Browsing Publicēti raksti (MII) / Published Articles by Author "Podnieks, Karlis"

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    • 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 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 ...

    • Comparing various types of limiting synthesis and prediction of functions 

      Podnieks, Karlis (Latvia State University, 1974)

    • 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 ...

    • 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 ...

    • 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 ...

    • 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 ...

    • On computation in the limit by non-deterministic Turing machines 

      Freivalds, Rusins; 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)

    • On speeding up synthesis and prediction of functions 

      Barzdins, Janis; Kinber, Efim; Podnieks, Karlis (Latvia State University, 1974)

    • 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, ...

    • 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 ...

    • 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 ...

    • 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 ...

    • Towards a theory of inductive inference 

      Barzdins, Janis; Podnieks, Karlis (1973)