On the Coalgebraic Theory of Kleene Algebra with Tests
dc.contributor.author | Kozen, Dexter | |
dc.date.accessioned | 2008-03-14T18:49:38Z | |
dc.date.available | 2008-03-14T18:49:38Z | |
dc.date.issued | 2008-03-14T18:49:38Z | |
dc.description.abstract | We develop a coalgebraic theory of Kleene algebra with tests (KAT) along the lines of Rutten (1998) for Kleene algebra (KA) and Chen and Pucella (2003) for a limited version of KAT, resolving two open problems of Chen and Pucella. Our treatment includes a simple definition of the Brzozowski derivative for KAT expressions and an automata-theoretic interpretation involving automata on guarded strings. We also give a complexity analysis, showing that an efficient implementation of coinductive equivalence proofs in this setting is tantamount to a standard automata-theoretic construction. It follows that coinductive equivalence proofs can be generated automatically in PSPACE. This matches the bound of Worthington (2008) for the automatic generation of equational proofs in KAT. | en_US |
dc.identifier.uri | https://hdl.handle.net/1813/10173 | |
dc.subject | Kleene algebra | en_US |
dc.subject | Kleene algebra with tests | en_US |
dc.subject | Brzozowski derivative | en_US |
dc.subject | coalgebra | en_US |
dc.subject | coinduction | en_US |
dc.title | On the Coalgebraic Theory of Kleene Algebra with Tests | en_US |
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