Complexity Issues for Preorders on Finite Labeled Forests

We prove that three preorders on the finite k-labeled forests are polynomial time computable. Together with an earlier result of the first author, this implies polynomial-time computability for an important initial segment of the corresponding degrees of discontinuity of k- partitions on the Baire space. Furthermore, we show that on ω-labeled forests the first of these three preorders is polynomial time computable as well while the other two preorders are NP-complete.

[1]  Sven Kosub.  NP-Partitions over Posets with an Application to Reducing the Set of Solutions of NP Problems , 2004, Theory of Computing Systems.

[2]  Michael R. Fellows,et al.  Parameterized Complexity , 1998 .

[3]  Erkko Lehtonen.  Labeled posets are universal , 2008, Eur. J. Comb..

[4]  Erkko Lehtonen,et al.  On the Homomorphism Order of Labeled Posets , 2009, Order.

[5]  Klaus W. Wagner,et al.  The boolean hierarchy of NP-partitions , 2008, Inf. Comput..

[6]  Victor L. Selivanov,et al.  Undecidability in the Homomorphic Quasiorder of Finite Labeled Forests , 2006, CiE.

[7]  A. Kechris.  Classical descriptive set theory , 1987 .

[8]  Victor L. Selivanov,et al.  Hierarchies of Δ02‐measurable k ‐partitions , 2007, Math. Log. Q..

[9]  Vasco Brattka,et al.  Effective Choice and Boundedness Principles in Computable Analysis , 2009, The Bulletin of Symbolic Logic.

[10]  K. Weihrauch.  The TTE-Interpretation of Three Hierarchies of Omniscience Principles , 1992 .

[11]  Victor L. Selivanov,et al.  A Gandy Theorem for Abstract Structures and Applications to First-Order Definability , 2009, CiE.

[12]  Peter Hertling,et al.  Unstetigkeitsgrade von Funktionen in der effektiven Analysis , 1996 .

[13]  Victor L. Selivanov,et al.  Undecidability in Weihrauch Degrees , 2010, CiE.

[14]  José L. Balcázar,et al.  Structural Complexity I , 1995, Texts in Theoretical Computer Science An EATCS Series.

[15]  Klaus Weihrauch,et al.  Computable Analysis: An Introduction , 2014, Texts in Theoretical Computer Science. An EATCS Series.

[16]  K. Weihrauch.  The Degrees of Discontinuity of some Translators Between Representations of the Real Numbers , 1992 .

[17]  José L. Balcázar,et al.  Structural complexity 2 , 1990 .

[18]  V. Selivanov.  Boolean Hierarchies of Partitions over a Reducible Base , 2004 .

[19]  Michael David Hirsch.  Applications of topology to lower bound estimates in computer science , 1991 .

[20]  José L. Balcázar,et al.  Structural complexity 1 , 1988 .

[21]  Victor L. Selivanov,et al.  Undecidability in the Homomorphic Quasiorder of Finite Labelled Forests , 2007, J. Log. Comput..

[22]  Vasco Brattka,et al.  Weihrauch degrees, omniscience principles and weak computability , 2009, J. Symb. Log..

[23]  José L. Balcázar,et al.  Some results about Logspace complexity measures , 1984, Bull. EATCS.