Abstract. The recent success of service-oriented architectures gives rise to some fundamental questions: To what extent do services constitute a new paradigm of computation? What are the elementary ingredients of this paradigm? What are adequate notions of semantics, composition, equivalence? How can services be modeled and analyzed? This paper addresses and answers those questions, thus preparing the ground for forthcoming software design techniques. Key words:models of computation, services, SOA, open workflow nets

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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.

Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then outline a quantum mechanical “algorithm” for one of the insoluble problems of mathematics, the Hilbert’s tenth and equivalently the Turing halting problem. The key element of this algorithm is the computability and measurability of both the values of physical observables and of the quantum-mechanical probability distributions for these values. The fact is that quantum computers can prove theorems by methods that neither a human brain nor any other Turing-computational arbiter will ever be able to reproduce. What if a quantum algorithm delivered a theorem that it was infeasible to prove classically. No such algorithm is yet known, but nor is anything known to rule out such a possibility, and this raises a question of principle: should we still accept such a theorem as undoubtedly proved? We believe that the rational answer ot this question is yes, for our confidence in quantum proofs rests upon the same foundation as our confidence in classical proofs: our acceptance of the physical laws underlying the computing operations. D. Deustch, A. Ekert and R. Lupacchini [1] 1

The theory of quantum computation is presented in a self contained way from a computer science perspective. The basics of classical computation and quantum mechanics is reviewed. The circuit model of quantum computation is presented aspects of computation and the interplay between them. This report is presented as a Master’s thesis at the department of Computer Science and Engineering at Göteborg University, Göteborg, Sweden. The text is part of a larger work that is planned to include chapters on quantum algorithms, the quantum Turing machine model and abstract approaches to quantum computation. Contents 1

Different types of physical unknowables are discussed. Provable unknowables are derived from reduction to problems which are known to be recursively unsolvable. Recent series solutions to the n-body problem and related to it, chaotic systems, may have no computable radius of convergence. Quantum unknowables include the random occurrence of single events, complementarity and value indefiniteness.