Relating Hierarchy of Temporal Properties to Model Checking

Deeper Connections Between LTL and Alternating Automata

“…This hierarchy has a strong connection to the hierarchy of temporal properties introduced by Manna and Pnueli [17,18]. Moreover, there is a relation between classes of until-release hierarchy and complexity of their model checking problem (see [4]). Let us note that the hierarchy collapses on the third level with respect to its expressive power.…”

“…The second part of this paper presents connections between A1W automata and some LTL fragments that are not covered by the pattern above, namely fragments of the until-release (alternating) hierarchy [4] and fragments of the hierarchy of temporal properties [17,18]. In particular, we show that alternation of until and release operators in a formula corresponds to alternation of nonaccepting and accepting states in an equivalent A1W automaton.…”

“…The until-release hierarchy of LTL formulae has been introduced in [4]. It is based on alternation depth of U and R operators.…”

“…See [19] for details. The theorem allows us to transform the results proved for the until-release hierarchy in [4] into statements about our hierarchy of Σ i and Π i classes. This is exemplified by the two following corollaries.…”

“…In the first part of the paper we show that the latter translation wastes temporal operators and we propose some improvements of this translation. The second part of the paper draws a direct connection between fragments of the Until-Release hierarchy [4] and alternation depth of nonaccepting and accepting states in A1W automata. We also indicate some corollaries and applications of these results.…”