### Citations

4745 |
Introduction to Automata Theory, Languages, and Computation
- Hopcroft, Ullman
- 1979
(Show Context)
Citation Context ... generators P and B. The construction of P is by induction on the structure of p, and corresponds to the combinatorial construction of an automaton from a regular expression as found for example 5 in =-=[4, 5]-=-. The matrix P is the transition matrix of the automaton equivalent to the regular expression p over the input alphabet P ∪ B ∪ B. The vectors u and v specify the start and final states of the automat... |

439 |
Propositional dynamic logic of regular programs.J
- Fischer, Ladner
- 1956
(Show Context)
Citation Context ... language-theoretic model involving sets of guarded strings introduced in Lecture ??, and matrices over Kleene algebras with tests. In contrast, propositional dynamic logic (PDL) is EXPTIME -complete =-=[3]-=-, which indicates that some savings can be achieved by using KAT in applications where PDL would previously have been used. We will show later that star-continuous KA in the presence of extra commutat... |

178 |
Automata and Computability
- Kozen
- 1997
(Show Context)
Citation Context ... generators P and B. The construction of P is by induction on the structure of p, and corresponds to the combinatorial construction of an automaton from a regular expression as found for example 5 in =-=[4, 5]-=-. The matrix P is the transition matrix of the automaton equivalent to the regular expression p over the input alphabet P ∪ B ∪ B. The vectors u and v specify the start and final states of the automat... |

145 | Kleene Algebra with tests
- Kozen
- 1997
(Show Context)
Citation Context ...we show that the equational theory of KAT is PSPACE -complete. Thus KAT, while considerably more expressive than KA without tests, is no more difficult to decide. The results of this lecture are from =-=[7, 2]-=-. We have shown (Lecture ??) that the Hoare theory of KAT (Horn formulas with premises of the form r = 0) reduces efficiently to the equational theory. We have also argued (Lecture ??) that the equati... |

34 | F.: Kleene algebra with tests: Completeness and decidability
- Kozen, Smith
- 1996
(Show Context)
Citation Context ...we show that the equational theory of KAT is PSPACE -complete. Thus KAT, while considerably more expressive than KA without tests, is no more difficult to decide. The results of this lecture are from =-=[7, 2]-=-. We have shown (Lecture ??) that the Hoare theory of KAT (Horn formulas with premises of the form r = 0) reduces efficiently to the equational theory. We have also argued (Lecture ??) that the equati... |

11 | On the complexity of reasoning in Kleene algebra
- Kozen
(Show Context)
Citation Context ... presence of extra commutativity conditions of the form pq = qp, even for primitive p and q, is undecidable. This was observed by Cohen [1]. In fact, the universal Horn theory of KAT∗ is Π11-complete =-=[6]-=-. Matrix Algebras Let K be a Kleene algebra with tests B. As argued in Lecture ??, the structure (Mat(n,K), ∆(n,B), +, ·, ∗, , 0n, In) again forms a Kleene algebra with tests, where Mat(n,K) denotes t... |