Undecidability and intractability results concerning datalog programs and their persistency numbers

The relation between Datalog programs and homomorphism problems, and, between Datalog programs and bounded treewidth structures has been recognized for some time and given much attention recently. Additionally, the essential role of persistent variables (in program expansions) for solving several relevant problems has also started to be observed. In Afrati et al. [2005] the general notion of program persistencies was refined into four notions (two syntactical ones and two semantical ones) and the interrelationship between these four persistency numbers was studied. In the present article (1) we prove undecidability results concerning the semantical notions of persistency number--modulo equivalence, of persistency number and of characteristic integer, (2) we exhibit new classes of programs for which boundedness is undecidable and (3) we prove intractabiltity results concerning the syntactical notions of weak persistency number and of weak characteristic integer.