## Posts

Showing posts from May, 2017

### Model Checking Markov Chains Against Unambiguous Automata: The Qualitative Case

This is my first blog post. The purpose of this blog is to describe some neat ideas from my research. Ideally only one idea per post, which explains the title of this blog.

Today I start with a classical topic from probabilistic verification: model checking Markov chains against $\omega$-regular specifications. I will focus on specifications given by Büchi automata, which are automata like this one:

This Büchi automaton accepts all infinite words over $\{a,b\}$ that start with $a$. The automaton is nondeterministic. The automaton is also unambiguous, which means that every infinite word has at most one accepting run.

A Markov chain, on the other hand, generates infinite words. A Markov chain looks like this:

For instance, with probability $\frac12 \cdot \frac12 \cdot 1 = \frac14$ it generates an infinite word that starts with $a b a$. For simplicity, we consider only a very simple Markov chain in this post:

This Markov chain generates an infinite word over $\{a,b\}$ uniformly at r…