The Sequential ASM Thesis

The thesis is that every sequential algorithm, on any level of abstraction, can be viewed as a sequential abstract state machine. Abstract state machines (ASMs) used to be called evolving algebras. The sequential ASM thesis and its extensions inspired diverse applications of ASMs. The early applications were driven, at least partially, by the desire to test the thesis. Different programming languages were the obvious challenges. (A programming language L can be viewed as an algorithm that runs a given L program on given data.) From there, applications of (not necessarily sequential) ASMs spread into many directions. So far, the accumulated experimental evidence seems to support the sequential thesis. There is also a speculative philosophical justification of the thesis. It was barely sketched in the literature, but it was discussed at much greater length in numerous lectures of mine. Here I attempt to write down some of those explanations. This article does not presuppose any familiarity with ASMs.

Reprinted in 2001 book World Scientific book, Current Trends in Theoretical Computer Science, pages 363-392. Sequential Abstract State Machines Capture Sequential Algorithms is a much revised and polished journal version.