## A Sub-Quadratic Algorithm for Conjunctive and Disjunctive BESs (2004)

Citations: | 6 - 2 self |

### BibTeX

@TECHREPORT{Groote04asub-quadratic,

author = {Jan Friso Groote and Misa Keinänen},

title = {A Sub-Quadratic Algorithm for Conjunctive and Disjunctive BESs},

institution = {},

year = {2004}

}

### OpenURL

### Abstract

We present an algorithm for conjunctive and disjunctive Boolean equation systems (BESs), which arise frequently in the verification and analysis of finite state concurrent systems. In contrast to the previously best known O(e²) time solutions, our algorithm computes the solution of such a fixpoint equation system with size e and alternation depth d in O(e log d) time.

### Citations

992 | Depth first search and linear graph algorithms
- Tarjan
- 1972
(Show Context)
Citation Context ...ms, and an empirical comparison between our approach and other related algorithms are left for future work. Our algorithm combines essentially graph theoretic techniques for finding strong components =-=[7, 8]-=- and hierarchical clustering [9]. King, Kupferman and Vardi [3] recently found an algorithm in the realm of parity word automata. Their algorithm is very similar to ours and also resorts to the ideas ... |

81 |
Model checking and boolean graphs
- Andersen
- 1994
(Show Context)
Citation Context ...n O(e 2 ) time solutions, our algorithm computes the solution of such a fixpoint equation system with size e and alternation depth d in O(e log d) time. 1 Introduction A Boolean Equation System (BES) =-=[1, 5, 6]-=- is a sequence of boolean equations with minimal and maximal fixpoints. It gives a useful framework for the verification of finite state concurrent systems. This is due to the fact that many interesti... |

46 |
Verification of Modal Properties Using Boolean Equation Systems
- Mader
- 1997
(Show Context)
Citation Context ...n O(e 2 ) time solutions, our algorithm computes the solution of such a fixpoint equation system with size e and alternation depth d in O(e log d) time. 1 Introduction A Boolean Equation System (BES) =-=[1, 5, 6]-=- is a sequence of boolean equations with minimal and maximal fixpoints. It gives a useful framework for the verification of finite state concurrent systems. This is due to the fact that many interesti... |

34 |
A Strong-connectivity Algorithm and Its Applications in Data Flow Analysis
- Sharir
- 1981
(Show Context)
Citation Context ...ms, and an empirical comparison between our approach and other related algorithms are left for future work. Our algorithm combines essentially graph theoretic techniques for finding strong components =-=[7, 8]-=- and hierarchical clustering [9]. King, Kupferman and Vardi [3] recently found an algorithm in the realm of parity word automata. Their algorithm is very similar to ours and also resorts to the ideas ... |

14 |
On the complexity of parity word automata
- King, Kupferman, et al.
- 2001
(Show Context)
Citation Context ...ated algorithms are left for future work. Our algorithm combines essentially graph theoretic techniques for finding strong components [7, 8] and hierarchical clustering [9]. King, Kupferman and Vardi =-=[3]-=- recently found an algorithm in the realm of parity word automata. Their algorithm is very similar to ours and also resorts to the ideas in [9]. But their algoritm has a very different purpose, namely... |

14 |
Results on the propositional µ-calculus. Theoretical Computer Science, 27:333–354
- Kozen
- 1983
(Show Context)
Citation Context ...ives a useful framework for the verification of finite state concurrent systems. This is due to the fact that many interesting properties of systems can naturally be specified in the modal µ-calculus=-= [4]-=-. The model checking problem says whether such a formula holds for a transition system. This problem, or more concretely a formula and a transition system, can be straightforwardly translated to a boo... |

14 | A Generic On-the-Fly Solver for Alternation-Free Boolean Equation Systems
- Mateescu
- 2003
(Show Context)
Citation Context ...n O(e 2 ) time solutions, our algorithm computes the solution of such a fixpoint equation system with size e and alternation depth d in O(e log d) time. 1 Introduction A Boolean Equation System (BES) =-=[1, 5, 6]-=- is a sequence of boolean equations with minimal and maximal fixpoints. It gives a useful framework for the verification of finite state concurrent systems. This is due to the fact that many interesti... |

7 | M.: Solving disjunctive/conjunctive boolean equation systems with alternating fixed points
- Groote, Keinänen
(Show Context)
Citation Context ...TEMS 2 is therefore interesting to develop specific resolution techniques for these particular fragments. All previous algorithms for solving conjunctive and disjunctive classes, including those from =-=[2, 5]-=-, take at least quadratic time in the size of a boolean equation system in the worst case. For large boolean equations which are typically encountered in model checking and preorder/equivalence checki... |

5 |
A hierarchical clustering algorithm using strong components
- Tarjan
- 1982
(Show Context)
Citation Context ...ween our approach and other related algorithms are left for future work. Our algorithm combines essentially graph theoretic techniques for finding strong components [7, 8] and hierarchical clustering =-=[9]-=-. King, Kupferman and Vardi [3] recently found an algorithm in the realm of parity word automata. Their algorithm is very similar to ours and also resorts to the ideas in [9]. But their algoritm has a... |