About: State complexity of union and intersection for two-way nondeterministic finite automata     Goto   Sponge   NotDistinct   Permalink

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  • The number of states in a two-way nondeterministic finite automaton (2NFA) needed to represent intersection of languages given by an m-state 2NFA and an n-state 2NFA is shown to be at least m + n and at most m + n + 1. For the union operation, the number of states is exactly m + n. The lower bound is established for languages over a one-letter alphabet. The key point of the argument is the following number-theoretic lemma: for all m,n >= 2 with m, n not equal to 6 (and with finitely many other exceptions), there exist partitions m = p1 +...+ pk and n = q1 +...+ ql, where all numbers p1,...,pk,q1,...,ql >= 2 are powers of pairwise distinct primes. For completeness, an analogous statement about partitions of any two numbers m,n not in {4,6} (with a few more exceptions) into sums of pairwise distinct primes is established as well.
  • The number of states in a two-way nondeterministic finite automaton (2NFA) needed to represent intersection of languages given by an m-state 2NFA and an n-state 2NFA is shown to be at least m + n and at most m + n + 1. For the union operation, the number of states is exactly m + n. The lower bound is established for languages over a one-letter alphabet. The key point of the argument is the following number-theoretic lemma: for all m,n >= 2 with m, n not equal to 6 (and with finitely many other exceptions), there exist partitions m = p1 +...+ pk and n = q1 +...+ ql, where all numbers p1,...,pk,q1,...,ql >= 2 are powers of pairwise distinct primes. For completeness, an analogous statement about partitions of any two numbers m,n not in {4,6} (with a few more exceptions) into sums of pairwise distinct primes is established as well. (en)
Title
  • State complexity of union and intersection for two-way nondeterministic finite automata
  • State complexity of union and intersection for two-way nondeterministic finite automata (en)
skos:prefLabel
  • State complexity of union and intersection for two-way nondeterministic finite automata
  • State complexity of union and intersection for two-way nondeterministic finite automata (en)
skos:notation
  • RIV/00216224:14310/11:00050220!RIV12-GA0-14310___
http://linked.open...avai/riv/aktivita
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  • P(GA201/09/1313)
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  • 1-4
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  • 232151
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  • RIV/00216224:14310/11:00050220
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  • finite automata; two-way automata; state complexity; partitions into sums of primes (en)
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  • NL - Nizozemsko
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  • [24D6D1C07644]
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  • 110
http://linked.open...iv/tvurceVysledku
  • Kunc, Michal
  • Okhotin, Alexander
http://linked.open...ain/vavai/riv/wos
  • 000294764900018
issn
  • 0169-2968
number of pages
http://bibframe.org/vocab/doi
  • 10.3233/FI-2011-540
http://localhost/t...ganizacniJednotka
  • 14310
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