Causal Graph Dynamics

Arrighi, Pablo; Dowek, Gilles

doi:10.1007/978-3-642-31585-5_9

Cited by 21 publications

(50 citation statements)

References 43 publications

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“…In many of these models the dynamics are given in terms of a colimit of updated versions of certain neighbourhoods of a state. This is explicit in [9,10], and suggested by the use of unions in [1,4]. In [9] the colimit to be taken is strikingly similar to the one implied by Proposition 1 of this paper.…”

Section: Introductionsupporting

confidence: 55%

“…Comparisons with later models, especially [9], may be more direct. In [1], a definition of local determinism is given in which a phenomenon in an updated graph is explained by a sub-graph of bounded radius around an 'antecedent' in the previous state. This is shown to be equivalent to taking a union of local updates.…”

Section: Discussion and Future Workmentioning

confidence: 99%

“…In a well-known paper [5], Gandy sets out principles which aim to characterize the possible behaviours of a discrete, deterministic mechanical computing device which could be realized in the physical world. Although in Gandy's detailed axiomatization there are four principles, they can be summarized by two conceptual insights (as emphasized by, for instance, [1,14]): first, that states of computation should be finite objects with a bounded amount of local detail; second, that changes should only propagate with a bounded velocity, and thus their effects on a given location should be determined by a neighbourhood of finite size.…”

Section: Introductionmentioning

confidence: 99%

“…As long as this is done sensibly, and the original model satisfies Gandy's conceptual principles, the resulting formalization will satisfy Gandy's axioms. Although some later studies keep within this set-theoretic framework [14], other work inspired by Gandy's principles replaces his arbitrary hereditarily finite sets with mathematical objects for which one has more direct spatial intuitions, such as graphs [1,10,13] or simplicial surfaces [4]. Indeed, when one has a concrete model of computation in mind, it is often easier to conduct detailed investigations into the operation of Gandy's principles by working with the models directly, in an environment which respects their extra structure, rather than their set-theoretic encodings.…”

Section: Introductionmentioning

confidence: 99%

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A Category Theoretic Interpretation of Gandy's Principles for Mechanisms

Razavi

Schalk

2019

Electron. Proc. Theor. Comput. Sci.

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Based on Gandy's principles for models of computation we give category-theoretic axioms describing locally deterministic updates to finite objects. Rather than fixing a particular category of states, we describe what properties such a category should have. The computation is modelled by a functor that encodes updating the computation, and we give an abstract account of such functors. We show that every updating functor satisfying our conditions is computable.

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Section: Introductionsupporting

confidence: 55%

Section: Discussion and Future Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Category Theoretic Interpretation of Gandy's Principles for Mechanisms

Razavi

Schalk

2019

Electron. Proc. Theor. Comput. Sci.

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“…See [43]. 6 As our 2D programming language contains no alphabetical symbols or numerals (only , •, arrows, and…”

Section: Discussionmentioning

confidence: 99%

Universality in two dimensions

Dershowitz¹,

Dowek²

2013

J Logic Computation

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Turing, in his immortal 1936 paper, observed that " [human] computing is normally done by writing. . . symbols on [two-dimensional] paper", but noted that use of a second dimension "is always avoidable" and that "the two-dimensional character of paper is no essential of computation". We propose to promote two-dimensional models of computation and exploit the naturalness of two-dimensional representations of data. In particular, programs for a two-dimensional Turing machine can be recorded most naturally on its own two-dimensional input-output grid in such a transparent fashion that schoolchildren would have no difficulty comprehending their behavior. This two-dimensional rendering allows, furthermore, for a most perspicacious rendering of Turing's universal machine.

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