## Interactive small-step algorithms I: Axiomatization, (2006)

Citations: | 4 - 2 self |

### BibTeX

@MISC{Blass06interactivesmall-step,

author = {Andreas Blass and Yuri Gurevich and Dean Rosenzweig and Benjamin Rossman},

title = { Interactive small-step algorithms I: Axiomatization, },

year = {2006}

}

### OpenURL

### Abstract

In earlier work, the Abstract State Machine Thesis — that arbitrary algorithms are behaviorally equivalent to abstract state machines — was established for several classes of algorithms, including ordinary, interactive, small-step algorithms. This was accomplished on the basis of axiomatizations of these classes of algorithms. Here we extend the axiomatization and, in a companion paper, the proof, to cover interactive small-step algorithms that are not necessarily ordinary. This means that the algorithms (1) can complete a step without necessarily waiting for replies to all queries from that step and (2) can use not only the environment’s replies but also the order in which the replies were received.

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Citation Context ...ernal intra-step interaction, but with communication between subprocesses in the parallel case), and ordinary interactive small-step algorithms in [7, 8, 9]. Also, Andreas Glausch and Wolfgang Reisig =-=[16, 17]-=- adapted the postulates of [23] to describe a restricted but important class of “small-step” distributed algorithms. In this section, we briefly overview the work in [23, 7, 8, 9] directly leading to ... |

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Citation Context ...science, the ASM computation model is the most generalINTERACTIVE SMALL-STEP ALGORITHMS I 3 computation model that we know. It supports for example computing with structures rather than strings; see =-=[12]-=- for particular examples leading to interesting theoretical results and questions. Finally it may be disappointing that, unlike the Church-Turing Thesis, the ASM thesis has not been used for negative ... |

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Citation Context ...ause ξ, being attainable, is coherent, which implies Dom( ˙ ξ) ⊆ IssuedX(ξ).INTERACTIVE SMALL-STEP ALGORITHMS I 25 4. Equivalence of Algorithms One of our principal aims in this paper and its sequel =-=[10]-=- is to show that every algorithm, in the sense defined above, is behaviorally equivalent, in a strong sense, to an ASM. Of course, this goal presupposes a precise definition of the notion of behaviora... |

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Citation Context ...istent Turing machine” [19]. But this is not so if one intends to preserve the abstraction level of the given interactive algorithm. In particular, PTMs cannot step-for step simulate interactive ASMs =-=[24]-=-. The topic of the present paper is intra-step interaction between a single sequential-time algorithm and its environment (that is, the rest of the world). We are not aware of any previous literature ... |

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Citation Context ...ernal intra-step interaction, but with communication between subprocesses in the parallel case), and ordinary interactive small-step algorithms in [7, 8, 9]. Also, Andreas Glausch and Wolfgang Reisig =-=[16, 17]-=- adapted the postulates of [23] to describe a restricted but important class of “small-step” distributed algorithms. In this section, we briefly overview the work in [23, 7, 8, 9] directly leading to ... |