Abstract. We introduce the concept of an algebraic state machine. This is a state transition machine all parts of that are described by algebraic and logical means. This way we base the description of state transition systems exclusively on the concept of algebraic specifications. Also the state of an algebraic state machine is represented by an algebra. In particular, we describe the state spaces of the state machine by algebraic techniques, and the state transitions by special axioms called transition rules. Then we show how known concepts from algebraic specifications can be used to provide a notion of parallel composition with asynchronous interaction for algebraic state machines. As example we introduce a notion of object-oriented component and show how algebraic state machines can formalize such components. 1

Many languages have been designed to date, of which a large number have never been implemented and the majority are specified in a very imprecise manner. For a language to receive serious consideration among the computer science community, it generally must have been implemented after its design. However, it is the matter of a precise definition which is often forgotten or ignored and yet it is one of the most important aspects of a language when considered in the context of the evolution of programming languages. The language definition is the vehicle by which the rules regarding syntax and semantics are clearly stated and conveyed. It allows for the comparison of languages independent of any implementation or machine architecture. Furthermore, by employing techniques with a formal basis, it is also possible to use the language definition as the source for the automatic generation of a language implementation. This strongly suggests that language designers should precisely define thei...

Abstract-State Machines have been introduced as “a computation model that is more powerful and more universal than standard computation models”, by Yuri Gurevich in 1985 ([Gur85]). ASM gained much attention as a specification method, in particular for the description of the semantics of programming languages, communication protocols, distributed algorithms, etc. Gurevich proved recently that a sequential algorithm must only meet a few, liberal requirements, to be representable as an ASM. We re-formulate Gurevich’s requirements for sequential algorithms, as well as the semantics of ASM-programs and the proof of his main theorem. A couple of examples support and explain intuition and motivation of ASM.