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From Decidability to Undecidability by Considering Regular Sets of Instances | | Petra Wolf
; | | Date: |
19 Jun 2019 | | Abstract: | We are lifting classical problems from single instances to regular sets of
instances. The task of finding a positive instance of the combinatorial problem
$P$ in a potentially infinite given regular set is equivalent to the so called
intreg-problem of $P$, which asks for a given DFA $A$, whether the intersection
of $P$ with $L(A)$ is non-empty. The intreg-problem generalizes the idea of
considering multiple instances at once and connects classical combinatorial
problems with the field of automata theory. While the question of the
decidability of the intreg-problem has been answered positively for several NP-
and even PSPACE-complete problems, we are presenting natural problems even from
L with an undecidable intreg-problem. We also discuss alphabet sizes and
different encoding-schemes elaborating the boundary between problem-variants
with a decidable respectively undecidable intreg-problem. | | Source: | arXiv, 1906.8027 | | Services: | Forum | Review | PDF | Favorites | |
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