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Vector addition system
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<p> A vector addition system (VAS) is one of several mathematical modeling languages for the description of <a href="/facts/Distributed_systems/o5nyhqTF">distributed systems</a>. Vector addition systems were introduced by <a href="/facts/Richard_M._Karp/XtYCL0nA">Richard M. Karp</a> and Raymond E. Miller in 1969, and generalized to vector addition systems with states (VASS) by <a href="/facts/John_Hopcroft/j42ejf1m">John E. Hopcroft</a> and Jean-Jacques Pansiot in 1979. Both VAS and VASS are equivalent in many ways to <a href="/facts/Petri_net/BK7eTHNm">Petri nets</a> introduced earlier by <a href="/facts/Carl_Adam_Petri/oT2q6jXA">Carl Adam Petri</a>. </p> <p><a href="/facts/Reachability_problem/jlBpsn98">Reachability</a> in vector addition systems is <a href="/facts/Ackermann_function/WQNpCWHn"> Ackermann</a>-complete (and hence <a href="/facts/Nonelementary_problem/PYLSyvHo"> nonelementary</a>). </p>