Related papers: Simulating Keystroke and Computing the Theoretical…
Predictability of behavior has emerged an an important characteristic in many fields including biology, medicine, and marketing. Behavior can be recorded as a sequence of actions performed by an individual over a given time period. This…
If a macroscopic (random) classical system is put into a random state in phase space, it will of course the most likely have an almost maximal entropy according to second law of thermodynamics. We will show, however, the following theorem:…
Given a pattern string $P$ of length $n$ consisting of $\delta$ distinct characters and a query string $T$ of length $m$, where the characters of $P$ and $T$ are drawn from an alphabet $\Sigma$ of size $\Delta$, the {\em exact string…
The notion of probability plays an important role in almost all areas of science and technology. In modern mathematics, however, probability theory means nothing other than measure theory, and the operational characterization of the notion…
A probabilistic model for computer-based generation of a machine translation system on the basis of English-Russian parallel text corpora is suggested. The model is trained using parallel text corpora with pre-aligned source and target…
Most hash tables have an insertion time of $O(1)$, possibly qualified as expected and/or amortised. While insertions into cuckoo hash tables indeed seem to take $O(1)$ expected time in practice, only polylogarithmic guarantees are proven in…
We propose a novel Markov chain Monte-Carlo (MCMC) method for reverse engineering the topological structure of stochastic reaction networks, a notoriously challenging problem that is relevant in many modern areas of research, like…
The problem of stochastic deadline scheduling is considered. A constrained Markov decision process model is introduced in which jobs arrive randomly at a service center with stochastic job sizes, rewards, and completion deadlines. The…
Time-arrow $s=+/-$, intrinsic to a concrete physical system, is associated with the direction of information loss $\Delta I$ displayed by the random evolution of the given system. When the information loss tends to zero the intrinsic…
Given uniform probability on words of length M=Np+k, from an alphabet of size p, consider the probability that a word (i) contains a subsequence of letters (p, p-1,...,1) in that order and (ii) that the maximal length of the disjoint union…
The fundamental problem of similarity studies, in the frame of data-mining, is to examine and detect similar items in articles, papers, books, with huge sizes. In this paper, we are interested in the probabilistic, and the statistical and…
We propose novel algorithms for sequence prediction based on ideas from stringology. These algorithms are time and space efficient and satisfy mistake bounds related to particular stringological complexity measures of the sequence. In this…
We study randomness beyond $\Pi^1_1$-randomness and its Martin-L\"of type variant, introduced in \cite{MR2340241} and further studied in \cite{Continuous-higher-randomness}. The class given by the infinite time Turing machines (\ITTM s),…
This paper is an experimental exploration of the relationship between the runtimes of Turing machines and the length of proofs in formal axiomatic systems. We compare the number of halting Turing machines of a given size to the number of…
Existing methods for the zero-shot detection of machine-generated text are dominated by three statistical quantities: log-likelihood, log-rank, and entropy. As language models mimic the distribution of human text ever closer, this will…
The proliferation of AI-generated text has intensified the need for reliable authorship verification, yet current output-based methods are increasingly unreliable. We observe that the ordinary typing interface captures rich cognitive…
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…
We present a targeted, scaled-up comparison of incremental processing in humans and neural language models by collecting by-word reaction time data for sixteen different syntactic test suites across a range of structural phenomena. Human…
We comment on some conceptual and and technical problems related to computational mechanics, point out some errors in several papers, and straighten out some wrong priority claims. We present explicitly the correct algorithm for…
The current cycle of hype and anxiety concerning the benefits and risks to human society of Artificial Intelligence is fuelled, not only by the increasing use of generative AI and other AI tools by the general public, but also by claims…