Relating automata-theoretic hierarchies to complexity-theoretic hierarchies

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1. [1] J.L. Balcázar, J. Díaz and J. Gabarró, Structural Complexity I, Vol. 11 of EATCS Monographs on Theoretical Computer Science. Springer-Verlag (1988). Zbl0638.68040MR1047862
2. [2] J.L. Balcázar, J. Díaz and J. Gabarró, Structural Complexity II, Vol. 11 of EATCS Monographs on Theoretical Computer Science. Springer-Verlag (1990). Zbl0746.68032MR1056474
3. [3] B. Borchert, On the acceptance power of regular languages. Theoret. Comput. Sci. 148 (1995) 207-225. Zbl0873.68121MR1355587
4. [4] B. Borchert, D. Kuske and F. Stephan, On existentially first-order definable languages and their relation to $NP$. RAIRO: Theoret. Informatics Appl. 33 (1999) 259-269. Zbl0949.03035MR1728426
5. [5] D.P. Bovet, P. Crescenzi and R. Silvestri, A uniform approach to define complexity classes. Theoret. Comput. Sci. 104 (1992) 263-283. Zbl0754.68049MR1186181
6. [6] J.A. Brzozowski and R Knast, The dot-depth hierarchy of star-free languages is infinite. J. Comput. Systems Sci. 16 (1978) 37-55. Zbl0368.68074MR471451
7. [7] H.-J. Burtschick and H. Vollmer, Lindström Quatifiers and Leaf Language Definability. Int. J. Found. Comput. Sci. 9 (1998) 277-294. Zbl1319.68104
8. [8] E. Hemaspaandra, L. Hemaspaandra and H. Hempel, What’s up with downward collapse: Using the easy-hard technique to link Boolean and polynomial hierarchy collapses. Compl. Theory Column 21, ACM-SIGACT Newslett. 29 (1998) 10-22. 
9. [9] U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer and K.W. Wagner, On the power of polynomial time bit-reductions, in Proc. 8th Structure in Complexity Theory (1993) 200-207. MR1310801
10. [10] U. Hertrampf, H. Vollmer and K.W. Wagner, On the power of number-theoretic operations with respect to counting, in Proc. 10th Structure in Complexity Theory (1995) 299-314. 
11. [11] U. Hertrampf, H. Vollmer and K.W. Wagner, On balanced vs. unbalanced computation trees. Math. Systems Theory 29 (1996) 411-421. Zbl0853.68097MR1389468
12. [12] B. Jenner, P. McKenzie and D. Therien, Logspace and logtime leaf languages. Inform. and Comput. 129 (1996) 21-33. Zbl0864.68057MR1408830
13. [13] K. Kuratowski and A. Mostowski, Set Theory. North Holland (1967). Zbl0165.01701MR229526
14. [14] J. Köbler, U. Shöning and K.W. Wagner, The difference and truth-table hierarchies for NP. Dep. of Informatics, Koblenz, Preprint 7 (1986). 
15. [15] R. McNaughton and S. Papert, Counter-free automata. MIT Press, Cambridge, Massachusets (1971). Zbl0232.94024MR371538
16. [16] D. Perrin and J.-E. Pin, First order logic and star-free sets. J. Comput. Systems Sci. 32 (1986) 393-406. Zbl0618.03015MR858236
17. [17] J.-E. Pin and P. Weil, Polynomial closure and unambiguous product. Theory Computing Systems 30 (1997) 383-422. Zbl0872.68119MR1450862
18. [18] S. Reith and K.W. Wagner, On Boolean lowness and Boolean highness, in Proc. 4-th Ann. Int. Computing and Combinatorics Conf. Springer, Berlin, Lecture Notes in Comput. Sci. 1449 (1998) 147-156. Zbl0912.68049MR1683382
19. [19] V.L. Selivanov, Two refinements of the polynomial hierarchy, in Proc. of Symposium on Theor. Aspects of Computer Science STACS-94. Springer, Berlin, Lecture Notes in Comput. Sci. 775 (1994) 439-448. Zbl0941.03544MR1288556
20. [20] V.L. Selivanov, Refining the polynomial hierarchy, Preprint No. 9. The University of Heidelberg, Chair of Mathematical Logic (1994) 20 p. MR1763384
21. [21] V.L. Selivanov, Fine hierarchies and Boolean terms. J. Symb. Logic 60 (1995) 289-317. Zbl0824.03022MR1324514
22. [22] V.L. Selivanov, Refining the polynomial hierarchy. Algebra and Logic 38 (1999) 456-475 (Russian, there is an English translation). Zbl0932.03052MR1763384
23. [23] V.L. Selivanov, A logical approach to decidability of hierarchies of regular star-free languages, in Proc. of 18-th Int. Symposium on Theor. Aspects of Computer Science STACS-2001 in Dresden, Germany. Springer, Berlin, Lecture Notes in Comput. Sci. 2010 (2001) 539-550 Zbl0976.03042MR1892340
24. [24] V.L. Selivanov and A.G. Shukin, On hierarchies of regular star-free languages (in Russian). Preprint 69 of A.P. Ershov Institute of Informatics Systems (2000) 28 p. 
25. [25] A.G. Shukin, Difference hierarchies of regular languages. Comput. Systems 161 (1998) 141-155 (in Russian). Zbl0932.03053MR1778013
26. [26] H. Schmitz and K.W. Wagner, The Boolean hierarchy over level 1/2 of the Straubing–Therien hierarchy, Technical Report 201. Inst. für Informatik, Univ. Würzburg available at http://www.informatik.uni-wuerzburg.de. 
27. [27] W. Thomas, Classifying regular events in symbolic logic. J. Comput. Systems Sci. 25 (1982) 360-376. Zbl0503.68055MR684265
28. [28] N.K. Vereshchagin, Relativizable and non-relativizable theorems in the polynomial theory of algorithms. Izvestiya Rossiiskoi Akademii Nauk 57 (1993) 51-90 (in Russian). Zbl0822.68035MR1230967
29. [29] G. Wechsung and K. Wagner, On the Boolean closure of NP, in Proc. of the 1985 Int. Conf. on Fundamentals of Computation theory. Springer-Verlag, Lecture Notes in Comput. Sci. 199 (1985) 485-493. Zbl0581.68043MR821265