Peter Hertling: Publications

 

 

Work as editor
  • J. Blanck, V. Brattka, and P. Hertling, editors:
    Computability and Complexity in Analysis,
    4th International Workshop, CCA 2000, Swansea, UK, September 2000, vol. 2064 of Lecture Notes in Computer Science, Springer, Berlin, 2001.
  • V. Brattka, P. Hertling, M. Yasugi, and N. Zhong, guest editors:
    Selected Papers of the Dagstuhl Seminar on Computability and Complexity in Analysis 2001. Special issue of Math. Logic Quarterly, 48 (Supplement 1), 2002.
  • V. Brattka, P. Hertling, K. Ko, and N. Zhong, guest editors:
    Computability and Complexity in Analysis,
    1st Int. Conference, CCA 2003, Cincinnati, USA, August 2003, Special issue of Math. Logic Quarterly, 50(4/5), 2005.
  • V. Brattka, P. Hertling, K. Ko, H. Tsuiki, guest editors:
    Computability and Complexity in Analysis,
    Selected Papers of the 2nd Int. Conference, CCA 2005, Kyoto, Japan, August 2005, Journal of Complexity, 22(6), 2006.
  • P. Hertling, C. M. Hoffmann, W. Luther, N. Revol:
    Reliable Implementation of Real Number Algorithms: Theory and Practice,
    International Seminar Dagstuhl Castle, Germany January 2006, Revised Papers, vol. 5045 of Lecture Notes in Computer Science, Springer, Berlin, 2008.
  • A. Bauer, P. Hertling, and K. Ko, guest editors:
    Computability and Complexity in Analysis, Special Issue on the occasion of the 6th Int. Conference, CCA 2009, Ljubljana, Slovenia, August, 2009. Journal of Universal Computer Science, 16(18), 2010.
  • M. Archibald, V. Brattka, M. Escardo, and P. Hertling, guest editors:
    Special Issue for the Ninth International Conference "Computability and Complexity in Analysis". Held at the University of Cape Town, South Africa, January 2011. Logical Methods in Computer Science, 2011.
  • V. Brattka and P. Hertling, editors:
    Handbook of Computability and Complexity in Analysis. Springer Nature Switzerland, 2021.

 

 

Journal papers
  • P. Hertling:
    Small spanning sets of cusp forms.
    Math. Ann., 303:629-651, 1995.
  • P. Hertling:
    Disjunctive omega-words und real numbers.
    J. UCS, 2(7):549-568, 1996.
  • P. Hertling:
    Topological complexity with continuous operations.
    J. of Complexity, 12(4):315-338, 1996.
    Special Issue for the Foundations of Computational Mathematics Conference, Rio de Janeiro, January 1997.
  • C. S. Calude, B. Khoussainov, and P. Hertling:
    Do the zeros of Riemann's zeta-function form a random sequence?
    Bulletin of the EATCS, 62:199-207, 1997.
  • P. Hertling, U. Günther, R. Nicolescu, and M. Titchener:
    Representing variable-length codes into fixed-length T-depletion format in encoders and decoders.
    J. UCS, 3(11):1207-1225, 1997.
  • P. Hertling:
    Surjective functions on computably growing Cantor sets.
    J. UCS, 3(11):1226-1240, 1997.
  • P. Hertling and Y. Wang:
    Invariance properties of random sequences.
    J. UCS, 3(11):1241-1249, 1997.
  • C. S. Calude and P. Hertling:
    Computable approximations of reals: An information-theoretic analysis.
    Fundamenta Informaticae, 33:105-120, 1998.
  • C. S. Calude, P. Hertling, and K. Svozil:
    Kochen-Specker theorem: Two geometric proofs.
    Tatra Mountains Math. Publ., 15:133-142, 1998.
  • V. Brattka and P. Hertling:
    Feasible real random access machines.
    J. of Complexity, 14(4):490-526, 1998.
  • C. S. Calude, P. Hertling, and K. Svozil:
    Embedding quantum universes into classical ones.
    Foundations of Physics, 29(3):349-379, 1999.
  • P. Hertling:
    A real number structure that is effectively categorical.
    Math. Logic Quarterly, 45(2):147-182, 1999.
  • P. Hertling:
    An effective Riemann mapping theorem.
    Theor. Comp. Sci., 219:225-265, 1999.
  • P. Hertling:
    Standard representations of real numbers.
    Chaos, Solitons & Fractals, 10(6):1087-1101, 1999.
  • C. S. Calude, P. Hertling, B. Khoussainov, and Y. Wang:
    Recursively enumerable reals and Chaitin Omega numbers.
    Theor. Comp. Sci., 255:125-149, 2001.
  • C. S. Calude, P. Hertling, H. Jürgensen, and K. Weihrauch:
    Randomness on full shift spaces.
    Chaos, Solitons & Fractals, 12(3):491-503, 2001.
  • P. Hertling:
    A limitation for underestimation via twin arithmetic.
    Reliable Computing, 7(2):157--169, 2001.
    Special Issue on Modal Intervals and Its Applications. Selected Papers from the First Workshop on Applications of Interval Analysis to Systems and Control, MISC'99, February 24-26, 1999, Girona, Spain.
  • P. Hertling:
    Nonlinear Lebesgue and Ito integration problems of high complexity.
    J. of Complexity, 17(2):366-387, 2001.
    Special Issue for the Foundations of Computational Mathematics Conference, Oxford, July 1999.
  • P. Hertling:
    Simply normal numbers to different bases.
    J. UCS, 8(2):235-242, 2002.
  • P. Hertling:
    A lower bound for range enclosure in interval arithmetic.
    Theor. Comp. Sci., 279:83-95, 2002.
    Special Issue for the Third Real Numbers and Computers Conference. Paris, April 1998.
  • V. Brattka and P. Hertling:
    Topological properties of real number representations.
    Theor. Comp. Sci., 284(2):241-257, 2002.
  • P. Hertling:
    Topological complexity of zero finding with algebraic operations.
    J. of Complexity, 18(4):912-942, 2002.
  • P. Hertling and K. Weihrauch:
    Random elements in effective topological spaces with measure.
    Information and Computation, 181:32-56, 2003.
  • P. Hertling:
    Is the Mandelbrot set computable?
    Math. Logic Quarterly, 51(1):5-18, 2005
  • P. Hertling:
    A Banach-Mazur computable but not Markov computable function on the computable real numbers.
    Annals of Pure and Applied Logic, 132(2-3):227-246, 2005
  • P. Hertling:
    Nonrandom sequences between random sequences.
    J. UCS, 11(12):1970-1985, 2005.
  • P. Hertling:
    A sequentially computable funktion that is not effectively continuous at any point.
    J. of Complexity, 22(6):752-767, 2006.
  • P. Hertling, C. Spandl:
    Computability theoretic properties of the entropy of gap shifts.
    Fundamenta Informaticae 83:141-157, 2008.
  • P. Hertling, C. Spandl:
    Shifts with decidable language and non-computable entropy.
    Discrete Mathematics and Theoretical Computer Science 10(3):75-94, 2008.
  • P. Hertling, C. Spandl:
    Computing a solution of Feigenbaum's functional equation in polynomial time.
    Log. Methods Comput. Sci. 10(4):7, 9 pages, 2014.
  • V. Bosserhoff, P. Hertling:
    Effective subsets under homeomorphism of R^n.
    Information and Computation, 245, pages 197-215, 2015.
  • P. Hertling:
    Clarke's generalized gradient and Edalat's L-derivative.
    Journal of Logic and Analysis, 9, 21 pages, 2017.
  • P. Hertling:
    Forests describing Wadge degrees and topological Weihrauch degrees of certain classes of functions and relations.
    Computability, vol. 9, no. 3-4, pages 249-307, 2020.
  • P. Hertling and G. Krommes:
    EXPSPACE-Completeness of the Logics K4 × S5 and S4 × S5 and the Logic of Subset Spaces.
    Transactions on Computational Logic, Vol. 22, Issue 4, October 2021, Article No.: 24, pp 1 - 71.

 

Full papers in conference proceedings and other books
  • P. Hertling and K. Weihrauch:
    Levels of degeneracy and exact lower complexity bounds for geometric algorithms.
    Proc. of the Sixth Canadian Conference on Computational Geometry, pages 237-242, Saskatoon, 1994.
  • P. Hertling:
    Embedding cellular automata into reversible ones.
    In: C. S. Calude et al., editors, Unconventional Models of Computation, Discrete Mathematics and Theoretical Computer Science, Proceedings of UMC'98, Auckland, pages 243-256, Springer, Singapore, 1998.
  • C. S. Calude, R. Coles, P. Hertling, and B. Khoussainov:
    Degree theoretic aspects of computably enumerable reals.
    In: S. B. Cooper and J. K. Truss, editors, Models and Computability, volume 259 of London Math. Society Lecture Note Series. Invited Papers from Logic Colloquium 1997, Leeds, pages 23-39, Cambridge University Press, Cambridge, 1999.
  • P. Hertling:
    Banach-Mazur computable functions on metric spaces.
    In: J. Blanck, V. Brattka, and P. Hertling, editors, Computability and Complexity in Analysis, 4th International Workshop, CCA 2000, Swansea, UK, September 2000, vol. 2064 of Lecture Notes in Computer Science, pages 69-81, Springer, Berlin, 2001.
  • P. Hertling:
    A comparison of certain representations of regularly closed sets.
    In: V. Brattka, M. Schröder, and K. Weihrauch, editors, Proceedings of the 5th Workshop on Computability and Complexity in Analysis, CCA 2002, Málaga, Spain, July 2002, Electronic Notes in Theoretical Computer Science (ENTCS) 66(1), 2002.
  • V. Brattka, P. Hertling, K. Weihrauch:
    A Tutorial on Computable Analysis.
    In: S.B. Cooper, B.Löwe., A. Sorbi, editors, New Computational Paradigms, Changing Conceptions of What is Computable, pages 425-491, Springer, New York, 2008.
  • P. Hertling and V. Selivanov:
    Complexity issues for preorders on finite labeled forests.
    In: V. Brattka, H. Diener, and D. Spreen (eds.), Logic, Computation, Hierarchies, Ontos Mathematical Logic, Walter de Gruyter, Boston, 2014, pages 165-190.
  • P. Hertling:
    On the computational complexity of the range computation problem.
    In: O. Kosheleva et al. (eds.), Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications, Springer Nature Switzerland, Studies in Computational Intelligence 835, 2020, pages 269-293.

 

Selected extended abstracts in conference proceedings
  • V. Brattka and P. Hertling:
    Feasible real random access machines.
    Proc. of the SOFSEM'96: Theory and Practice of Informatics, vol. 1175 of Lecture Notes in Computer Science, pages 335-342, Berlin, 1996. Springer-Verlag.
  • P. Hertling:
    Effectivity and effective continuity of functions between computable metric spaces.
    In: D. S. Bridges et al., editors, Combinatorics, Complexity, and Logic, Discrete Mathematics and Theoretical Computer Science, pages 264-275, Singapore, 1997. Springer-Verlag. Proceedings of DMTCS'96, Auckland.
  • C. S. Calude, P. Hertling, B. Khoussainov, and Y. Wang:
    Recursively enumerable reals and Chaitin Omega numbers.
    In: M. Morvan et al., editors, Proceedings of the 15th Symposium on Theoretical Aspects of Computer Science, STACS 98, Paris, France, February 1998, volume 1373 of Lecture Notes in Computer Science, pages 596-606, Berlin, 1998. Springer-Verlag.
  • P. Hertling:
    A quadratic lower bound for range computation in interval arithmetic.
    In: International Conference on Interval Methods and their Applications on Global Optimization (INTERVAL'98), pages 49-51, Nanjing, April 1998. Department of Mathematics of Nanjing University, The Editorial Board of the International Journal ``Reliable Computing''.
  • C. S. Calude and P. Hertling:
    Computable approximations of reals: An information-theoretic analysis (extended abstract).
    In: P. Blackburn, N. Braisby, L. Cavedon, S. Glasbey, and A. Shimojima, editors, Proceedings of the 3rd Conference in Information-Theoretic Approaches to Logic, Languages, and Computation (ITALLC'98), pages 29-38, Hsitou, Taiwan, June 1998.
  • P. Hertling and K. Weihrauch:
    Randomness spaces.
    In: K. G. Larsen, S. Skyum, and G. Winskel, editors, Automata, Languages and Programming, vol. 1443 of Lecture Notes in Computer Science, pages 796-807, Berlin, 1998. Springer. 25th International Colloquium, ICALP'98, Aalborg, Denmark, July 1998.
  • P. Hertling:
    A Banach-Mazur computable but not Markov computable function on the computable real numbers (extended abstract).
    In: P. Widmayer et al., editors, Automata, Languages and Programming, vol. 2380 of Lecture Notes in Computer Science, pages 962-972, Berlin, 2002. Springer. 29th International Colloquium, ICALP'02, Málaga, Spain, July 2002.
  • P. Hertling:
    Topological complexity of zero finding for continuous functions (Abstract).
    In: V. Brattka, M. Schröder, K. Weihrauch, and N. Zhong, editors, Proc. of the First Int. Conference on Computability and Complexity in Analysis, Cincinnati, August 2003, p. 13, Informatik-Bericht 302, FernUniversität Hagen, 2003.
  • P. Hertling and V. Selivanov:
    Complexity issues for preorders on finite labeled forests.
    In: B. Löwe, D. Normann, I. Soskov, and A. Soskova (eds.), Models of computation in context, vol. 6735 of Lecture Notes in Computer Science, Springer, Heidelberg, 2011, pages 112-121.

 

Doctoral dissertation (Phd thesis)
  • P. Hertling:
    Unstetigkeitsgrade von Funktionen in der effektiven Analysis.
    Doktorarbeit (Phd thesis, in German).
    FernUniversität Hagen, Informatik-Bericht 208, November 1996.

 

Selected workshop proceedings and technical reports
  • P. Hertling:
    A topological complexity hierarchy of functions with finite range.
    Technical Report 223, Centre de Recerca Matematica, Institut d'Estudis Catalans, Barcelona, October 1993.
    Workshop on Continuous Algorithms and Complexity.
  • P. Hertling:
    Topologische Komplexitätsgrade von Funktionen mit endlichem Bild.
    Informatik-Bericht 152, FernUniversität Hagen, Hagen, December 1993.
  • P. Hertling:
    Stetige Reduzierbarkeit auf Σ^ω von Funktionen mit zweielementigem Bild und von zweistetigen Funktionen mit diskretem Bild.
    Informatik-Bericht 153, FernUniversität Hagen, Hagen, December 1993.
  • V. Brattka and P. Hertling:
    Continuity and computability of relations.
    Informatik-Bericht 164, FernUniversität Hagen, September 1994.
  • V. Brattka and P. Hertling:
    Feasible real random access machines.
    In: K.-I Ko, K. Weihrauch, editors, Proc. of the Workshop on Computability and Complexity in Analysis, Hagen, August 1995, pages 71-82, Informatik-Bericht 190,FernUniversität Hagen, 1995.
  • P. Hertling:
    Computable real functions: Type 1 computability versus type 2 computability.
    In: K.-I Ko, N. Müller, and K. Weihrauch, editors, Proc. of the 2nd Workshop on Computability and Complexity in Analysis, Trier, August 1996, pages 31-42, Forschungsbericht Nr. 96-44, Universität Trier, Mathematik/Informatik. 1996.

 

Last modified: September 29, 2021.
 peter.hertling@unibw.de

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