A theory of nondeterminism
A construction is described which takes an arbitrary set of machines, an arbitray set of tests, and an arbitrary relation on machines and tests defining which machines pass which tests. It produces a domain of specifications, which is a retract of the lattice of sets of tests (with the subset ordering), and a domain of nondeterministic machines (ndms), which is a retract of the lattice of sets of machines (with the superset ordering). These two domains are isomorphic. Simple conditions ensure that they are ω-algebraic.
Functions on such domains may be defined equivalently either as transformations of ndms (an operational definition) or as transformations of specifications (an axiomatic definition). Conditions for the "realism" of such functions are formulated.
Keywordsaxiomatic sematnics operational semantics complementary definitions nondeterminism powerdomains
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