Is there a polynomial time algorithm to tell if an NFA over an unary alphabet is universal?

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Given an Nondeterministic Finite State Automaton with $n$ states over an unary alphabet, is there some algorithm to check if the automata is universal in time polynomial in the number of states?



I would not expect this would work over an alphabet of size two or more, since it is PSPACE-complete to check whether a regular expression is universal. However, since regular languages over unary alphabets have nice characterizations, I would expect there would be some way to check the universality of an NFA over an unary alphabet.






algorithms formal-languages finite-automata







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    Given an Nondeterministic Finite State Automaton with $n$ states over an unary alphabet, is there some algorithm to check if the automata is universal in time polynomial in the number of states?



    I would not expect this would work over an alphabet of size two or more, since it is PSPACE-complete to check whether a regular expression is universal. However, since regular languages over unary alphabets have nice characterizations, I would expect there would be some way to check the universality of an NFA over an unary alphabet.






    algorithms formal-languages finite-automata







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      up vote
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      favorite









      up vote
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      down vote

      favorite











      Given an Nondeterministic Finite State Automaton with $n$ states over an unary alphabet, is there some algorithm to check if the automata is universal in time polynomial in the number of states?



      I would not expect this would work over an alphabet of size two or more, since it is PSPACE-complete to check whether a regular expression is universal. However, since regular languages over unary alphabets have nice characterizations, I would expect there would be some way to check the universality of an NFA over an unary alphabet.






      algorithms formal-languages finite-automata







      share|cite|improve this question













      Given an Nondeterministic Finite State Automaton with $n$ states over an unary alphabet, is there some algorithm to check if the automata is universal in time polynomial in the number of states?



      I would not expect this would work over an alphabet of size two or more, since it is PSPACE-complete to check whether a regular expression is universal. However, since regular languages over unary alphabets have nice characterizations, I would expect there would be some way to check the universality of an NFA over an unary alphabet.






      algorithms formal-languages finite-automata




      algorithms formal-languages finite-automata






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      Agnishom Chattopadhyay

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          Determining whether a unary NFA is universal is coNP-complete, as proved by Stockmeyer and Meyer, Word Problems Requiring Exponential Time. See Gruber and Holzer, Computational Complexity of NFA Minimization for
          Finite and Unary Languages, for more results in this vein.






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            Determining whether a unary NFA is universal is coNP-complete, as proved by Stockmeyer and Meyer, Word Problems Requiring Exponential Time. See Gruber and Holzer, Computational Complexity of NFA Minimization for
            Finite and Unary Languages, for more results in this vein.






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              2
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              Determining whether a unary NFA is universal is coNP-complete, as proved by Stockmeyer and Meyer, Word Problems Requiring Exponential Time. See Gruber and Holzer, Computational Complexity of NFA Minimization for
              Finite and Unary Languages, for more results in this vein.






              share|cite|improve this answer






















                up vote
                2
                down vote










                up vote
                2
                down vote









                Determining whether a unary NFA is universal is coNP-complete, as proved by Stockmeyer and Meyer, Word Problems Requiring Exponential Time. See Gruber and Holzer, Computational Complexity of NFA Minimization for
                Finite and Unary Languages, for more results in this vein.






                share|cite|improve this answer












                Determining whether a unary NFA is universal is coNP-complete, as proved by Stockmeyer and Meyer, Word Problems Requiring Exponential Time. See Gruber and Holzer, Computational Complexity of NFA Minimization for
                Finite and Unary Languages, for more results in this vein.







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                answered 3 hours ago









                Yuval Filmus

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