Abstract
In proving the complexity of the satisfiability problem there was for many modal and temporal logics until now still a gap between upper and lower bounds, mainly expressed by the nondeterministic and the deterministic version of the same complexity class. By showing that the (non-) emptiness problem of tree automata and alternating tree automata of Büchi-, Rabin-1- and Muller-1-type can be solved in polynomial time (thereby getting polynomial time completeness for these problems) we are now able to close these gaps therefore showing these satisfiability problems complete for the corresponding complexity classes. For Rabin-tree-automata of arbitrary type testing (non-) emptiness is shown to be in NP∩cc-NP.
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© 1989 Springer-Verlag Berlin Heidelberg
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Wagner, H. (1989). On the emptiness problem of tree automata and completeness of modal logics of programs. In: Börger, E., Büning, H.K., Richter, M.M. (eds) CSL '88. CSL 1988. Lecture Notes in Computer Science, vol 385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0026315
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DOI: https://doi.org/10.1007/BFb0026315
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