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Abstract
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Motivated by enumeration problems, we define linear orders
on Cartesian
products
and on
subsets of
where
each component set
is
or
, ordered in the natural way.
We require that
be isomorphic
to
if it is infinite. We want
linear orderings of
such that,
in two consecutive tuples
and
, at
most two components differ, and they differ by at most 1.
We are interested in algorithms that determine the next tuple in
by using
local information, where “local” is meant with respect to certain graphs associated with
.
We want these algorithms to work as well for finite and infinite components
. We
will formalise them by
deterministic graph-walking automata and compare their
enumeration powers according to the finiteness of their sets of states and the kinds of
moves they can perform.
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Keywords
enumeration algorithm, diagonal enumeration, graph-walking
automaton, linear order
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Mathematical Subject Classification 2010
Primary: 06A05, 05C38, 68R10, 68P10
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Milestones
Received: 27 November 2019
Revised: 2 April 2020
Accepted: 17 April 2020
Published: 15 October 2020
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