Vector addition system
![Example of a vector addition with states. In this VASS, e.g., q(1,2) can be reached from p(0,0), but q(0,0) cannot be reached from p(0,0).](/Images/godic/202502/19/Vector_addition_with_states.svg1814.png")
A vector addition system (VAS) is one of several mathematical modeling languages for the description of distributed systems. Vector addition systems were introduced by Richard M. Karp and Raymond E. Miller in 1969, and generalized to vector addition systems with states (VASS) by John E. Hopcroft and Jean-Jacques Pansiot in 1979. Both VAS and VASS are equivalent in many ways to Petri nets introduced earlier by Carl Adam Petri.