The paper is devoted to the problem specifying causality relationships in distributed (including cyber-physical) systems. This problem is studied based on the coalgebraic approach used authors for studying safety constraints for distributed systems. The special class of coalgebras, counter-based detectors, is introduced and studied in the paper. It is shown that this approach allows using the technique of Diophantine equations for specifying clock constraints of the system being studied. The advantage of the approach is the possibility for defining the complexity of detectors that provides to control respond time of the detectors in the system.