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. 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 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.
The characterization theorem of @cite_12 establishes the ASM thesis for the class A of algorithms defined by Sequential Time, Abstract State, and Bounded Exploration and the class M of machines defined by the basic ASM language of update rules, parallel rules and conditional rules @cite_3 @cite_15 @cite_12 .
@cite_15 @cite_3 @cite_12
1969402593 121166499 1998333922
2 Static Algebras and Updates 4 2.1 Static Algebras: Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Vocabularies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Definition of Static Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.5 Locations and Updates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.6 Update Sets and Families of Update Sets . . . . . . . . . . . . . . . . . . . . . . . . 6 2.7 Conservative Determinism vs. Local Nondeterminism . . . . . . . . . . . . . . . . . . 7 A firing kiln, especially for use as a vacuum firing kiln for dental ceramic purposes, having a lower portion having a fixed firing platform, an upper portion raisable from the lower portion and in abutting relationship therewith, the lower portion having a hollow firing chamber in facing relationship with a fixed firing platform. The firing chamber includes means for emitting heat into the hollow chamber and toward the fixed firing platform, the surface of the fixed firing platform being at or above the level of the upper edge of the lower portion. We examine sequential algorithms and formulate a sequential-time postulate, an abstract-state postulate, and a bounded-exploration postulate . Analysis of the postulates leads us to the notion of sequential abstract-state machine and to the theorem in the title. First we treat sequential algorithms that are deterministic and noninteractive. Then we consider sequential algorithms that may be nondeterministic and that may interact with their environments.