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## Kleene algebras with tests and the static analysis of programs (2003)

Citations: | 9 - 1 self |

### Citations

603 | Enforceable security policies
- Schneider
- 2000
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Citation Context ...lity of KAT as a general framework for many verification tasks in computer science. Security automata are a popular mechanism for the specification and enforcement of a large class of safety policies =-=[16]-=-. A security automaton is an ordinary finite-state automaton in which certain states are designated as error states. A transition to a new state may occur when a critical operation of a program is exe... |

469 | The SLAM project: debugging system software via static analysis
- Ball, Rajamani
- 2002
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Citation Context ...says that if the propositional abstraction of the program fails to verify, then there is a relational interpretation in which the program is unsafe. Finally, we illustrate the method on an example of =-=[3]-=- involving the verification of a device driver. 2s2 Preliminary Definitions 2.1 Kleene Algebra Kleene algebra (KA) is the algebra of regular expressions [9, 7]. The axiomatization used here is from [1... |

466 |
Representation of events in nerve nets and finite automata, automata studies
- Kleene
- 1956
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Citation Context ..., we illustrate the method on an example of [3] involving the verification of a device driver. 2s2 Preliminary Definitions 2.1 Kleene Algebra Kleene algebra (KA) is the algebra of regular expressions =-=[9, 7]-=-. The axiomatization used here is from [10]. A Kleene algebra is an algebraic structure (K, +, ·, ∗ , 0, 1) that is an idempotent semiring under +, ·, 0, 1 such that p∗q is the ≤-least solution to q +... |

439 |
Propositional dynamic logic of regular programs.J
- Fischer, Ladner
- 1956
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Citation Context ...re denoted p,q,r,... . The set of terms in the language of KAT over atomic actions P and atomic tests B is denoted RExp P,B. The while program constructs are encoded as in propositional Dynamic Logic =-=[8]-=-: p ; q def = pq if b then p else q def = bp + bq while b do p def = (bp) ∗ b. 3sThe Hoare partial correctness assertion {b} p {c} is expressed in KAT in any one of the following three equivalent form... |

354 |
Regular Algebra and Finite Machines
- Conway
- 1971
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Citation Context ..., we illustrate the method on an example of [3] involving the verification of a device driver. 2s2 Preliminary Definitions 2.1 Kleene Algebra Kleene algebra (KA) is the algebra of regular expressions =-=[9, 7]-=-. The axiomatization used here is from [10]. A Kleene algebra is an algebraic structure (K, +, ·, ∗ , 0, 1) that is an idempotent semiring under +, ·, 0, 1 such that p∗q is the ≤-least solution to q +... |

243 | A completeness theorem for Kleene algebras and the algebra of regular events
- Kozen
- 1994
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Citation Context ...3] involving the verification of a device driver. 2s2 Preliminary Definitions 2.1 Kleene Algebra Kleene algebra (KA) is the algebra of regular expressions [9, 7]. The axiomatization used here is from =-=[10]-=-. A Kleene algebra is an algebraic structure (K, +, ·, ∗ , 0, 1) that is an idempotent semiring under +, ·, 0, 1 such that p∗q is the ≤-least solution to q + px ≤ x and qp∗ is the ≤-least solution to ... |

145 | Kleene Algebra with tests
- Kozen
- 1997
(Show Context)
Citation Context ...en applied successfully in substantial verification tasks involving communication protocols, source-to-source program transformation, concurrency control, compiler optimization, and dataflow analysis =-=[2, 4, 5, 6, 11, 14]-=-. The system is PSPACE-complete and deductively complete for partial correctness over relational and trace models [12]. KAT has a rich algebraic theory with many natural and useful models: language-th... |

56 | On Hoare logic and Kleene algebra with tests
- Kozen
- 2000
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Citation Context ...concurrency control, compiler optimization, and dataflow analysis [2, 4, 5, 6, 11, 14]. The system is PSPACE-complete and deductively complete for partial correctness over relational and trace models =-=[12]-=-. KAT has a rich algebraic theory with many natural and useful models: language-theoretic, relational, trace-based, matrix. Because of its roots in classical algebra and equational logic, KAT provides... |

45 | Certification of Compiler Optimizations Using Kleene Algebra with Tests, in
- Kozen, Patron
(Show Context)
Citation Context ...en applied successfully in substantial verification tasks involving communication protocols, source-to-source program transformation, concurrency control, compiler optimization, and dataflow analysis =-=[2, 4, 5, 6, 11, 14]-=-. The system is PSPACE-complete and deductively complete for partial correctness over relational and trace models [12]. KAT has a rich algebraic theory with many natural and useful models: language-th... |

22 | D.: Kleene algebra with tests and program schematology
- Angus, Kozen
- 2001
(Show Context)
Citation Context ...en applied successfully in substantial verification tasks involving communication protocols, source-to-source program transformation, concurrency control, compiler optimization, and dataflow analysis =-=[2, 4, 5, 6, 11, 14]-=-. The system is PSPACE-complete and deductively complete for partial correctness over relational and trace models [12]. KAT has a rich algebraic theory with many natural and useful models: language-th... |

17 | Hypotheses in kleene algebra
- Cohen
- 1994
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15 | D.: Equational verification of cache blocking in LU decomposition using Kleene algebra with tests
- Barth, Kozen
- 2002
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12 | D.: KAT-ML: An interactive theorem prover for Kleene algebra with tests
- Aboul-Hosn, Kozen
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Citation Context ...ock. This annotation is necessary, because the first critical operation performed by the driver is an acquire operation kA. The formula (33) has been formally verified using the KAT-ML theorem prover =-=[1]-=-. 7 Future Work The structure of security automata can be generalized to handle other types of static analysis. For example, let L be an upper semilattice such that all ascending chains are finite. Th... |

7 | Lazy caching in Kleene algebra
- Cohen
- 1994
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4 | Some results in dynamic model theory - Kozen |

3 |
and Jerzy Tiuryn. Substructural logic and partial correctness
- Kozen
- 2003
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Citation Context ...rmulas, andKAT is deductively complete for the Hoare theory of relational models [12]; that is, all relationally valid Hoare formulas are theorems of KAT. This theory is also decidable in PSPACE. See =-=[10, 11, 12, 15]-=- for a more detailed introduction to KA and KAT. 2.3 Trace and Relational Models 2.3.1 Kripke Frames For applications in program verification, one usually interprets programs and tests over a KAT cons... |