Model checking interval temporal logics with regular expressions

In this paper, we investigate the model checking (MC) problem for Halpern and Shoham's modal logic of time intervals (HS) and its fragments, where labeling of intervals is defined by regular expressions. The MC problem for HS has recently emerged as a viable alternative to the traditional (point-based) temporal logic MC. Most expressiveness and complexity results have been obtained by imposing suitable restrictions on interval labeling, namely, by either defining it in terms of interval endpoints, or by constraining a proposition letter to hold over an interval if and only if it holds over each component state (homogeneity assumption). In both cases, the expressiveness of HS gets noticeably limited, in particular when fragments of HS are considered.