3,058 research outputs found
A Theme-Rewriting Approach for Generating Algebra Word Problems
Texts present coherent stories that have a particular theme or overall
setting, for example science fiction or western. In this paper, we present a
text generation method called {\it rewriting} that edits existing
human-authored narratives to change their theme without changing the underlying
story. We apply the approach to math word problems, where it might help
students stay more engaged by quickly transforming all of their homework
assignments to the theme of their favorite movie without changing the math
concepts that are being taught. Our rewriting method uses a two-stage decoding
process, which proposes new words from the target theme and scores the
resulting stories according to a number of factors defining aspects of
syntactic, semantic, and thematic coherence. Experiments demonstrate that the
final stories typically represent the new theme well while still testing the
original math concepts, outperforming a number of baselines. We also release a
new dataset of human-authored rewrites of math word problems in several themes.Comment: To appear EMNLP 201
String rewriting for Double Coset Systems
In this paper we show how string rewriting methods can be applied to give a
new method of computing double cosets. Previous methods for double cosets were
enumerative and thus restricted to finite examples. Our rewriting methods do
not suffer this restriction and we present some examples of infinite double
coset systems which can now easily be solved using our approach. Even when both
enumerative and rewriting techniques are present, our rewriting methods will be
competitive because they i) do not require the preliminary calculation of
cosets; and ii) as with single coset problems, there are many examples for
which rewriting is more effective than enumeration.
Automata provide the means for identifying expressions for normal forms in
infinite situations and we show how they may be constructed in this setting.
Further, related results on logged string rewriting for monoid presentations
are exploited to show how witnesses for the computations can be provided and
how information about the subgroups and the relations between them can be
extracted. Finally, we discuss how the double coset problem is a special case
of the problem of computing induced actions of categories which demonstrates
that our rewriting methods are applicable to a much wider class of problems
than just the double coset problem.Comment: accepted for publication by the Journal of Symbolic Computatio
The algebra of rewriting for presentations of inverse monoids
We describe a formalism, using groupoids, for the study of rewriting for
presentations of inverse monoids, that is based on the Squier complex
construction for monoid presentations. We introduce the class of pseudoregular
groupoids, an example of which now arises as the fundamental groupoid of our
version of the Squier complex. A further key ingredient is the factorisation of
the presentation map from a free inverse monoid as the composition of an
idempotent pure map and an idempotent separating map. The relation module of a
presentation is then defined as the abelianised kernel of this idempotent
separating map. We then use the properties of idempotent separating maps to
derive a free presentation of the relation module. The construction of its
kernel - the module of identities - uses further facts about pseudoregular
groupoids.Comment: 22 page
Finite Gr\"obner--Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids
This paper shows that every Plactic algebra of finite rank admits a finite
Gr\"obner--Shirshov basis. The result is proved by using the combinatorial
properties of Young tableaux to construct a finite complete rewriting system
for the corresponding Plactic monoid, which also yields the corollaries that
Plactic monoids of finite rank have finite derivation type and satisfy the
homological finiteness properties left and right . Also, answering a
question of Zelmanov, we apply this rewriting system and other techniques to
show that Plactic monoids of finite rank are biautomatic.Comment: 16 pages; 3 figures. Minor revision: typos fixed; figures redrawn;
references update
Termination orders for 3-dimensional rewriting
This paper studies 3-polygraphs as a framework for rewriting on
two-dimensional words. A translation of term rewriting systems into
3-polygraphs with explicit resource management is given, and the respective
computational properties of each system are studied. Finally, a convergent
3-polygraph for the (commutative) theory of Z/2Z-vector spaces is given. In
order to prove these results, it is explained how to craft a class of
termination orders for 3-polygraphs.Comment: 30 pages, 35 figure
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