The complexity of problems on implicitly represented inputs

Abstract

Highly regular data can be represented succinctly by various kinds of implicit data structures. Many problems in P are known to be hard if their input is given as circuit or Ordered Binary Decision Diagram (OBDD). Nevertheless, in practical areas like CAD and Model Checking, symbolic algorithms using functional operations on OBDD-represented data are well-established. Their theoretical analysis has mostly been restricted to the number of functional operations yet. We show that P-complete problems have no symbolic algorithms using a polylogarithmic number of functional operations, unless P=NC. Moreover, we complement PSPACE-hardness results for problems on OBDD-represented inputs by fixed-parameter intractability results, where the OBDD width serves as the fixed parameter. © Springer-Verlag Berlin Heidelberg 2006.