Now showing items 1-20 of 26

    • On the reducibility of function classes 

      Podnieks, Karlis (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 m-reducible 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, ...
    • Towards a theory of inductive inference 

      Barzdins, Janis; Podnieks, Karlis (1973)
    • Comparing various concepts of function prediction. Part 1. 

      Podnieks, Karlis (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 ...
    • Comparing various types of limiting synthesis and prediction of functions 

      Podnieks, Karlis (Latvia State University, 1974)
    • On computation in the limit by non-deterministic Turing machines 

      Freivalds, Rusins; Podnieks, Karlis (Latvia State University, 1974)
    • On speeding up synthesis and prediction of functions 

      Barzdins, Janis; Kinber, Efim; Podnieks, Karlis (Latvia State University, 1974)
    • On computation in the limit by non-deterministic Turing machines 

      Freivalds, Rūsiņš; Podnieks, Karlis (Scientific Proceedings of Latvia State University, 1974)
    • Comparing various concepts of function prediction. Part 2. 

      Podnieks, Karlis (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 double-incompleteness theorem 

      Podnieks, Karlis (Latvia State University, 1975)
      Let T be a theory, Q - a metatheory of T. Under certain conditions there exist T-undecidable sentences for which this undecidability cannot be proved in Q. For English translation and proof, see K. Podnieks What is ...
    • The double-incompleteness theorem 

      Podnieks, Karlis (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 T-unprovable, nor that H is ...
    • Probabilistic program synthesis 

      Podnieks, Karlis (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 

      Podnieks, Karlis (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 n-th function of T making no more than log2(n) errors (Barzdins-Freivalds). It is proved in the ...
    • An Exhaustive Search Algorithm for Finding Hamiltonian Cycles 

      Zeps, Dainis (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 depth-first search and working successfully on sparse graphs. The method is based on the idea not to ...
    • Prediction of the next value of a function 

      Podnieks, Karlis (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 

      Podnieks, Karlis (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 

      Freivalds, Rusins; Barzdins, Janis; Podnieks, Karlis (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? 

      Podnieks, Karlis (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 

      Gritsans, A.; Sadyrbaev, F. (Vilnius Gediminas Technical University, 2009)
    • Ornamental sign language in the first order tracery belts 

      Tenisons, Modris; Zeps, Dainis (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 

      Bārzdiņš, Jānis; Bārzdiņš, Guntis; Čerāns, Kārlis; Liepiņš, Renārs; Sproģis, Artūrs (Springer, 2010)