Information Flow and Homotopy Theory

Simulation and bisimulation are used in many areas of security in Computing Science, however the methods used do not come with a supporting logic giving the regularities of information flow. We have developed Distributed Logic to represent regularities governing information flow between localities of a distributed system, each locality can be outfitted with its own notion of state and language. The flows, either internal to a locality or between localities, follow a connection structure specified by a graph in the logic and semantically by relations in a category. We use some basic homotopy notions for use in distributed systems by using the notions as a template for properties of (bi)simulations useful for security and other properties of distributed systems. The logic can express formulas whose validity is unwritten by the (bi)simulations. This presents new ways of formalizing and proving properties of distributed systems.