Alternating Turing Machines output Boolean values and combine the values returned by branches via the
all operators. Is there a name or theory behind the class of Turing Machines where there is no restriction to the Boolean space and the
For example, I want a machine where terminal states output real values and non-terminal states use the
min operator to combine the outputs of branches.
Additionally, are there subclasses of this class? I imagine operators which have certain properties (associativity, idempotence, and especially properties related to ordering or transitivity) would have interesting guarantees regarding interruptibility in the same way that a machine using only the
any operator can terminate as soon as it finds one accepting state.