Publications of Xizhong Zheng

Book

• X. Zheng, Effective Hierarchy of Real Numbers, Shaker Verlag, Aachen, 2007 (ISBN 978-3-8322-6343-0.

Journal Papers

1. X. Zheng. A hierarchy of computably enumerable reals, Fundamenta Informaticae, Vol. 83 (2008), 219 - 230.
2. X. Zheng. Classification of Computably Approximable Real Numbers Theory of Computing Systems, Vol. 43(2008), No. 3-4, 603-624.
3. Q. Chen, K. Su and X. Zheng. Primitive recursive real numbers. Mathematical Logic Quarterly,  Vol. 53(2007), No. 4/5, 345 -- 360.
4. X. Zheng. On the hierarchy of Delta_2 real numbers, Theor.Inform. Appl.41(2007), no.1, 3--25.
5. R. Rettinger and X. Zheng. A hierarchy of Turing degrees for divergence bounded computable real numbers, J. Complexity. Vol. 22 (2006), No. 6, 818-826..
6. X. Zheng, D. Lu and K. Bao. Divergence bounded computable real numbers, Theor. Comput. Sci., Vol. 351(2006), 27-38.
7. K. Su, Q. Chen, A. Sattar, W. Yue, G. Lv and X. Zheng. Verification of Authentication Protocols for Epistemic Goals via SAT Compilation, Journal of Computer Science and Technology, 21(2006), No. 6, 932 -- 943, Springer-Verlag.
8. X. Zheng, R. Rettinger and R. Gengler.   Closure properties of real numbers classes under CBV functions. Theory of Comnputing Systems, 38(2005), 701 - 729.
9. X. Zheng and R. Rettinger.  Effective Jordan decomposition. Theory of Comnputing Systems, 38(2005), No. 2, 189 - 209
10. X. Zheng, R. Rettinger and G. Barmpalias. h-Monotonically computable real numbers. Mathematical Logic Quarterly, 51(2005) No. 2, 157-170.
11. R. Downey, G. Wu and X. Zheng.   Degrees of d.c.e. reals. Mathematical Logic Quarterly, 50(2004) No.4/5, 345-350.
12. X. Zheng and R. Rettinger.   Weak computability and representation of real numbers. Mathematical Logic Quarterly, 50(2004) No.4/5, 431-442.
13. R. Rettinger and X. Zheng.   On the hierarchy and extension of monotonically computable real numbers. Journal of Complexity, 19(2003) 672-691.
14. X. Zheng.   On the Turing degrees of weakly computable real numbers. Journal of Logic and Computation, Vol. 13 (2003) No.2, 159-172 .
15. X. Zheng.   Recursive approximability of real numbers. Mathematical Logic Quarterly,48(2002), Suppl. 1, 131 - 156.
16. X. Zheng.   Closure properties on real numbers under limits and computable operators. Theor. Comput. Sci., Vol. 284 (2002), No. 2, 499 - 518.
17. R. Rettinger, X. Zheng, R. Gengler and B. von Braunmühl.   Monotonically computable real numbers. Mathematical Logic Quarterly, 48(2002), no 3, 459 - 479.
18. X. Zheng and K. Weihrauch.    The arithmetical hierarchy of real numbers. Mathematical Logic Quarterly.Vol. 47(2001), no.1 51 - 65.
19. X. Zheng, K. Weihrauch and K. Ambos-Spies.    Weakly computable real numbers. Journal of Complexity16(2000), 676 -690.
20. K. Weihrauch and X. Zheng.   Computability on Continuous, Lower Semi-Continuous and Upper Semi-Continuous Real Functions. Theor. Comput. Sci.234(2000)109-133.
21. X. Zheng, V. Brattka, K. Weihrauch.   Approaches to effective semi-continuity of real functions. Math. Log. Quart.Vol. 45(1999), no. 4, 481-496
22. K. Weihrauch and X. Zheng.   Effectiveness of the Global Modulus of Continuity on Metric Spaces. Theor. Comput. Sci.Vol. 219(1999) 439-450.
23. K. Ambos-Spies, S. A. Terwijn and X. Zheng.   Resource Bounded Randomness and Weakly Complete Problems. Theor. Comput. Sci. 172(1997) no.1-2, 195-207.
24. X. Gu and X. Zheng.   The reduction of double recursion, J. of Nanjing university, Mathematical Biquartly, 11(1994) no. 1, 56--69 (in Chinese.) (MR 95j:03078)
25. X. Zheng.   The splitting of polynomial time degrees by minimal pairs, Acta Mathematics Sinica37(1994) no.2, (in Chinese)
26. X. Zheng.    On the splitting of p-m degrees, J. of Software, 5(1994) no.4, ( in Chinese)
27. X. Zheng and L.Qian.   An Extension of Grzegorczyk´s Hierarchy J. of Software, 5(1994) no.3, 55-64 (in Chinese)
28. X. Zheng.   The rhombus classes of degrees of unsolvability (I), the jump properties, Archive for Mathematical Logic. 3(1994) no.1 1-12.
29. X. Zheng; D. Ding and Z. Sun.    On the definition of degrees of unsolvability for reals, Chinese Science Bulletin, 38(1993)no.3, 172-175. (in Chinese)
30. D. Lu and X. Zheng.   On the ninth Grzegorczyk´s problem, J. of Jiangsu Polytechnic University, 13(1992) no.3, 94-101. (in Chinese)
31. L. Qian and X. Zheng.   The lattice embedding properties of the quasi-contigious degrees, Chinese Science Bulletin, 37(1992)no.23, 2200-2202. (in Chinese)
32. X. Zheng and L. Qian.    The hierarchy and Grzegorczyk´s problem of multiple recursive functions. Chinese Science Bulletin, 37(1992) no.15, 1319-1320
33. X. Zheng.   Double recursive functions and their hierarchy, J. of Mathematical Research and Exposition, 13(1993) no.2, 303-308. (in Chinese)
34. X. Zheng.   A hierarchy of double recursive functions, J. of Nanjing University, Mathematical Biquarterly, 10(1993) no.1, 39-45.(in Chinese)
35. X. Zheng.   On the maximality of some pairs of polynomial time degrees, Notre Dame J. of Formal Logic, 34(1993) no.1, 29-35. (the abstract appeared in Chinese Science Bulletin 37(1991) no.6, 521-523)
36. X. Zheng.   Combine the splitting and branching of polynomial time degrees, J. of Nanjing University, Mathematical Biquarterly, 9(1992), no.2, 158-162 (in Chinese)
37. X. Zheng.   There is no maximal minimal pair of p-m degrees, J. of Nanjing University, Mathematical Biquarterly, 9(1992) no.1, 18-22 (in Chinese)
38. X. Zheng.   On the minimal covers for sets of degrees of unsolvability, Chinese Annals of Mathematics, 13A(1992) no.6, 728-733. (in Chinese)
39. X. Zheng.   P =? NP problem and polynomial time degrees, J. of Nanjing University, Mathematical Biquarterly, 8(1991) no.2 187-192 (in Chinese)
40. X. Zheng.   Immunity and simplicity of partial functions, J. of Nanjing University, Mathematical Biquarterly, 8(1991) no.1, 52-55.
41. X. Zheng.   Elementary system of concatenation, elementary arithmetic and protosyntax, Chinese Quarterly J. of Mathematics, 6(1991) no.2, 12-30.
42. X. Zheng.   The rhombus classes of degrees of unsolvability (II), the jump classes and chain properties, J. of Nanjing University, Mathematical Biquarterly, 7(1990) no.1, 13-25.

Refereed Conference Papers

1. R. Rettinger and X. Zheng. Points on Computable Curves of Computable Lengths. MFCS 2009: 736-743.
2. R. Rettinger and X. Zheng. On the computability of the rectifiable simple curves. CCA 2009. Informatik Berichte 353-7/2009, Hagen University, 243-253.
3. X. Zheng. A computability theory of real numbers CCA'08, August 21-24, Hagen, Germany 2008
4. X. Zheng. Initially-bounded computability and hierarchy of computably enumerable sets, COCOON 07, Banff, Canada, July 16-19, 2007. (accepted)
5. X. Zheng. Finitely bounded effective computability, CCA'07, June 16-18, 2007, Siena, Italy. (accepted)
6. Y. Fan, D. Ding and X. Zheng. Totally d-c.e. Real Numbers, CiE 2007, Siena, Italy, June 19-23, 2007. (accepted)
7. X. Zheng. Classification of the Computable Approximations. CCA 2006, Florida, USA, ENTCS 167(2007), 325--344, Elsevier.
8. Q. Chen, K. Su and X. Zheng. Primitive Recursiveness of Real Numbers under Different Representations, CCA 2006, Florida, USA, ENTCS 167(2007), 303--304, Elsevier.
9. K. Su, Q. Chen, X. Zheng and W. Yue. Reasoning about Knowledge by SAT Solving, CIS 2006, pp536--539, Guangzhou China, IEEE Press.
10. X. Zheng. A computability theory of real numbers. CiE 2006, 30 June - 5 July, Swansea. LNCS 3988, pp 584 -594.
11. R. Rettinger and X. Zheng. A hierarchy of Turing degrees of divergence bounded computable real numbers. CCA 2005, August 25-29, Kyoto, Japan.
12. R. Rettinger and X. Zheng. Solovay reducibility on d-c.e. real numbers, COCOON 2005, August 16-19, 2005, Kunming, China. LNCS 3595, pp359-368, Springer.
13. R. Rettinger and X. Zheng. On the Turing degrees of divergence bounded computable reals, CiE 2005, New Computational Paradigms Amsterdam, June 8-12, 2005, LNCS 3526, pp418-428, Springer.
14. X. Zheng. On the hierarchy of $\Delta^0_2$-real numbers, RNC'6, International Conference on Real Numbers and Computers, Schloss Dagstuhl, Germany, November 15-17, 2004.
15. X. Zheng and R. Rettinger. A note on the Turing degrees of divergence bounded computable reals, CCA 2004, August 16-20, 2004, Lutherstadt Wittenberg, Germany.
16. X. Zheng and R. Rettinger  On the extensions of Solovay Reducibility. COOCON 2004, August 17-20, 2004, Jeju Island, Korea, LNCS 3106, pp360 -369, Springer 2004.
17. X. Zheng, R. Rettinger, and R. Gengler.    Ershov's hierarchy of real numbers. MFCS 2003 August 25 - 29, 2003 ,  Bratislava Slovak Republic, LNCS 2747, 681-690, Springer 2003.
18. X. Zheng and R. Rettinger. h-Monotonically computable real numbers. CCA 2003, August28 - 30. 2003, Cincinnati, USA. pp375 - 388.
19. X. Zheng.   On the divergence bounded computable real numbers. COOCON 2003, July 25-28, 2003, Big Sky, MT, USA, LNCS 2697, pp102-111, Springer 2003..
20. X. Zheng, and G. Barmpalias.   On the monotonic computability of semi-computable real numbers. DMTCS 2003, July 7-12, 2003, Dijon, LNCS 2731, 290-300, Springer 2003.
21. X. Zheng, R. Rettinger and B. von Braunmühl.   On the effective Jordan decomposability. STACS 2003, Feb. 27 - March 1, 2003, Berlin, LNCS 2607, 167-178. Springer 2003.
22. X. Zheng, R. Rettinger and B. von Braunmühl.   Effectively absolute continuity and effective Jordan decomposability. Electronic Notes in Theoretical Computer Science, 66(2002) no. 1. pp.12. Proceedings of CCA'02, July 12 - 13, Malaga, Spain.
23. R. Rettinger, X. Zheng and B. von Braunmühl.   Computable Real Functions of Bounded Variation and semi-Computable Real Numbers. COCOON'02, Aug. 15-17, Singapore, LNCS 2387, pp47 - 56. Springer 2002.
24. R. Rettinger and X. Zheng.   Hierarchy of the monotonically computable real numbers. MFCS'01August 27-31, 2001, Marianske Lazne, Czech Republic.LNCS 2136, pp633-644. Springer 2001.
25. R. Rettinger, X. Zheng, R. Gengler and B. von Braunmühl.    Monotonically computable real numbers. DMTCS01July 2-6, 2001, Constantza, Romania. Springer 2001.
26. R. Rettinger, X. Zheng, R. Gengler and B. von Braunmühl.  Weakly computable real numbers and total computable real functions. COCOON01 August 20-23, 2001, Guilin, China. LNCS 2108, pp586-595, Springer 2001.
27. X. Zheng.   Closure properties on real numbers under limits and computable operators. COCOON'00, Sydney, July 26-28, 2002, LNCS 1858, 170 - 179, Springer 2000.
28. X. Zheng and K. Weihrauch.    The arithmetical hierarchy of real numbers. MFCS'99, Szklarska Poreba, Poland. September 6 - 10, 1999, LNCS 1672, 23-33, Springer 1999.
29. X. Zheng.    Binary enumerability of real numbers. COCOON'99, Tokyo, Japan. July, 26-28 1999, LNCS 1627, 300-309, Springer 1999.
30. K. Weihrauch and X. Zheng.   A finite hierarchy of recursively enumerable real numbers. MFCS'98, Brno, Czech Republic. Aug. 24 - 28, 1998, LNCS 1450, pp798--806,  Springer 1998.
31. V. Brattka, K. Weihrauch and X. Zheng.   Approaches to effective semi-continuity of real functions. COCOON'98 Taipei, China. Aug. 12-14, 1998, LNCS 1449, pp184--193, Springer 1998.
32. K. Weihrauch and X. Zheng.   Effectiveness of the Global Modulus of Continuity on Metric Spaces. in Category Theory and Computer Science", Proc. of CTCS'97, Santa Margherita Ligure, Italy, September 1997 LNCS 1290, pp210 - 219, Springer 1997.
33. K. Weihrauch and X. Zheng.   Computability on Continuous, Lower Semi-Continuous and Upper Semi-Continuous Real Functions. in Computing and Combinatorics", Proc. of COCOON'97, Shanghai, China, August 1997. LNCS 1276, pp166-175, Springer 1997.
34. K. Ambos-Spies, E. Mayordomo and X. Zheng.  A comparison of weak completeness notions. In "Proceedings Eleventh Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference), May 24-27, 1996, Philadelphia, Pennsylvania, USA", 1996, 171-178, IEEE Computer Society Press.
35. K. Ambos-Spies, E. Mayordomo, Y. Wang and X. Zheng.   Resource-Bounded Balanced Genericity, Stochasticity and Weak Randomness. STACS'96, 13th AnnoualSymposium on Theoretical Aspects of Computer Science, Feb. 1996, Claude Puech and Ruedinger Reischuk (Eds), LNCS 1046, pp63-74.
36. K. Ambos-Spies, S. A. Terwijn and X. Zheng.   Resource Bounded Randomness and Weakly Complete Problems. Algorithms and Computatiom 5th International Symposium, ISAAC'94, Beijing, Lecture Notes in Computer Science 834, pp369-377.
37. X. Zheng and L. Qian.   An extension of Grzegorczyk´s hierarchy, in "Proc. of the Chinese Conference of Theoretic Computer Science, Langzhou, 1991.8", 32-46,
38. X. Zheng.   Hierarchy of a class of subrecursive functions, in Proc. of the Chinese Conference of heoretic Computer Science, Langzhou, August 1991. pp77-82. (in Chinese)
39. X. Zheng.   Primitive recursive reducibility, in Selected Papers on BCK, BCI-algebras and Computer Logic Shen Baiying ed., pp173-178, Shanghai Jiaotong University Press, 1991. (in Chinese)
40. X. Zheng.   Generating bases and jump classes, in Proc. of the Chinese Mathematical Logic Conference, Yangzhou, October 1989. Special issue of J. of Nanjing University, Mathematical Biquarterly (1991), pp119-121. (in Chinese)

Others

1. X. Zheng, Computability Theory of Real Numbers, Habilitation Thesis, BTU Cottbus, Computer Science Report 03/05, 2005.
2. X. Zheng, R. Rettinger and B. von Braunmühl. Weakly computability and representation of real numbers. Computer Science Reports, BTU Cottbus Report 02/03, 2003.
3. R. Rettinger, X. Zheng and B. von Braunmühl. On the Jordan decomposability for computable functions of bounded variation. Computer Science Reports, BTU CottbusReport 03/02, 2002.
4. R. Rettinger, X. Zheng and B. von Braunmühl. Computable functions of bounded variation and semi-computable real numbers. Computer Science Reports, BTU CottbusReport 02/02, 2002.
5. X. Zheng.   Beyond computable real numbers. Computability and Complexity in Analysis, Dagstuhl-Seminar 01461, Nov. 12--16, 2001.
6. R. Rettinger and X. Zheng.   Hierarchy of the monotonically computable real numbers. Computer Science Reports, BTU CottbusReport 06/01, 2001.
7. R. Rettinger, X. Zheng, R. Gengler and B. von Braunmühl.   Monotonically computable real numbers. Computer Science Reports, BTU CottbusReport 03/01, 2001.
8. R. Rettinger, X. Zheng, R. Gengler and B. von Braunmühl.   Weakly computable real numbers and total computable real functions. Computer Science Reports, BTU CottbusReport 01/01, 2001.
9. X. Zheng.   On the Turing degrees of real numbers. Computer Science Reports, BTU CottbusReport 02/01, 2001.
10. X. Zheng.   Weakly Computable Real Number and Closure Properties. Computability and Complexity in Analysis Dagstuhl-Seminar, Nov. 15--19, 1999.
11. X. Zheng.   Weak Computability and Semi-Continuity in Analysis, Ph.D Thesis, Department of Computer Science of FernUniversität Hagen, Nov. 1998, (Advisor: Klaus Weihrauch).
12. K. Weihrauch and X. Zheng.   Computability on Continuous, Lower Semi-Continuous and Upper Semi-Continuous Real Functions. Computability and Complexity in Analysis Dagstuhl-Seminar, Apr. 21--24, 1997.
13. K. Ambos-Spies and X. Zheng.   n^k- random sets are weakly complete for exponential time. Structure and Complexity, Dagstuhl Seminar. Feb. 14--18, 1994.
14. X. Zheng.   The rhombus classes of degrees of unsolvability, Ph.D Thesis, Department of Mathematics of Nanjing University, December 1987 (Advisor: Mo Shaoqui).