The balance problem of min–max systems is co-NP hard

Abstract

Min–max systems are timed discrete event dynamic systems containing min, max and plus operations. A min–max system is balanced if it admits a global cycle time (generalized eigenvalue) for every possible assignment of parameters. This paper proves that the testing of the balance property for min–max systems is co-NP hard by showing that the test of inseparability is co-NP hard. The latter result is established on a new complexity result, namely, that the testing of existence of non-trivial fixed points for monotone Boolean functions is NP-complete.