## Abstract

Abstract We study the distinguishing and expressive power of branching temporal logics with bounded nesting depth of path quantifiers. We define the fragments CTL^{*}_{i} and CTL_{i} of CTL ^{*} and CTL, where at most i nestings of path quantifiers are allowed. We show that for all i ≥ 1, the logic CTL^{*} _{i+1} has more distinguishing and expressive power than CTL ^{*}_{i}; thus the branching-depth hierarchy is strict. We describe equivalence relations H_{i} that capture CTL ^{*}_{i}: two states in a Kripke structure are H _{i}-equivalent iff they agree on exactly all CTL^{*} _{i} formulas. While H_{1} corresponds to trace equivalence, the limit of the sequence H_{1}, H_{2},... is Milner's bisimulation. These results are not surprising, but they give rise to several interesting observations and problems. In particular, while CTL ^{*} and CTL have the same distinguishing power, this is not the case for CTL^{*}_{i} and CTL_{i}. We define the branching depth of a structure as the minimal index i for which H _{i+1}=H_{i}. The branching depth indicates on the possibility of using bisimulation instead of trace equivalence (and similarly for simulation and trace containment). We show that the problem of finding the branching depth is PSPACE-complete.

Original language | English |
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Pages (from-to) | 65-78 |

Number of pages | 14 |

Journal | Electronic Notes in Theoretical Computer Science |

Volume | 39 |

Issue number | 1 |

DOIs | |

State | Published - 2003 |

Event | EXPRESS'00, 7th International Workshop on Expressiveness in Concurrency (Satellite Workshop from CONCUR 2000) - , United States Duration: 21 Aug 2000 → 21 Aug 2000 |