An Algorithm for Timing Verification of Systems Constrained by Min–max Inequalities

Abstract

To determine the maximum separation between events for nonrepetitive systems with max and linear constraints, there are the "iterative tightening from above" (ITA) approach and the "iterative tightening from below" (ITB) approach. Since such systems can be formulated as systems constrained by min---max inequalities, this paper gives an algorithm named MMIMaxSep for solving min---max inequalities. The algorithm is a generalization and a mathematically elegant reformulation of Yen et al.'s MaxSeparation algorithm which uses the ITB approach. Our numerical experiments indicate that MMIMaxSep is very efficient. Moreover, MMIMaxSep has a unique advantage of being able to directly handle tree-represented min---max functions, and its complexity is closely related to the complexity of computing cycle time of min---max functions.