Decision Problems for Subclasses of Rational Relations over Finite and
Infinite Words
release_o37d6xmppvcgdnenoo2k27ousy
by
Christof Löding RWTH Aachen
University
2018
Abstract
We consider decision problems for relations over finite and infinite words
defined by finite automata. We prove that the equivalence problem for binary
deterministic rational relations over infinite words is undecidable in contrast
to the case of finite words, where the problem is decidable. Furthermore, we
show that it is decidable in doubly exponential time for an automatic relation
over infinite words whether it is a recognizable relation. We also revisit this
problem in the context of finite words and improve the complexity of the
decision procedure to single exponential time. The procedure is based on a
polynomial time regularity test for deterministic visibly pushdown automata,
which is a result of independent interest.
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