The State Explosion Problem

One from main approaches to checking correctness of a concurrent system are state space methods. They are suitable for automatic analysis and verification of the behaviour of systems. In their basic form, they construct a structure that consist of all states that a system can reach, and all transitions that system can make between those states. This structure is called state space. State spaces can be constructed fully automated. Given the state space of a system, there are many practical practical algorithms for answering some verification and analysis questions. Unlike theorem provers, user don’t have to provide invariants or variants. It suffices to formulate an analysis or verification question and start a tool. State space methods have many advantages and sound like almost ideal behavioural analysis and verification technique. Unfortunately they suffer from one big and fundamental problem state explosion. Almost any system has huge number of states. Often, the size of a state space of a system tends to grow exponentially in the number of its processes and variables. The base of the exponentiation depends on the number of local states a process has, the number of values a variable may store and the extent to which the local states of components are determined by the local states of other components. The advantages of state space methods motivated researchers. For answering certain verification and analysis questions, many methods have been suggested that reduce number of required states. The size of systems that can be analysed or verified increased significantly. Unfortunately, advanced state space methods can often answer only certain kinds of analysis or verification questions. For other kinds they lose ability to reduce the number of states.