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In earlier work, the Abstract State Machine Thesis -- that arbitraryalgorithms are behaviorally equivalent to abstract state machines -- wasestablished for several classes of algorithms, including ordinary, interactive,small-step algorithms. This was accomplished on the basis of axiomatizations ofthese classes of algorithms. In Part I (Interactive Small-Step Algorithms I:Axiomatization), the axiomatization was extended to cover interactivesmall-step algorithms that are not necessarily ordinary. This means that thealgorithms (1) can complete a step without necessarily waiting for replies toall queries from that step and (2) can use not only the environment's repliesbut also the order in which the replies were received. In order to prove thethesis for algorithms of this generality, we extend here the definition ofabstract state machines to incorporate explicit attention to the relativetiming of replies and to the possible absence of replies. We prove thecharacterization theorem for extended abstract state machines with respect togeneral algorithms as axiomatized in Part I.

Interactive Small-Step Algorithms II: Abstract State Machines and the Characterization Theorem

Interactive Small-Step Algorithms II: Abstract State Machines and the
Characterization Theorem