Related papers: Simulating Keystroke and Computing the Theoretical…
It has often been said, correctly, that a monkey forever randomly typing on a keyboard would eventually produce the complete works of William Shakespeare. Almost just as often it has been pointed out that this "eventually" is well beyond…
Does combining a finite collection of objects infinitely many times guarantee the construction of a particular object? Here we use recursive function theory to examine the popular scenario of an infinite collection of typing monkeys…
This article explores the theoretical and computational aspects of the Infinite Monkey Theorem, investigating the number of attempts and the time required for a set of pseudorandom characters to assemble and recite Hamlets iconic phrase, To…
Suppose that your mother gave you n candies. You have to eat at least one candy each day. One possibility is to eat all n of them the first day. The other extreme is to make them last n days, and only eat one candy a day. Altogether, you…
Let $f$ denote length preserving function on words. A classical algorithm can be considered as $T$ iterated applications of black box representing $f$, beginning with input word $x$ of length $n$. It is proved that if $T=O(2^{n/(7+e)}), e…
The availability of quantitative text analysis methods has provided new ways of analyzing literature in a manner that was not available in the pre-information era. Here we apply comprehensive machine learning analysis to the work of William…
Consider a stationary discrete random process with alphabet size d, which is assumed to be the output process of an unknown stationary Hidden Markov Model (HMM). Given the joint probabilities of finite length strings of the process, we are…
The window mean-payoff objective strengthens the classical mean-payoff objective by computing the mean-payoff over a finite window that slides along an infinite path. Two variants have been considered: in one variant, the maximum window…
We show that the exponent in the inverse power law of word frequencies for the monkey-at-the-typewriter model of Zipf's law will tend towards -1 under broad conditions as the alphabet size increases to infinity and the letter probabilities…
We analyse correspondence of a text to a simple probabilistic model. The model assumes that the words are selected independently from an infinite dictionary. The probability distribution correspond to the Zipf---Mandelbrot law. We count…
Consider the following Markov chain on permutations of length $n$. At each time step we choose a random position. If the letter at that position is smaller than the letter immediately to the left (cyclically) then these letters swap…
Recent proposals advocate using keystroke timing signals, specifically the coefficient of variation ($\delta$) of inter-keystroke intervals, to distinguish human-composed text from AI-generated content. We demonstrate that this class of…
A "monkey book" is a book consisting of a random distribution of letters and blanks, where a group of letters surrounded by two blanks is defined as a word. We compare the statistics of the word distribution for a monkey book with the…
We characterize the meaning of words with language-independent numerical fingerprints, through a mathematical analysis of recurring patterns in texts. Approximating texts by Markov processes on a long-range time scale, we are able to…
Consider infinite random words over a finite alphabet where the letters occur as an i.i.d. sequence according to some arbitrary distribution on the alphabet. The expectation and the variance of the waiting time for the first completed…
The distribution of word probabilities in the monkey model of Zipf's law is associated with two universality properties: (1) the power law exponent converges strongly to $-1$ as the alphabet size increases and the letter probabilities are…
The classical pattern matching paradigm is that of seeking occurrences of one string - the pattern, in another - the text, where both strings are drawn from an alphabet set $\Sigma$. Assuming the text length is $n$ and the pattern length is…
We investigate the behavior of the periods and border lengths of random words over a fixed alphabet. We show that the asymptotic probability that a random word has a given maximal border length $k$ is a constant, depending only on $k$ and…
We study algorithms to analyze a particular class of Markov population processes that is often used in epidemiology. More specifically, Markov binomial chains are the model that arises from stochastic time-discretizations of classical…
We study the problem of computing the probability that a given stochastic context-free grammar (SCFG), G, generates a string in a given regular language L(D) (given by a DFA, D). This basic problem has a number of applications in…