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Cascades of tree-automata and computations in universal algebras

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Abstract

It is possible to define a general notion of cascade composition for tree-automata in a way very similar to the case of ordinary automata. For this cascade composition we show necessary and sufficient conditions of decomposability like those of the ordinary case. Also some kinds of associativity properties continue to hold.

A further generalization leads us to apply these results to a large class of universal algebras, and by some examples it is shown that we can decompose some familiar algebras into cascades of tree-automata. Moreover, the cascades obtained identify some algorithms that are the common ones for computing in the algebras considered.

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Authors and Affiliations

  1. Department of Applied Analysis and Computer Science, University of Waterloo, Waterloo, Ontario, Canada

    G. Ricci

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  1. G. Ricci
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Additional information

Supported by CNR Rome, and by N.R.C. of Canada, grant A-4096.

Supported by CNR Rome, and by N.R.C. of Canada, grant A-4096.

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Ricci, G. Cascades of tree-automata and computations in universal algebras. Math. Systems Theory 7, 201–218 (1973). https://doi.org/10.1007/BF01795940

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  • DOI: https://doi.org/10.1007/BF01795940

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