A. Szepietowski, \Two-dimensional on-line tesselation acceptors are not closed under complement", Information Sciences, 64 (1992) 115-120. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Complexity of Two-Dimensional Patterns - Lindgren, Moore, Nordahl (2000) (7 citations) (Correct)
....i (s) if s 2 A i for i = 1; 2. For complement, consider pictures consisting of a single row of 2 s, with rows of 0 s and 1 s above and below it, such that there is a row above the 2 s which is not equal to any of the rows below the 2 s. It is easy to see that this is an h(LLL) but it is shown in [56] that its complement is not. In [13] it is shown that h(LLL) s are closed under horizontal and vertical versions of concatenation and the operator; DFA s and NFA s are not [29, 27] It is an open question whether NFA s are closed under complement. It seems unlikely, since (for instance) the set ....
A. Szepietowski, \Two-dimensional on-line tesselation acceptors are not closed under complement", Information Sciences, 64 (1992) 115-120.
New Results on Alternating and Non-Deterministic.. - Kari, Moore (2001) (1 citation) (Correct)
....tree. This gives a loop free DFA which accepts if and only if the original DFA accepts, and since a loop free DFA always halts, we can then switch accepting and rejecting states to recognize the complement of the original language. Furthermore, it is known that REC is not closed under complement [Sze92]. In contrast, up to now it has been an open question whether the 4 way NFA and AFA language classes are closed under complement [GR96,LMN98] In this paper we resolve both these questions in the negative, thus completing the following matrix of Boolean closure properties: co DFA yes yes ....
A. Szepietowski, \Two-dimensional on-line tesselation acceptors are not closed under complement." Information Sciences, 64 (1992) 115-120.
Complexity of Two-Dimensional Patterns - Lindgren, Moore, Nordahl (1997) (7 citations) (Correct)
....i (s) if s 2 A i for i = 1; 2. For complement, consider pictures consisting of a single row of 2 s, with rows of 0 s and 1 s above and below it, such that there is a row above the 2 s which is not equal to any of the rows below the 2 s. It is easy to see that this is an h(LLL) but it is shown in [51] that its complement is not. It is an open question whether NFA s are closed under complement. It seems unlikely, since (for instance) the set of mazes with no route from a to b would be NFA. The basic problem is that NFA s are defined with an existential quantifier, 9 ( there exists ) an ....
A. Szepietowski, "Two-dimensional on-line tesselation acceptors are not closed under complement", Information Sciences, 64 (1992) 115--120.
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