0000000000011303
AUTHOR
Kalvis Apsitis
Towards efficient inductive synthesis of expressions from input/output examples
Our goal through several years has been the development of efficient search algorithm for inductive inference of expressions using only input/output examples. The idea is to avoid exhaustive search by means of taking full advantage of semantic equality of many considered expressions. This might be the way that people avoid too big search when finding proof strategies for theorems, etc. As a formal model for the development of the method we use arithmetic expressions over the domain of natural numbers. A new approach for using weights associated with the functional symbols for restricting search space is considered. This allows adding constraints like the frequency of particular symbols in t…
On Duality in Learning and the Selection of Learning Teams
AbstractPrevious work in inductive inference dealt mostly with finding one or several machines (IIMs) that successfully learn collections of functions. Herein we start with a class of functions and considerthe learner setof all IIMs that are successful at learning the given class. Applying this perspective to the case of team inference leads to the notion ofdiversificationfor a class of functions. This enable us to distinguish between several flavours of IIMs all of which must be represented in a team learning the given class.
Derived sets and inductive inference
The paper deals with using topological concepts in studies of the Gold paradigm of inductive inference. They are — accumulation points, derived sets of order α (α — constructive ordinal) and compactness. Identifiability of a class U of total recursive functions with a bound α on the number of mindchanges implies \(U^{(\alpha + 1)} = \not 0\). This allows to construct counter-examples — recursively enumerable classes of functions showing the proper inclusion between identification types: EXα⊂EXα+1.
Effects of Kolmogorov complexity present in inductive inference as well
For all complexity measures in Kolmogorov complexity the effect discovered by P. Martin-Lof holds. For every infinite binary sequence there is a wide gap between the supremum and the infimum of the complexity of initial fragments of the sequence. It is assumed that that this inevitable gap is characteristic of Kolmogorov complexity, and it is caused by the highly abstract nature of the unrestricted Kolmogorov complexity.
Closedness Properties in EX-Identification of Recursive Functions
In this paper we investigate in which cases unions of identifiable classes of recursive functions are also necessarily identifiable. We consider identification in the limit with bounds on mindchanges and anomalies. Though not closed under the set union, these identification types still have features resembling closedness. For each of them we find such n that 1) if every union of n - 1 classes out of U1;, . . ., Un is identifiable, so is the union of all n classes; 2) there are such classes U1;, . . ., Un-1 that every union of n-2 classes out of them is identifiable, while the union of n - 1 classes is not. We show that by finding these n we can distinguish which requirements put on the iden…
Team learning as a game
A machine FIN-learning machine M receives successive values of the function f it is learning; at some point M outputs conjecture which should be a correct index of f. When n machines simultaneously learn the same function f and at least k of these machines outut correct indices of f, we have team learning [k,n]FIN. Papers [DKV92, DK96] show that sometimes a team or a robabilistic learner can simulate another one, if its probability p (or team success ratio k/n) is close enough. On the other hand, there are critical ratios which mae simulation o FIN(p2) by FIN(p1) imossible whenever p2 _< r < p1 or some critical ratio r. Accordingly to [DKV92] the critical ratio closest to 1/2 rom the let is…
Unions of identifiable classes of total recursive functions
J.Barzdin [Bar74] has proved that there are classes of total recursive functions which are EX-identifiable but their union is not. We prove that there are no 3 classes U1, U2, U3 such that U1∪U2,U1∪U3 and U2∪U3 would be in EX but U1∪U2∪U3∉ EX. For FIN-identification there are 3 classes with the above-mentioned property and there are no 4 classes U1, U2, U3, U4 such that all 4 unions of triples of these classes would be identifiable but the union of all 4 classes would not. For identification with no more than p minchanges a (2p+2−1)-tuple of such classes do exist but there is no (2p+2)-tuple with the above-mentioned properly.
Tally languages accepted by alternating multitape finite automata
We consider k-tape 1-way alternating finite automata (k-tape lafa). We say that an alternating automaton accepts a language L\(\subseteq\)(Σ*)k with f(n)-bounded maximal (respectively, minimal) leaf-size if arbitrary (respectively, at least one) accepting tree for any (w1, w2,..., wk) ∈ L has no more than $$f\mathop {(\max }\limits_{1 \leqslant i \leqslant k} \left| {w_i } \right|)$$ leaves. The main results of the paper are the following. If k-tape lafa accepts language L over one-letter alphabet with o(log n)-bounded maximal leaf-size or o(log log n)-bounded minimal leaf-size then the language L is semilinear. Moreover, if a language L is accepted with o(log log(n))-bounded minimal (respe…
Unions of identifiable families of languages
This paper deals with the satisfiability of requirements put on the identifiability of unions of language families. We consider identification in the limit from a text with bounds on mindchanges and anomalies. We show that, though these identification types are not closed under the set union, some of them still have features that resemble closedness. To formalize this, we generalize the notion of closedness. Then by establishing “how closed” these identification types are we solve the satisfiability problem.
Topological considerations in composing teams of learning machines
Classes of total recursive functions may be identifiable by a team of strategies, but not by a single strategy, in accordance with a certain identification type (EX, FIN, etc.). Qualitative aspects in composing teams are considered. For each W ∉ EX all recursive strategies can be split into several families so that any team identifying W contains strategies from all the families. For W ∉ FIN the possibility of such splitting depends upon W. The relation between these phenomena and “voting” properties for types EX, FIN, etc. is revealed.