On locally checkable properties

The large computational price of formal verification of general ω-regular properties has led to the study of restricted classes of properties, and to the development of verification methodologies for them. Examples that have been widely accepted by the industry include the verification of safety properties, and bounded model checking. We introduce and study another restricted class of properties - the class of locally checkable properties. For an integer k ≥ 1, a language L ⊆ Σ ^ω is k-checkable if there is a language R ⊆ Σ^k (of "allowed subwords") such that a word w belongs to L iff all the subwords of w of length k belong to R. A property is locally checkable if its language is k-checkable for some k. Locally checkable properties, which are a special case of safety properties, are common in the specification of systems. In particular, one can often bound an eventuality constraint in a property by a fixed time frame. The practical importance of locally checkable properties lies in the low memory demand for their run-time verification. A monitor for a k-checkable property needs only a record of the last k computation cycles. Furthermore, even if a large number of k-checkable properties are monitored, the monitors can share their memory, resulting in memory demand that do not depend on the number of properties monitored. This advantage of locally checkable properties makes them particularly suitable for run-time verification. In the paper, we define locally checkable languages, study their relation to other restricted classes of properties, study the question of deciding whether a property is locally checkable, and study the relation between the size of the property (specified by an LTL formula or an automaton) and the smallest k for which the property is k-checkable.