A linear time algorithm for monadic querying of indefinite data over linearly ordered domains

Temporal databases, databases of events in an ordered domain, have attracted attention since the early 90’s, and the complexity of evaluating various queries on such databases has been analyzed [1, 10]. One important issue is an efficient algorithm for a query on an indefinite data over a linearly ordered domain, i.e., efficiently answering a query as to whether all possible models of incomplete (partial) information satisfy it. Ref. [20] gives the nice overview of the applications. In general, query answering on an indefinite database is a hard problem by any measure: combined complexity, expression complexity, and data complexity [21]. Combined complexity is complexity in the usual sense, expression complexity is the complexity when the database is fixed, and data complexity is the complexity when the query is fixed. The complexity of query answering using a search engine on the Web would be measured using expression complexity, and the complexity of finding the best-fit gene to several characteristic alignments would be measured using data complexity. Van der Meyden estimated the precise complexity of query answering on an indefinite database, as illustrated in Table 1 [20]. The table includes the answer to an open problem that the combined complexity of evaluating a conjunctive (n-ary) query containing inequalities is Πp2-complete [9]. He also investigated tractable subclasses and demonstrated that the restriction to monadic queries on monadic indefinite databases reduces the complexity drastically, as shown in Table 2. While the class of monadic queries is restrictive, still contains nontrivial problems, such as a comparison between two gene alignments (assuming C,G,A, and T to be monadic predicates).