Technical Report 2009 - 001 Unrestricted and Disjoint Operations over Multi - Stack Visibly

Visibly Pushdown Languages (VPL) have been proposed as a formalism useful for specifying and verifying complex, recursive systems such as application software. However, VPL turn out to be unsuitable for the compositional specification of concurrent software, as they are not closed under shuffle. Multi-stack Visibly Pushdown Languages (MVPL) express naturally concurrent constructions. We find however that concurrency cannot be expressed compositionally (for indeed MVPL are not closed under shuffle either). Furthermore, MVPL operations must be expressed under rigid restrictions on the input alphabet, that hinder between others the specification of dynamic creation of threads of execution. If we remove the restrictions, then MVPL loose almost all their closure properties; we find however a natural renaming process that yields the notion of disjoint MVPL operations. These operations eliminate the restrictions and also creates closure under shuffle. This effort opens the area of MVPL-based compositional specification and verification of complex systems.