H. Schmitz. Boolean Hierarchies inside Dot-Depth One. Oktober 1999. Home/Search Document Details and Download
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The Boolean Structure of Dot-Depth One - Glaßer, Schmitz (2000) (1 citation) Self-citation (Schmitz) (Correct)
....hierarchy over B 1=2;k . This approach combines techniques from complexity theory and automata theory, and develop a machinery to attack membership problems in Boolean hierarchies, potentially also in more general settings. A comprehensive treatment of the presented issues is given in [Gla99,Sch99] 2 Preliminaries We consider languages as subsets of A . For a class C of languages we de ne coC = def A n L L 2 C . Let k 0. We will look at w 2 A as a word over A k 1 by taking together each k 1 consecutive letters. Denote elements from A k 1 as ; If ....
....u 2 g l and h j = w 1 u 2 g m for some l m. From fact 1 it follows that h i F h j which in turn implies w 0 u 1 w 1 u 2 g l F w 0 u 1 w 1 u 2 g m . So f i l F f i m and it follows that f i l F f i m , again a contradiction. In a similar way one shows the following theorem (cf. Sch99, Theorem 4.3] Theorem 2. Let k 0. Then (A ; k ) is a wpos. 4 Boolean Hierarchies and their Characterizations Since B 1=2 is closed under nite union and intersection [Arf91] we can de ne classes B 1=2 (l) and coB 1=2 (l) which form the Boolean hierarchy over B 1=2 . From Lemma 1 it ....
H. Schmitz. Boolean hierarchies inside dot-depth one. Technical Report 240, Inst. fur Informatik, Univ. Wurzburg, 1999. Available at http://www.informatik.uni-wuerzburg.de/reports/tr.html.
Equivalence Problems for Boolean Constraint Satisfaction - Böhler, Hemaspaandra.. (2001) (Correct)
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H. Schmitz. Boolean Hierarchies inside Dot-Depth One. Oktober 1999.
Lecture Notes for Logic and Interaction - Böhler, Vollmer (2002) (Correct)
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H. Schmitz. Boolean Hierarchies inside Dot-Depth One. Oktober 1999.
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