Process Petri Nets with Time Stamps and Their Using in Project Management

Process Petri nets with time stamps (PPNTS) are the newly introduced class of low-level Petri nets, whose definition and the properties are the main topic of this chapter; they generalize the properties of Petri net processes in the area of design, modeling and verification of generally parallel systems with the discrete time. Property-preserving Petri net process algebras (PPPAs) were originally designed for the specification and verification of manufacturing systems. PPPA does not need to verify composition of Petri net processes because all their algebraic operators preserve the specified set of the properties. These original PPPAs are generalized for the class of the PPNTSs in this chapter. The new COMP, SYNC and JOIN algebraic operators are defined for the class of PPNTS and their chosen properties are proved. With the support of these operators, the PPNTSs can be extended also to the areas of project management and the determination of the project critical path with the support of the critical path method (CPM). The new CPNET subclass of PPNTS class is defined in this chapter. It is specially designed for the generalization of the CPM activity charts and their properties. This fact is then demonstrated on the simple project example and its critical path and other property specifications

Regular Separability of Well-Structured Transition Systems

We investigate the languages recognized by well-structured transition systems (WSTS) with upward and downward compatibility. Our first result shows that, under very mild assumptions, every two disjoint WSTS languages are regular separable: There is a regular language containing one of them and being disjoint from the other. As a consequence, if a language as well as its complement are both recognized by WSTS, then they are necessarily regular. In particular, no subclass of WSTS languages beyond the regular languages is closed under complement. Our second result shows that for Petri nets, the complexity of the backwards coverability algorithm yields a bound on the size of the regular separator. We complement it by a lower bound construction

A unified view of parameterized verification of abstract models of broadcast communication

We give a unified view of different parameterized models of concurrent and distributed systems with broadcast communication based on transition systems. Based on the resulting formal models, we discuss related verification methods and tools based on abstractions and symbolic state exploration

Parameterized verification

The goal of parameterized verification is to prove the correctness of a system specification regardless of the number of its components. The problem is of interest in several different areas: verification of hardware design, multithreaded programs, distributed systems, and communication protocols. The problem is undecidable in general. Solutions for restricted classes of systems and properties have been studied in areas like theorem proving, model checking, automata and logic, process algebra, and constraint solving. In this introduction to the special issue, dedicated to a selection of works from the Parameterized Verification workshop PV \u201914 and PV \u201915, we survey some of the works developed in this research area