Aggregated (Bi-)Simulation of Finite Valued Networks

Abstract: The paper provides a method to approximate a large-scale finite-valued network by a smaller model called the aggregated simulation, which is a combination of aggregation and (bi-)simulation. First, the algebraic state space representation (ASSR) of a transition system is presented. Under output equivalence, the quotient system is obtained, which is called the simulation of the original transition system. The ASSR of the quotient system is obtained. The aggregated (bi-)simulation is execueted in several steps: a large scale finite-valued network is firstly aggregated into several blocks, each of which is considered as a network where the in-degree nodes and out-degree nodes are considered as the block inputs and block outputs respectively. Then the dynamics of each block is converted into its quotient system, called its simulation. Then the overall network can be approximated by the quotient systems of each blocks, which is called the aggregated simulation. If the simulation of a block is a bi-simulation, the approximation becomes a lossless transformation. Otherwise, the quotient system is only a (non-deterministic) transition system, and it can be replaced by a probabilistic networks. Aggregated simulation can reduce the dimension of the original network, while a tradeoff between computation complexity and approximation error need to be decided.