Abstract: We introduce a logic for non distributed, deterministic Abstract State Machines with parallel function updates. Unlike other logics for ASMs which are based on dynamic logic, our logic is based on an atomic predicate for function updates and on a definedness predicate for the termination of the evaluation of transition rules. We do not assume that the transition rules of ASMs are in normal form, for example, that they concern distinct cases. Instead we allow structuring concepts of ASM rules including sequential composition and possibly recursive submachine calls. We show that several axioms that have been proposed for reasoning about ASMs are derivable in our system. We provide also an extension of the logic with explicit step information which allows to eliminate modal operators in certain cases. The main technical result is that the logic is complete for hierarchical (non-recursive) ASMs. We show that, for hierarchical ASMs, the logic is a definitional extension of first-order predicate logic.

Abstract. Turbo Abstract State Machines are ASMs with parallel and sequential composition and possibly recursive submachine calls. Turbo ASMs are viewed as black-boxes that can combine arbitrary many steps of one or more submachines into one big step. The intermediate steps of a turbo ASM are not observable from outside. It is not even clear what exactly the intermediate steps are, because the semantics of turbo ASMs is usually defined inductively along the call graph of the ASM and the structure of the rule bodies. The most important application of turbo ASMs are recursive algorithms. Such algorithms can directly be simulated on turbo ASMs without transforming them into multi-agent (distributed) ASMs. In this article we analyze the hidden intermediate steps of turbo ASMs and characterize them using PAR/SEQ trees. We also address the problem of the reserve in the presence of recursion and sequential composition. 1

Gurevich's [26] Abstract State Machines (ASMs), characterized by the parallel execution of abstract atomic actions in a global state, have been equipped in [13] with a refinement by standard composition concepts for structuring large machines that allows reusing machine components.

Abstract not found