Higher-order Petri nets are a class of high-level Petri nets, in which Petri nets themselves are first-class objects. Here tokens may represent Petri nets and Petri nets may be the values of parameters and variables, as well as the result of computations performed during the occurrence of transitions. These features facilitate a number of very powerful higher-order modelling techniques, making Petri nets much more flexible, compositional, and the resulting models more reusable. This work explores the usefulness of some of these techniques by looking at them from an application point of view and by illustrating them with small to medium-sized application examples.

models An important part of the design of complex systems is the evaluation of the large number of potential alternative designs. Due to the number and complexity of design parameters, this design space is potentially huge and very complex. Automating part of the design exploration task can be an invaluable help in finding the optimal or near optimal settings of design parameters. The choice of the most appropriate exploration strategy depends on the nature of the parameters, such as their role in the model, the dimensionality and structure of the design space including the number and location of local optima, etc. This paper advocates the use of higher-order modeling techniques to express exploration strategies. This allows users to formulate them in the same set of languages used to model the original system. Hence the set of design space exploration tools can be extended and parameterized as easily as the model itself. In this paper a higher-order modeling langage is presented. As an example a number of simple exploration tools are modeled and applied to a small optimization problem. 1

We collaborate in a research program aimed at creating a rigorous framework, experimental infrastructure, and computational environment for understanding, experimenting with, manipulating, and modifying a diverse set of fundamental biological processes at multiple scales and spatio-temporal modes. The novelty of our research is based on an approach that (i) requires coevolu- # The work reported in this paper was supported by grants from NSF's Qubic program, DARPA, HHMI biomedical support research grant, the US Department of Energy, the US Air Force, National Institutes of Health, and New York State O#ce of Science, Technology & Academic Research.

ABSTRACT We collaborate in a research program aimed at creating a rigorous framework, experimental infrastructure and computational environment for understanding, experimenting, manipulating and modifying a diverse set of fundamental biological processes at multiple scales and spatio-temporal modes. The novelty of our research is based on an approach (i) that requires coevolution of experimental science and theoretical techniques and (ii) that exploits certain universality in biology guided by a parsimonious model of evolu-