Uncountable Realtime Probabilistic Classes

Uncountable Realtime Probabilistic Classes

We investigate the minimum cases for realtime probabilistic machines that can define uncountably many languages with bounded error. We show that logarithmic space is enough for realtime PTMs on unary languages. On binary case, we follow the same result for double logarithmic space, which is tight. When replacing the worktape with some limited memories, we can follow uncountable results on unary...

Uncountable Automatic Classes and Learning

In this paper we consider uncountable classes recognizable by ω-automata and investigate suitable learning paradigms for them. In particular, the counterparts of explanatory, vacillatory and behaviourally correct learning are introduced for this setting. Here the learner reads in parallel the data of a text for a language L from the class plus an ω-index α and outputs a sequence of ω-automata s...

Uncountable classical and quantum complexity classes

Polynomial–time constant–space quantum Turing machines (QTMs) and logarithmic–space probabilistic Turing machines (PTMs) recognize uncountably many languages with bounded error (Say and Yakaryılmaz 2014, arXiv:1411.7647). In this paper, we investigate more restricted cases for both models to recognize uncountably many languages with bounded error. We show that double logarithmic space is enough...

Uncountable categoricity of local abstract elementary classes with amalgamation

We give a complete and elementary proof of the following upward categoricity theorem: LetK be a local abstract elementary class with amalgamation and joint embedding, arbitrarily large models, and countable LöwenheimSkolem number. If K is categorical in א1 then K is categorical in every uncountable cardinal. In particular, this provides a new proof of the upward part of Morley’s theorem in firs...

ICC and Probabilistic Classes