Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decidable Classes of Tree Automata Mixing Local and Global Constraints
  Modulo Flat Theories   We define a class of ranked tree automata TABG generalizing both the tree
automata with local tests between brothers of Bogaert and Tison (1992) and with
global equality and disequality constraints (TAGED) of Filiot et al. (2007).
TABG can test for equality and disequality modulo a given flat equational
theory between brother subterms and between subterms whose positions are
defined by the states reached during a computation. In particular, TABG can
check that all the subterms reaching a given state are distinct. This
constraint is related to monadic key constraints for XML documents, meaning
that every two distinct positions of a given type have different values. We
prove decidability of the emptiness problem for TABG. This solves, in
particular, the open question of the decidability of emptiness for TAGED. We
further extend our result by allowing global arithmetic constraints for
counting the number of occurrences of some state or the number of different
equivalence classes of subterms (modulo a given flat equational theory)
reaching some state during a computation. We also adapt the model to unranked
ordered terms. As a consequence of our results for TABG, we prove the
decidability of a fragment of the monadic second order logic on trees extended
with predicates for equality and disequality between subtrees, and cardinality.

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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an