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Computing measures of weak-MSO definable sets of trees
arXiv:2410.13479v2 Announce Type: replace
Abstract: This work addresses the problem of computing measures of recognisable sets of infinite trees. An algorithm is provided to compute the probability measure of a tree language recognisable by a weak alternating automaton, or equivalently definable in weak monadic second-order logic. The measure is the uniform coin-flipping measure or more generally it is generated by a~branching stochastic process. The class of tree languages in consideration, although smaller than all regular tree languages, comprises in particular the languages definable in the alternation-free mu-calculus or in temporal logic CTL. Thus, the new algorithm may enhance the toolbox of probabilistic model checking.
Abstract: This work addresses the problem of computing measures of recognisable sets of infinite trees. An algorithm is provided to compute the probability measure of a tree language recognisable by a weak alternating automaton, or equivalently definable in weak monadic second-order logic. The measure is the uniform coin-flipping measure or more generally it is generated by a~branching stochastic process. The class of tree languages in consideration, although smaller than all regular tree languages, comprises in particular the languages definable in the alternation-free mu-calculus or in temporal logic CTL. Thus, the new algorithm may enhance the toolbox of probabilistic model checking.
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