 In the modal realm there are also such cases, some of them in which seemingly harmless combinations produce dramatic results. An example of this can be found in Blackburn, Rijke, and Venema (2001: Section 6.5), where it is shown that the fusion of two decidable systems, a PDL-like system (with sequential composition and intersection as the syntactic constructors) and a system with the global modality (Goranko &amp; Passy 1992), crosses the border into undecidability. Even if the new multi-agent system turns out not to be undecidable, its complexity might be such that solving its validity problem for relatively small instances is, for all practical purposes, impossible. An example of such case is the basic multi-agent epistemic logic, with no requirements on the accessibility relations. The validity problem for formulas in \(\cL_{\left\{ \oK{1}, \ldots, \oK{n} \right\}}\) is  PSPACE: the space (and thus time) required to decide whether any given \(\varphi\) is valid is given by a polynomial function. However, adding the common knowledge operator makes the validity problem for formulas in \(\cL_{\left\{ \oK{1}, \ldots, \oK{n}, C \right\}}\) EXPTIME (sometimes also called  EXP):  the required time is now given by an exponential  function.[14]