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.






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    up vote
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    favorite
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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







      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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      asked Sep 25 at 4:07









      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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          • Could you please point out which result in the first paper you are refering to?
            – Agnishom Chattopadhyay
            Sep 26 at 11:43










          • The first paper is cited in the second paper as containing this classical result. Unfortunately no pointer is given. The main hurdle toward reading the first paper is the antiquated terminology.
            – Yuval Filmus
            Sep 26 at 15:54










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          1 Answer
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          active

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          active

          oldest

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          active

          oldest

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          up vote
          3
          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




















          • Could you please point out which result in the first paper you are refering to?
            – Agnishom Chattopadhyay
            Sep 26 at 11:43










          • The first paper is cited in the second paper as containing this classical result. Unfortunately no pointer is given. The main hurdle toward reading the first paper is the antiquated terminology.
            – Yuval Filmus
            Sep 26 at 15:54














          up vote
          3
          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




















          • Could you please point out which result in the first paper you are refering to?
            – Agnishom Chattopadhyay
            Sep 26 at 11:43










          • The first paper is cited in the second paper as containing this classical result. Unfortunately no pointer is given. The main hurdle toward reading the first paper is the antiquated terminology.
            – Yuval Filmus
            Sep 26 at 15:54












          up vote
          3
          down vote










          up vote
          3
          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.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Sep 25 at 5:29









          Yuval Filmus

          183k12171332




          183k12171332











          • Could you please point out which result in the first paper you are refering to?
            – Agnishom Chattopadhyay
            Sep 26 at 11:43










          • The first paper is cited in the second paper as containing this classical result. Unfortunately no pointer is given. The main hurdle toward reading the first paper is the antiquated terminology.
            – Yuval Filmus
            Sep 26 at 15:54
















          • Could you please point out which result in the first paper you are refering to?
            – Agnishom Chattopadhyay
            Sep 26 at 11:43










          • The first paper is cited in the second paper as containing this classical result. Unfortunately no pointer is given. The main hurdle toward reading the first paper is the antiquated terminology.
            – Yuval Filmus
            Sep 26 at 15:54















          Could you please point out which result in the first paper you are refering to?
          – Agnishom Chattopadhyay
          Sep 26 at 11:43




          Could you please point out which result in the first paper you are refering to?
          – Agnishom Chattopadhyay
          Sep 26 at 11:43












          The first paper is cited in the second paper as containing this classical result. Unfortunately no pointer is given. The main hurdle toward reading the first paper is the antiquated terminology.
          – Yuval Filmus
          Sep 26 at 15:54




          The first paper is cited in the second paper as containing this classical result. Unfortunately no pointer is given. The main hurdle toward reading the first paper is the antiquated terminology.
          – Yuval Filmus
          Sep 26 at 15:54

















           

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