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

TL;DR

This paper extends the Abstract State Machine Thesis to more general interactive small-step algorithms by incorporating reply timing and absence, and proves the characterization theorem for these extended machines.

Contribution

It introduces an extended definition of abstract state machines that accounts for reply timing and absence, and proves the thesis for these general algorithms.

Findings

Extended abstract state machines incorporate reply timing and absence.

Proved the characterization theorem for these extended machines.

Validated the behavioral equivalence of algorithms and extended machines.

Abstract

In earlier work, the Abstract State Machine Thesis -- that arbitrary algorithms are behaviorally equivalent to abstract state machines -- was established for several classes of algorithms, including ordinary, interactive, small-step algorithms. This was accomplished on the basis of axiomatizations of these classes of algorithms. In Part I (Interactive Small-Step Algorithms I: Axiomatization), the axiomatization was extended to cover interactive small-step algorithms that are not necessarily ordinary. This means that the algorithms (1) can complete 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. In order to prove the thesis for algorithms of this generality, we extend here the definition of abstract state machines to incorporate explicit attention to the relative timing of replies and to the possible absence of replies. We prove the characterization theorem for extended abstract state machines with respect to general algorithms as axiomatized in Part I.