do not present their satisfiability procedure for the extensional theory, but in =-=[9]-=-, Nelson gives a detailed presentation of a satisfiability procedure for a non-extensional theory. Levitt In Chapter 5 of his PhD thesis [7], Levitt presents a decision procedure for an extensional th... |

30 | A framework for cooperating decision procedures. In
- Barrett, Dill, et al.
- 2000
(Show Context)
Citation Context ...y of arrays is justified by the fact that, as will be shown in Section 6 below, the satisfiability procedure for Arr is suitable for incorporation into a framework for cooperating decision procedures =-=[2]-=-. In such a framework, separate decision procedures for arithmetic and uninterpreted functions may be combined with the decision procedure for Arr to decide the combined theory. The first two works pr... |

25 | Abstract Congruence Closure and Specializations
- Bachmair, Tiwari
(Show Context)
Citation Context ...on the observation that in the absence of write, arrays behave like uninterpreted functions and read behaves like function application. So in the absence of write, a congruence closure algorithm (cf. =-=[1]-=-) could be used to decide the theory. The algorithm must be modified to work with partial equations as well as equations, but this can be done. For simplicity, the very simple congruence closure algor... |

17 |
Assignment commands with array references
- Downey, Sethi
(Show Context)
Citation Context ...thm to treat PERM shows that it could just as easily be used to extend the algorithm for Arr, as long as their restriction disallowing equations between array terms were retained. Downey and Sethi In =-=[4]-=-, Downey and Sethi present a decision procedure for an extensional equational theory with just 1-dimensional arrays. Equations between array terms are allowed. They prove that determining the invalidi... |

16 |
Formal Verification Techniques for Digital Systems
- Levitt
- 1999
(Show Context)
Citation Context ...satisfiability procedure for the extensional theory, but in [9], Nelson gives a detailed presentation of a satisfiability procedure for a non-extensional theory. Levitt In Chapter 5 of his PhD thesis =-=[7]-=-, Levitt presents a decision procedure for an extensional theory of arrays based on solving equations and canonizing terms, in the style of Shostak [13]. A detailed proof of correctness is not given, ... |

9 | A theory of finite maps
- Collins, Syme
- 1995
(Show Context)
Citation Context ...s. The PVS theorem-prover [11] has an undocumented decision procedure for a theory of arrays [12], and HOL has some automatic support for a theory of arrays via a library for finite partial functions =-=[3]-=-. Two kinds of array theories have been studied previously. Extensional theories require that if two arrays store the same value at index i, for each index i, then the arrays must be the same. Non-ext... |

3 |
Some Completeness Results in the Mathematical Theory of Computation
- Kaplan
- 1968
(Show Context)
Citation Context ...nal theory of arrays based on them. Collins and Syme Collins and Syme present in HOL a theory of finite higher-order partial functions similar to a theory with multi-dimensional arrays [3]. Kaplan In =-=[6]-=-, Kaplan gives a decision procedure for a non-extensional equational theory with just 1-dimensional arrays. He considers equations between index terms only, which is reasonable since his theory contai... |