Learnability of Kolmogorov-easy circuit expressions via queries

  title={Learnability of Kolmogorov-easy circuit expressions via queries},
  author={Jos{\'e} Lu{\'i}s Balc{\'a}zar and Harry Buhrman and Montserrat Hermo},
Circuit expressions were introduced to provide a natural link between Computational Learning and certain aspects of Structural Complexity. Upper and lower bounds on the learnability of circuit expressions are known. We study here the case in which the circuit expressions are of low (time-bounded) Kolmogorov complexity. We show that these are polynomial-time learnable from membership queries in the presence of an NP oracle. We also exactly characterize the sets that have such circuit expressions… 

Characterizing the learnability of Kolmogorov easy circuit expressions

We show that Kolmogorov easy circuit expressions can be learned with membership queries in polynomial time if and only if every NE-predicate is E-solvable. Moreover we show that the previously known

Compressibility and Uniform Complexity

Coding Complexity: The Computational Complexity of Succinct Descriptions

This paper surveys how structural complexity theory investigation has proceeded, and explains the current status of knowledge about succinct description of strings.

An Introduction to Kolmogorov Complexity and Its Applications



Oracles and queries that are sufficient for exact learning (extended abstract)

There is a randomized polynomial-time algorithm that learns any class that is learnable from membership queries with unlimited computational power.

Characterizations of Logarithmic Advice Complexity Classes

The novel proof technique of "doubly exponential skip" is introduced, and characterizations for P=log and Full-P=log are found in terms of several other concepts, among them easy-to-describe boolean circuits and reduction classes of tally sets with high regularity.

The complexity of learning with queries

  • Ricard Gavaldà
  • Computer Science
    Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory
  • 1994
This work surveys recent research concerning the qualitative complexity of Angluin's (1993) model of learning with queries, and characterizations of the power of different learning protocols by complexity classes of oracle machines are reviewed.

On infinite sequences (almost) as easy as pi

This work proposes some definitions, based on Kobayashi's notion of compressibility, and compares them to the standard resource-bounded Kolmogorov complexity of infinite strings, and proves some nontrivial coincidences and disagreements.

On Innnite Sequences (almost) as Easy As

This work proposes some deeni-tions, based on Kobayashi's notion of compressibility, and compares them to the standard resource-bounded Kolmogorov complexity of innnite strings, and some non-trivial coincidences and disagreements are proved.

An Introduction to Kolmogorov Complexity and Its Applications

The book presents a thorough treatment of the central ideas and their applications of Kolmogorov complexity with a wide range of illustrative applications, and will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics.

Structural Complexity I

This volume is written for undergraduate students who have taken a first course in Formal Language Theory and presents the basic concepts of structural complexity, thus providing the background necessary for the understanding of complexity theory.

Degrees and Reducibilities of Easy Tally Sets

The logarithmic advice class, Full-P/log, is known to coincide with the class of languages that are polynomial time reducible to special “easy” tally sets.

Locating P/poly Optimally in the Extended Low Hierarchy

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