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Computation on Structures

Behavioural Theory, Logic, Complexity

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Book cover Logic, Computation and Rigorous Methods

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12750))

Abstract

Over the last decades the field of computer science has changed a lot. In practice we are now dealing with very complex systems, but it seems that the theoretical foundations have not caught up with the development. This article is dedicated to a demonstration how a modernised theory of computation may look like. The theory is centred around the notion of algorithmic systems addressing behavioural theory, logic and complexity theory.

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Notes

  1. 1.

    Note a full behavioural theory of non-deterministic algorithms does not yet exist.

  2. 2.

    Strictly speaking, all these previous computational models are still based on Turing machines, which are coupled with queries on relational stores.

  3. 3.

    Insignificant choice imposes two conditions on the update sets yielded by a choice. The first of these conditions is similar to semi-determinism [38].

  4. 4.

    More precisely: unbounded parallel algorithms, as sequential algorithms algorithms already subsume bounded parallelism. The difference is that in the unbounded case the parallel branches of a computation depend on the state.

  5. 5.

    It must be multiset terms and not set terms, as there may be multiple branches doing the same.

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Authors and Affiliations

  1. UIUC Institute, Zhejiang University, Haining, China

    Klaus-Dieter Schewe

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  1. Institut für Softwaretechnik und Programmiersprachen, University of Ulm, Ulm, Germany

    Alexander Raschke

  2. Dipartimento di Informatica, Università degli Studi di Milano, Crema, Italy

    Elvinia Riccobene

  3. UIUC Institute, Zhejiang University, Haining, China

    Klaus-Dieter Schewe

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Schewe, KD. (2021). Computation on Structures. In: Raschke, A., Riccobene, E., Schewe, KD. (eds) Logic, Computation and Rigorous Methods. Lecture Notes in Computer Science(), vol 12750. Springer, Cham. https://doi.org/10.1007/978-3-030-76020-5_15

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  • DOI: https://doi.org/10.1007/978-3-030-76020-5_15

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