Reasoning about the past with two-way automata [chapter]

Moshe Y. Vardi
1998 Lecture Notes in Computer Science  
The -calculus can be viewed as essentially the \ultimate" program logic, as it expressively subsumes all propositional program logics, including dynamic logics, process logics, and temporal logics. It is known that the satis ability problem for the -calculus is EXPTIMEcomplete. This upper bound, however, is known for a version of the logic that has only forward modalities, which express weakest preconditions, but not backward modalities, which express strongest postconditions. Our main result
more » ... this paper is an exponential time upper bound for the satis ability problem of the -calculus with both forward and backward modalities. To get this result we develop a theory of two-way alternating automata on in nite trees.
doi:10.1007/bfb0055090 fatcat:6ce6jqcjzbehjdk5gh4xstnn5y