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.
Note a full behavioural theory of non-deterministic algorithms does not yet exist.
- 2.
Strictly speaking, all these previous computational models are still based on Turing machines, which are coupled with queries on relational stores.
- 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.
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.
It must be multiset terms and not set terms, as there may be multiple branches doing the same.
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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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