We describe algorithms that directly infer very simple forms of 1-unambiguous regular expressions from positive data. Thus, we characterize the regular language classes that can be learned this way, both in terms of regular expressions and in terms of (not necessarily minimal) deterministic finite automata.

Algorithms for learning regular expressions from positive data

There has been developed and implemented an algorithm for the automatic synthesis of therapy plans for complex dynamic systems This algorithm is the core of some control synthesis module which is embedded in a larger knowledge-based system for control, diagnosis and therapy There are several applications

Therapy Plan Generation as Program Synthesis

Fast algorithm for inductive synthesis of term rewriting systems is described and proved to be correct. It is implemented and successfully applied for inductive synthesis of different algorithms, including the binary multiplication. The algorithm proposed supports automatic learning process and can be used for designing and implementation of ADT.

Inductive Synthesis of Term Rewritin Systems

We consider the problem of the synthesis of algorithms by sample computations. We introduce a formal language, namely, the so-called dot expressions, which is based on a formalization of the intuitive notion of ellipsis (‘...’). Whilst formally the dot expressions are simply a language describing sets of words, on the other hand, it can be considered as a programming language supporting quite a wide class of programs. Equivalence and asymptotical equivalence of dot expressions are defined and proved to be decidable. A formal example of a dot expression is defined in the way that, actually, it represents a sample computation of the program presented by the given dot expression. A system of simple inductive inference rules synthesizing dot expressions (programs) by their formal examples (sample computations) is developed and proved to synthesize a correct (i.e., asymptotically equivalent to the given) expression by one sufficiently long example. Some instances of the application of the model for program inductive synthesis are also given. Particularly, there are given examples of the euclidean and bubblesort algorithm synthesis within acceptable time from completely natural sample descriptions.

Inductive Synthesis of Dot Expressions

In designing a new algorithm we usually begin with considering a number of examples and then try to generalize them. These examples are mainly input-output examples or sample computations (computation traces, histories of computations) explaining the algorithm's behavior. The aim of our research is to understand and formalize the process of this generalization and eventually to design practical synthesizers.

E Kinber

Papers

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