In earlier work, the Abstract State Machine Thesis — that arbitrary algo- rithms are behaviorally equivalent to abstract state machines — was established for several classes of algorithms, including ordinary, interactive, small-step algorithms. This was ac- complished on the basis of axiomatizations of these classes of algorithms. Here we extend the axiomatization and, in a companion paper, the proof, to cover interactive small-step algorithms that are not necessarily ordinary. This means that the algorithms (1) can com- plete a step without necessarily waiting for replies to all queries from that step and (2) can use not only the environment's replies but also the order in which the replies were received.
['Andreas Blass', 'Yuri Gurevich', 'Dean Rosenzweig', 'Benjamin Rossman']
Interactive Small-Step Algorithms I: Axiomatization