Assumption-based truth maintenance systems have developed into powerful and popular means for considering multiple contexts simultaneously during problem solving. Unfortunately, increasing problem complexity can lead to explosive growth of node labels.
In this paper, we present a new ATMS algorithm (CATMS) which avoids the problem of label explosions, while preserving most of the query time efficiencies resulting from label compilations. CATMS generalizes the standard ATMS subsumption relation, allowing it to compress an entire label into a single assumption.
This compression of labels is balanced by an expansion of environments to include any implied assumptions. The result is a new dimension of flexibility, allowing CATMS to trade-off the query-time efficiency of uncompressed labels against the costs of computing them. To demonstrate the significant computational gains of CATMS over de Kleer’s ATMS,we compare the performance of the ATMS-based QPE  problem-solver using each.