Efim B. Kinber

Pattern languages with and without erasing

The paper deals with the problems related to finding a pattern common to all words in a given set. We restrict our attention to patterns expressible by the use of variables ranging over words. Two essentially different cases result, depending on whether or not the empty word belongs to the range. We investigate equivalence and inclusion problems, patterns descriptive for a set, as well as some complexity issues. The inclusion problem between two pattern languages turns out to be of fundamental theoretical importance because many problems in the classical combinatorics of words can be reduced to it.

On the power of inductive inference from good examples

The usual information in inductive inference available for the purposes of identifying an unknown recursive function f is the set of all input/output examples (x,f(x)),n eN. In contrast to this approach we show that it is considerably more powerful to work with finite sets of “good” examples even when these good examples are required to be effectively computable. The influence of the underlying numberings, with respect to which the identification has to be realized, to the capabilities of inference from good examples is also investigated. It turns out that nonstandard numberings can be much more powerful than Godel numberings.

On the impact of forgetting on learning machines

People tend not to have perfect memories when it comes to learning, or to anything else for that matter. Most formal studies of learning, however, assume a perfect memory. Some approaches have restricted the number of items that could be retained. We introduce a

Learning A Class of Regular Expressions via Restricted Subset Queries

A wide class of regular expressions non-representable as unions of “smaller” expressions is shown to be polynomial-time learnable via restricted subset queries from arbitrary representative examples “reflecting” the loop structure and a way the input example is obtained from the unknown expression. The corresponding subclass of regular expressions of loop depth at most 1 is shown to be learnable from representative examples via membership queries. A wide class of expressions with loops A+ of arbitrary loop depth is shown to be learnable via restricted subset queries from arbitrary examples.

Learning from Good Examples

The usual information in inductive inference for the purposes of learning an unknown recursive function f is the set of all input /output examples (n,f(n)), n ∈ ℕ. In contrast to this approach we show that it is considerably more powerful to work with finite sets of “good” examples even when these good examples are required to be effectively computable. The influence of the underlying numberings, with respect to which the learning problem has to be solved, to the capabilities of inference from good examples is also investigated. It turns out that nonstandard numberings can be much more powerful than Godel numberings.

Some Models of Inductive Syntactical Synthesis from Sample Computations

The paper is a survey of several models of inductive program synthesis from sample computations. Synthesis tools are basically syntactical: the synthesis is based on the detection of regular fragments related with shuffled arithmetical progressions. Input sample computations are supposed to be representative: they have to reflect all loops occurring in the target program. Programs are synthesized in nontraditional form of generalized regular expressions having Cleene stars and unions for loops and CASE-like operators. However, if input samples are somehow annotated (we consider two different approaches), then loops can be synthesized in more traditional WHILE-form, where loop conditions are separated from actions. The model in Section 3 is developed to handle the synthesis from incomplete sample computations (initial fragments). This model can be useful for the synthesis of some divide-and-conquer algorithms.

Error Detecting in Inductive Inference

Several well-known inductive inference strategies change the actual hypothesis only when they discover that it “provably misclassifies” an example seen so far. This notion is made mathematically precise and its general power is characterized. In spite of its strength it is shown that this approach is not of universal power. Consequently, then hypotheses are considered which “unprovably misclassify” examples and the properties of this approach are studied. Among others it turns out that this type is of the same power as monotonic identification. Then it is shown that universal power can be achieved only when an unbounded number of alternations of these dual types of hypotheses is allowed. Finally, a universal method is presented enabling an inductive inference strategy to verify the incorrectness of any of its incorrect intermediate hypotheses.

Dual Types of Hypotheses in Inductive Inference

Several well-known inductive inference strategies change the actual hypothesis only when they discover that it “provably misclassifies” an example seen so far. This notion is made mathematically precise and its general power is characterized. In spite of its strength it is shown that this approach is not of “universal” power. Consequently, then hypotheses are considered which “unprovably misclassify” examples and the properties of this approach are studied. Among others it turns out that this type is of the same power as monotonic identification. Finally, it is shown that “universal” power can be achieved only when an unbounded number of alternations of these dual types of hypotheses is allowed.