Quantified CTL: Expressiveness and Complexity

While it was defined long ago, the extension of CTL with quantification over atomic propositions has never been studied extensively. Considering two different semantics (depending whether propositional quantification refers to the Kripke structure or to its unwinding tree), we study its expressiveness (showing in particular that QCTL coincides with Monadic Second-Order Logic for both semantics) and characterise the complexity of its model-checking and satisfiability problems, depending on the number of nested propositional quantifiers (showing that the structure semantics populates the polynomial hierarchy while the tree semantics populates the exponential hierarchy)

Querying Schemas With Access Restrictions

We study verification of systems whose transitions consist of accesses to a Web-based data-source. An access is a lookup on a relation within a relational database, fixing values for a set of positions in the relation. For example, a transition can represent access to a Web form, where the user is restricted to filling in values for a particular set of fields. We look at verifying properties of a schema describing the possible accesses of such a system. We present a language where one can describe the properties of an access path, and also specify additional restrictions on accesses that are enforced by the schema. Our main property language, AccLTL, is based on a first-order extension of linear-time temporal logic, interpreting access paths as sequences of relational structures. We also present a lower-level automaton model, Aautomata, which AccLTL specifications can compile into. We show that AccLTL and A-automata can express static analysis problems related to "querying with limited access patterns" that have been studied in the database literature in the past, such as whether an access is relevant to answering a query, and whether two queries are equivalent in the accessible data they can return. We prove decidability and complexity results for several restrictions and variants of AccLTL, and explain which properties of paths can be expressed in each restriction.Comment: VLDB201

Parametrised Complexity of Model Checking and Satisfiability in Propositional Dependence Logic

In this paper, we initiate a systematic study of the parametrised complexity in the field of Dependence Logics which finds its origin in the Dependence Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parametrisations with respect to the central decision problems. The model checking problem (MC) of PDL is NP-complete. The subject of this research is to identify a list of parametrisations (formula-size, treewidth, treedepth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) showing a different picture: under team-size, or dep-arity SAT is paraNP-complete whereas under all other mentioned parameters the problem is in FPT. Finally, we introduce a variant of the satisfiability problem, asking for teams of a given size, and show for this problem an almost complete picture.Comment: Update includes refined result