23,845 research outputs found
Remarks on Parikh-recognizable omega-languages
Several variants of Parikh automata on infinite words were recently
introduced by Guha et al. [FSTTCS, 2022]. We show that one of these variants
coincides with blind counter machine as introduced by Fernau and Stiebe
[Fundamenta Informaticae, 2008]. Fernau and Stiebe showed that every
-language recognized by a blind counter machine is of the form
for Parikh recognizable languages , but
blind counter machines fall short of characterizing this class of
-languages. They posed as an open problem to find a suitable
automata-based characterization. We introduce several additional variants of
Parikh automata on infinite words that yield automata characterizations of
classes of -language of the form for all
combinations of languages being regular or Parikh-recognizable. When
both and are regular, this coincides with B\"uchi's classical
theorem. We study the effect of -transitions in all variants of
Parikh automata and show that almost all of them admit
-elimination. Finally we study the classical decision problems
with applications to model checking.Comment: arXiv admin note: text overlap with arXiv:2302.04087,
arXiv:2301.0896
The omega-inequality problem for concatenation hierarchies of star-free languages
The problem considered in this paper is whether an inequality of omega-terms
is valid in a given level of a concatenation hierarchy of star-free languages.
The main result shows that this problem is decidable for all (integer and half)
levels of the Straubing-Th\'erien hierarchy
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