Abstract
AbstractKleene Algebra (KA) is the algebra of regular expressions. Central to the study of KA is Kozen’s (1994) completeness result, which says that any equivalence valid in the language model of KA follows from the axioms of KA. Also of interest is the finite model property (FMP), which says that false equivalences always have a finite counterexample. Palka (2005) showed that, for KA, the FMP is equivalent to completeness.We provide a unified and elementary proof of both properties. In contrast with earlier completeness proofs, this proof does not rely on minimality or bisimilarity techniques for deterministic automata. Instead, our approach avoids deterministic automata altogether, and uses Antimirov’s derivatives and the well-known transition monoid construction.Our results are fully verified in the Coq proof assistant.
Publisher
Springer International Publishing
Reference39 articles.
1. Anderson, C.J., et al.: NetKAT: semantic foundations for networks. In: POPL, pp. 113–126 (2014). https://doi.org/10.1145/2535838.2535862
2. Antimirov, V.M.: Partial derivatives of regular expressions and finite automaton constructions. Theor. Comput. Sci. 155(2), 291–319 (1996). https://doi.org/10.1016/0304-3975(95)00182-4
3. Backhouse, R.: Closure algorithms and the star-height problem of regular languages. Ph.D. thesis, University of London (1975). https://hdl.handle.net/10044/1/22243
4. Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development - Coq’Art: The Calculus of Inductive Constructions. Texts in Theoretical Computer Science. An EATCS Series (2004). https://doi.org/10.1007/978-3-662-07964-5
5. Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic, Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press, Cambridge (2001). https://doi.org/10.1017/CBO9781107050884
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献