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## Certification of compiler optimizations using Kleene algebra with tests (2000)

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Venue: | STUCKEY (EDS.), PROC. RST INTERNAT. CONF. COMPUTATIONAL LOGIC (CL2000), LECTURE NOTES IN ARTI CIAL INTELLIGENCE |

Citations: | 45 - 13 self |

### Citations

2873 |
The Design and Analysis of Computer Algori thms
- Hopcroft
- 1966
(Show Context)
Citation Context ...of regular expressions. It was first introduced by Kleene in 1956 [9] and further developed in the 1971 monograph of Conway [6]. It has reappeared in many contexts in mathematics and computer science =-=[23, 10, 22, 16, 17, 1, 8]-=-. In [12], an extension of KA called Kleene algebra with tests (KAT) was introduced. This system combines programs and assertions in a simple, purely equational system. In [14] it was shown that KAT s... |

1235 | Proof-carrying code
- Necula
- 1997
(Show Context)
Citation Context ...he verification of compiler optimizations is more than just a theoretical exercise. We were led to these investigations by recent work in typed assembly language (TAL) [18], proof-carrying code (PCC) =-=[19]-=-, and efficient code certification (ECC) [13]. These are systems that provide a means for an untrusted compiler to convince a trusted verifier that the object code it produces meets certain safety req... |

617 | From System F to typed assembly language
- Morrisett, Walker, et al.
- 1999
(Show Context)
Citation Context ...the optimizing transformation. The verification of compiler optimizations is more than just a theoretical exercise. We were led to these investigations by recent work in typed assembly language (TAL) =-=[18]-=-, proof-carrying code (PCC) [19], and efficient code certification (ECC) [13]. These are systems that provide a means for an untrusted compiler to convince a trusted verifier that the object code it p... |

466 |
Representation of events in nerve nets and finite automata, automata studies
- Kleene
- 1956
(Show Context)
Citation Context ...give a formal equational proof of the correctness of the optimizing transformation. 1 Introduction Kleene algebra (KA) is the algebra of regular expressions. It was first introduced by Kleene in 1956 =-=[9]-=- and further developed in the 1971 monograph of Conway [6]. It has reappeared in many contexts in mathematics and computer science [23, 10, 22, 16, 17, 1, 8]. In [12], an extension of KA called Kleene... |

439 |
Propositional dynamic logic of regular programs.J
- Fischer, Ladner
- 1956
(Show Context)
Citation Context ...e elements are sets of traces (sequences of states) and the boolean elements are sets of states (traces of length 0). The encoding of the while program constructs is as in Propositional Dynamic Logic =-=[7]-=-: p ; q def = pq (15) if b then p else q def = bp + bq (16) while b do p def = (bp) b: (17) The following result, also observed in [12], follows directly from Lemma 2.1. Intuitively, if the execution ... |

354 |
Regular Algebra and Finite Machines
- Conway
- 1971
(Show Context)
Citation Context ...ptimizing transformation. 1 Introduction Kleene algebra (KA) is the algebra of regular expressions. It was first introduced by Kleene in 1956 [9] and further developed in the 1971 monograph of Conway =-=[6]-=-. It has reappeared in many contexts in mathematics and computer science [23, 10, 22, 16, 17, 1, 8]. In [12], an extension of KA called Kleene algebra with tests (KAT) was introduced. This system comb... |

274 | The design and implementation of a certifying compiler
- Necula, Lee
- 1998
(Show Context)
Citation Context ...oduces meets certain safety requirements. 1 PCC is the most powerful of these systems. It quite flexible in the security policies it can express, but a significant problem is the size of certificates =-=[20]-=-. ECC addresses this issue by taking advantage of compiler conventions, giving a significant reduction in certificate size. In ECC, the production and verification of certificates is very efficient an... |

243 | A completeness theorem for Kleene algebras and the algebra of regular events
- Kozen
- 1994
(Show Context)
Citation Context ...ght be based on the system KAT as described here. 2 Kleene Algebra and Kleene Algebra with Tests In this section we briefly review the definitions of Kleene algebra and Kleene algebra with tests; see =-=[11]-=- for a more thorough introduction. 2.1 Kleene Algebra (KA) The following axiomatization is from [11]. A Kleene algebra (K; +; \Delta; ; 0; 1) is an idempotent semiring under +; \Delta; 0; 1 satisfying... |

145 | Kleene Algebra with tests - Kozen - 1997 |

56 | On Hoare logic and Kleene algebra with tests
- Kozen
- 2000
(Show Context)
Citation Context ...e [23, 10, 22, 16, 17, 1, 8]. In [12], an extension of KA called Kleene algebra with tests (KAT) was introduced. This system combines programs and assertions in a simple, purely equational system. In =-=[14]-=- it was shown that KAT strictly subsumes propositional Hoare logic, is of no greater complexity, and is deductively complete over relational models (Hoare logic is not). Moreover, KAT requires nothing... |

43 | Dynamic Algebras as a Well-Behaved Fragment of Relation Algebras
- Pratt
- 1990
(Show Context)
Citation Context ...of regular expressions. It was first introduced by Kleene in 1956 [9] and further developed in the 1971 monograph of Conway [6]. It has reappeared in many contexts in mathematics and computer science =-=[23, 10, 22, 16, 17, 1, 8]-=-. In [12], an extension of KA called Kleene algebra with tests (KAT) was introduced. This system combines programs and assertions in a simple, purely equational system. In [14] it was shown that KAT s... |

37 | Efficient code certification
- Kozen
- 1998
(Show Context)
Citation Context ...more than just a theoretical exercise. We were led to these investigations by recent work in typed assembly language (TAL) [18], proof-carrying code (PCC) [19], and efficient code certification (ECC) =-=[13]-=-. These are systems that provide a means for an untrusted compiler to convince a trusted verifier that the object code it produces meets certain safety requirements. 1 PCC is the most powerful of thes... |

34 | F.: Kleene algebra with tests: Completeness and decidability
- Kozen, Smith
- 1996
(Show Context)
Citation Context ... all cases the truth of the premise is directly evident. Moreover, it has been observed that in the decision procedure for KAT, premises of the form p = 0 can be eliminated without loss of efficiency =-=[2, 15]-=-. 3 Verifying Optimizations in KAT In this section we consider several examples of common compiler optimizations and show how they can be encoded and verified in KAT. In each case, we give the program... |

28 | Relation Algebras with Transitive Closure - Ng - 1984 |

28 | Representation of events in nerve nets and nite automata, in \Automata Studies - Kleene - 1956 |

24 |
The Kleene and Parikh theorem in complete semirings
- Kuich
- 1987
(Show Context)
Citation Context ...of regular expressions. It was first introduced by Kleene in 1956 [9] and further developed in the 1971 monograph of Conway [6]. It has reappeared in many contexts in mathematics and computer science =-=[23, 10, 22, 16, 17, 1, 8]-=-. In [12], an extension of KA called Kleene algebra with tests (KAT) was introduced. This system combines programs and assertions in a simple, purely equational system. In [14] it was shown that KAT s... |

23 |
Using Kleene Algebra to Reason About Concurrency Control
- Cohen
- 1994
(Show Context)
Citation Context ...s. KAT has been applied successfully in various low-level verification tasks involving communication protocols, basic safety analysis, source-to-source program transformation, and concurrency control =-=[12, 2, 3, 4]-=-. A useful feature of KAT in this regard is its ability to accommodate certain basic equational assumptions regarding the interaction of atomic instructions. This feature makes KAT ideal for reasoning... |

20 | On induction vs. ∗-continuity
- Kozen
- 1982
(Show Context)
Citation Context |

14 |
A semiring on convex polygons and zero-sum cycle problems
- Iwano, Steiglitz
- 1990
(Show Context)
Citation Context |

4 |
Hypotheses in Kleene algebra. Available as ftp://ftp.bellcore.com/pub/ernie/research/homepage.html
- Cohen
- 1994
(Show Context)
Citation Context ...s. KAT has been applied successfully in various low-level verification tasks involving communication protocols, basic safety analysis, source-to-source program transformation, and concurrency control =-=[12, 2, 3, 4]-=-. A useful feature of KAT in this regard is its ability to accommodate certain basic equational assumptions regarding the interaction of atomic instructions. This feature makes KAT ideal for reasoning... |

2 |
Lazy caching. Available as ftp://ftp.bellcore.com/pub/ernie/research/homepage.html
- Cohen
- 1994
(Show Context)
Citation Context ...s. KAT has been applied successfully in various low-level verification tasks involving communication protocols, basic safety analysis, source-to-source program transformation, and concurrency control =-=[12, 2, 3, 4]-=-. A useful feature of KAT in this regard is its ability to accommodate certain basic equational assumptions regarding the interaction of atomic instructions. This feature makes KAT ideal for reasoning... |

2 | E cient code certi cation - Kozen - 1998 |