Generalized regular expressions—A language for synthesis of programs with branching in loops

AbstractRegular expressions are generalized to the effect that, besides letters from a finite alphabet, they may also contain natural numbers. Within the framework of these generalized expressions the task of the inductive synthesis of programs from its sample run is formalized. Special automata recognizing the sets defined by generalized expressions are introduced, and their equivalence problem is shown to be recursively solvable. The set-theoretic properties of the sets defined by generalized expressions are also studied

A Map of Update Constraints in Inductive Inference

We investigate how different learning restrictions reduce learning power and how the different restrictions relate to one another. We give a complete map for nine different restrictions both for the cases of complete information learning and set-driven learning. This completes the picture for these well-studied \emph{delayable} learning restrictions. A further insight is gained by different characterizations of \emph{conservative} learning in terms of variants of \emph{cautious} learning. Our analyses greatly benefit from general theorems we give, for example showing that learners with exclusively delayable restrictions can always be assumed total.Comment: fixed a mistake in Theorem 21, result is the sam

Frequency Computation and Bounded Queries

There have been several papers over the last ten years that consider the number of queries needed to compute a function as a measure of its complexity. The following function has been studied extensively in that light: F A a (x 1 ; : : : ; x a ) = A(x 1 ) \Delta \Delta \Delta A(x a ): We are interested in the complexity (in terms of the number of queries) of approximating F A a . Let b a and let f be any function such that F A a (x 1 ; : : : ; x a ) and f(x 1 ; : : : ; x a ) agree on at least b bits. For a general set A we have matching upper and lower bounds that depend on coding theory. These are applied to get exact bounds for the case where A is semirecursive, A is superterse, and (assuming P 6= NP) A = SAT. We obtain exact bounds when A is the halting problem using different methods. 1 Introduction The complexity of a function can be measured by the number of queries (to some oracle) needed to compute it. This notion has been studied in both a Dept. of Computer Science, ..

Inductive inference of languages from samplings

10.1007/978-3-642-16108-7_27Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)6331 LNAI330-34

Learning languages from positive data and a finite number of queries

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)3328360-37

Automatic learning from positive data and negative counterexamples

10.1007/978-3-642-34106-9_9Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)7568 LNAI66-8

Intrinsic complexity of partial learning

10.1016/j.tcs.2018.12.022Theoretical Computer Science77643-6

Learning multiple languages in groups

10.1007/11564089_21Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)3734 LNAI256-26

Learning languages from positive data and negative counterexamples

10.1016/j.jcss.2007.06.012Journal of Computer and System Sciences744431-456JCSS

Mind change speed-up for learning languages from positive data

10.1016/j.tcs.2013.04.009Theoretical Computer Science489-49037-47TCSC