MONA: Monadic Second-Order Logic in Practice

Abstract

The purpose of this article is to introduce Monadic Second-order
Logic as a practical means of specifying regularity. The logic is a
highly succinct alternative to the use of regular expressions. We have built a tool MONA, which acts as a decision procedure and as a translator to finite-state automata. The tool is based on new algorithms for minimizing finite-state automata that use binary decision diagrams (BDDs) to represent
transition functions in compressed form. A byproduct of this work is a
new bottom-up algorithm to reduce BDDs in linear time without hashing.
The potential applications are numerous. We discuss text processing,
Boolean circuits, and distributed systems. Our main example is an automatic proof of properties for the "Dining Philosophers with Encyclopedia" example by Kurshan and MacMillan. We establish these properties for the parameterized case without the use of induction.
Our results show that, contrary to common beliefs, high computational
complexity may be a desired feature of a specification formalism.