Abstract State Machines: a unifying view of models of computation and of system design frameworks

Egon Börger
2005 Annals of Pure and Applied Logic  
We capture the principal models of computation and specification in the literature by a uniform set of transparent mathematical descriptions which-starting from scratch-provide the conceptual basis for a comparative study. 1 . 1 Helmut Schwichtenberg gewidmet, dem Freund und Kollegen seit der gemeinsamen Studienzeit in Münster. 0168-0072/$ -see front matter for computation theory [44] which covers also system specification frameworks. The exposition is driven by systematic and not by historical
more » ... considerations, for detailed historical references we refer the reader to [14] or to the update in [23, Ch. 9]. Our basis are Abstract State Machines, briefly reviewed in Section 2, which were defined in [32] and became an integral part of the powerful high-level system design and analysis method explained in the AsmBook [23] . Elaborating upon [13] we provide here for representative algorithmic systems a uniform set of simple ASM definitions which are faithful to the basic intuitions and concepts of each investigated system. The particularly natural, 'coding-free' way in which ASMs allow one to capture other computation models and thus turn out to be 'universal' contrasts with the difficulties one usually encounters when trying to reverse the simulation with a definition of ASMs in other computational frameworks. This is related to the universality claim known as 'ASM thesis' and analysed by Blass and Gurevich in [33, 8] . The ASM models we construct in this paper are however different from the ones which come out of the proofs for the two special versions of the ASM thesis in op.cit. where a small number of postulates is exhibited from which every sequential or synchronous parallel computational device can be proved to be simulatable in lockstep by an appropriate ASM. The construction in [8] depends on the way the abstract postulates capture the amount of computation performed by every single agent, and of the communication between synchronized agents, which are allowed in a synchronous parallel computation step. The desire to prove computational universality from abstract postulates implies the necessity to first capture (a) the huge class of data structures and (b) the many ways they can be used in a basic computation step and then to unfold every concrete basic parallel communication and computation step from the postulates. This unavoidably yields some 'encoding' and 'decoding' overhead to guarantee, for every computational system which possibly could be proposed, a representation by the abstract concepts of the postulates. As a side effect of this generality of the postulates, the application of Blass and Gurevich's proof scheme to established models of computation tends to yield 'abstract' machine models which are more involved than necessary and may blur features which really distinguish different concrete systems. Furthermore, postulating by an existential statement that 'states' are appropriate equivalence classes of structures of a fixed signature (in the sense of logic), that the evolution happens as an iteration of single 'steps', that the single-step 'exploration space' is bounded (i.e. that there is a uniform bound on memory locations basic computation steps depend upon, up to isomorphism), does not by itself provide, for a given computation or specification model, a standard reference description of its characteristic states, of the objects entering a basic computation step, and of its nextstep function. The goal in this paper is that of naturally capturing the basic data structures and single computation steps which characterize current systems of specification and computation, and of formulating them in a way which is uniform enough to pave the way for explicit technical comparisons. By deliberately keeping the ASM model for each proposed system as close as possible to the original usual description of the system, so that it can be recognized straight-forwardly to be simulated correctly and step by step by the ASM model, we provide for the ASM thesis a strong argument which includes asynchronous
doi:10.1016/j.apal.2004.10.007 fatcat:273ludxmbrehtftfxwagx2yfha