On Reasoning about Infinite-State Systems in the Modal µ-Calculus

This paper presents a proof method for proving that infinite-state systems satisfy properties expressed in the modal µ-calculus. The method is sound and complete relative to externally proving inclusions of sets of states. It can be seen as a recast of a tableau method due to Bradfield and Stirling following lines used by Winskel for finite-state systems. Contrary to the tableau method, it avoids the use of constants when unfolding fixed points and it replaces the rather involved global success criterion in the tableau method with local success criteria. A proof tree is now merely a means of keeping track of where possible choices are made -- and can be changed -- and not an essential ingredient in establishing the correctness of a proof: A proof will be correct when all leaves can be directly seen to be valid. Therefore, it seems well-suited for implementation as a tool, by, for instance, integration into existing general-purpose theorem provers

Boolean Expression Diagrams

This paper presents a new data structure called Boolean Expression Diagrams (BEDs) for representing and manipulating Boolean functions. BEDs are a generalization of Binary Decision Diagrams (BDDs) which can represent any Boolean circuit in linear space and still maintain many of the desirable properties of BDDs. Two algorithms are described for transforming a BED into a reduced ordered BDD. One is a generalized version of the BDD apply-operator while the other can exploit the structural information of the Boolean expression. This ability is demonstrated by verifying that two di erent circuit implementations of a 16-bit multiplier implement the same Boolean function. Using BEDs, this veri cation problem is solved in less than a second, while using standard BDD techniques this problem is infeasible. Generally, BEDs are useful in applications, for example tautology checking, where the end-result as a reduced ordered BDD is small

Calculating Valid Domains for BDD-Based Interactive Configuration

In these notes we formally describe the functionality of Calculating Valid Domains from the BDD representing the solution space of valid configurations. The formalization is largely based on the CLab configuration framework

A Compositional Proof System for the Modal mu-Calculus

We present a proof system for determining satisfaction between processes in a fairly general process algebra and assertions of the modal mu-calculus. The proof system is compositional in the structure of processes. It extends earlier work on compositional reasoning within the modal mu-calculus and combines it with techniques from work on local model checking. The proof system is sound for all processes and complete for a class of finite-state processes