How can a programmer ensure a critical piece of software is bug-free? Theoretical computer scientists use a fundamental question called the reachability problem, which determines whether a computer will reach or avoid various dangerous states when running a program. To better understand the complexity of the problem, researchers turned to a mathematical tool called vector addition systems. In a series of recent breakthroughs, computer scientists have now determined that the complexity of the reachability problem for vector addition systems is defined by a famous function called the Ackermann function, which becomes extremely complex even with small inputs.
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