Alberto Molinari

A Model Checking Procedure for Interval Temporal Logics based on Track Representatives

Model checking is commonly recognized as one of the most effective tool in system verification. While it has been systematically investigated in the context of classical, point-based temporal logics, it is still largely unexplored in the interval logic setting. Recently, a non-elementary model checking algorithm for Halpern and Shohams modal logic of time intervals HS, interpreted over finite Kripke structures, has been proposed, together with a proof of the EXPSPACE-hardness of the problem. In this paper, we devise an EXPSPACE model checking procedure for two meaningful HS fragments. It exploits a suitable contraction technique, that allows one to replace long enough tracks of a Kripke structure by equivalent shorter ones.

Complexity of ITL Model Checking: Some Well-Behaved Fragments of the Interval Logic HS

Model checking has been successfully used in many computer science fields, including artificial intelligence, theoretical computer science, and databases. Most of the proposed solutions make use of classical, point-based temporal logics, while little work has been done in the interval temporal logic setting. Recently, a non-elementary model checking algorithm for Halpern and Shohams modal logic of time intervals HS over finite Kripke structures (under the homogeneity assumption) and an EXPSPACE model checking procedure for two meaningful fragments of it have been proposed. In this paper, we show that more efficient model checking procedures can be developed for some expressive enough fragments of HS.

Interval Temporal Logic Model Checking: The Border Between Good and Bad HS Fragments

The model checking problem has thoroughly been explored in the context of standard point-based temporal logics, such as LTL, CTL, and CTL

Model checking for fragments of the interval temporal logic HS at the low levels of the polynomial time hierarchy

^{*}

Model checking for fragments of Halpern and Shoham's interval temporal logic based on track representatives☆

, whereas model checking for interval temporal logics has been brought to the attention only very recently. In this paper, we prove that the model checking problem for the logic of Allens relations started-by and finished-by is highly intractable, as it can be proved to be

Model checking well-behaved fragments of HS: the (almost) final picture

{{\mathrm{\mathbf {EXPSPACE}}}}