Pattern Markov Chains: Optimal Markov Chain Embedding Through Deterministic Finite Automata

Pattern Markov Chains: Optimal Markov Chain Embedding through Deterministic Finite Automata

In the framework of patterns in random texts, the Markov chain embedding techniques consist of turning the occurrences of a pattern over an order-m Markov sequence into those of a subset of states into an order-1 Markov chain. In this paper we use the theory of language and automata to provide space-optimal Markov chain embedding using the new notion of pattern Markov chains (PMCs), and we give...

Random Generation of Deterministic Acyclic Automata Using Markov Chains

In this article we propose an algorithm, based on Markov chain techniques, to generate random automata that are deterministic, accessible and acyclic. The distribution of the output approaches the uniform distribution on n-state such automata. We then show how to adapt this algorithm in order to generate minimal acyclic automata with n states almost uniformly.

Finite Markov Chains

This paper provides basic information and theorems about finite Markov chains. The inspiration for this paper came from Professor Laci Babai’s Discrete Mathematics lecture notes from the REU program of 2003. After reading through his chapter on Markov chains, I decided to proceed by answering as many exercises from the notes as possible. Below is what I have finished.

Finite Markov Chain Analysis

Finite, discrete-time Markov chain models of genetic algorithms have been used successfully in the past to understand the complex dynamics of a simple GA. Markov chains can exactly model the GA by accounting for all of the stochasticity introduced by various GA operators, such as initialization, selection, crossover, and mutation. Although such models quickly become unwieldy with increasing pop...

Lectures on finite Markov chains