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On the reducibility of function classes
(Latvia State University, 1972)N – the set of all natural numbers, F – the set of all total functions N→N, A, B<=F. We say that A is mreducible to B (A<=m B), iff there is a recursive operator M such that f in A, iff M(f) in B for all f in F. Similarly, ... 
Comparing various concepts of function prediction. Part 1.
(Latvia State University, 1974)Prediction: f(m+1) is guessed from given f(0), ..., f(m). Program synthesis: a program computing f is guessed from given f(0), ..., f(m). The hypotheses are required to be correct for all sufficiently large m, or with some ... 
On computation in the limit by nondeterministic Turing machines
(Latvia State University, 1974) 
On speeding up synthesis and prediction of functions
(Latvia State University, 1974) 
On computation in the limit by nondeterministic Turing machines
(Scientific Proceedings of Latvia State University, 1974) 
Comparing various types of limiting synthesis and prediction of functions
(Latvia State University, 1974) 
Comparing various concepts of function prediction. Part 2.
(Latvia State University, 1975)Prediction: f(m+1) is guessed from given f(0), ..., f(m). Program synthesis: a program computing f is guessed from given f(0), ..., f(m). The hypotheses are required to be correct for all sufficiently large m, or with some ... 
The doubleincompleteness theorem
(Latvia State University, 1975)Let T be a theory, Q  a metatheory of T. Under certain conditions there exist Tundecidable sentences for which this undecidability cannot be proved in Q. For English translation and proof, see K. Podnieks What is ... 
The doubleincompleteness theorem
(Stiinca, Kishinev, 1976)Let T be a strong enough theory, and M  its metatheory, both are consistent. Then there is a closed arithmetical formula H that is undecidable in T, but one cannot prove in M neither that H is Tunprovable, nor that H is ... 
Probabilistic program synthesis
(Latvia State University, 1977)The following model of inductive inference is considered. Arbitrary numbering tau = {tau_0, tau_1, tau_2, ... } of total functions N>N is fixed. A "black box" outputs the values f(0), f(1), ..., f(m), ... of some function ... 
Computational complexity of prediction strategies
(Latvia State University, 1977)The value f(m+1) is predicted from given f(1), ..., f(m). For every enumeration T(n, x) there is a strategy that predicts the nth function of T making no more than log2(n) errors (BarzdinsFreivalds). It is proved in the ... 
An Exhaustive Search Algorithm for Finding Hamiltonian Cycles
(EIK,Elektronische Informationsverarbeitung und Kybernetik, Universität Trier, Akademie Verlag, 1980)The paper suggests an exhaustive search algorithm for finding Hamiltonian circuits in an undirected graph based on depthfirst search and working successfully on sparse graphs. The method is based on the idea not to ... 
Prediction of the next value of a function
(1981)The following model of inductive inference is considered. Arbitrary set tau = {tau_1, tau_2, ..., tau_n} of n total functions N>N is fixed. A "black box" outputs the values f(0), f(1), ..., f(m), ... of some function f ... 
Platonism, intuition and the nature of mathematics
(Bulgarian Academy of Sciences, Sofia, 1988)Platonism is an essential aspect of mathematical method. Mathematicians are learned ability " t o l i v e " in the "world" of mathematical concepts. Here we have the main source of the creative power of mathematics, and ... 
Inductive inference of recursive functions: complexity bounds
(Springer Verlag, 1991)This survey includes principal results on complexity of inductive inference for recursively enumerable classes of total recursive functions. Inductive inference is a process to find an algorithm from sample computations. ... 
MDA: correctness of model transformations. Which models are schemas?
(IOS Press, 2005)How to determine, is a proposed model transformation correct, or not? In general, the answer may depend on the model semantics. Of course, a model transformation is “correct”, if we can extend it to a “correct” instance ... 
Nonlinear Spectra: the Neumann Problem
(Vilnius Gediminas Technical University, 2009) 
Ornamental sign language in the first order tracery belts
(Prespacetime Journal, 2010)We consider an ornamental sign language of first order where principles of sieve displacement, of asymmetric building blocks as a base of ornament symmetry, color exchangeability and side equivalence principles work. Generic ... 
UML Style Graphical Notation
(Springer, 2010)