We verified two versions of the CPS transformation in Isabelle/HOL: one by Plotkin and one by Danvy and Filinski. We adopted first order abstract syntax so that the formalization is close to that of hand-written proofs and compilers. To simplify treatment of fresh variables introduced by the transformation we introduce parameterized first order abstract syntax implemented as a polymorphic datat...

We study the computational problem of checking whether a quantified conjunctive query (a first-order sentence built using only conjunction as Boolean connective) is true in a finite poset (a reflexive, antisymmetric, and transitive directed graph). We prove that the problem is already NP-hard on a certain fixed poset, and investigate structural properties of posets yielding fixedparameter tract...

Over the past two decades the main focus of research into first-order (FO) model checking algorithms has been on sparse relational structures – culminating in the FPT algorithm by Grohe, Kreutzer and Siebertz for FO model checking of nowhere dense classes of graphs. On contrary to that, except the case of locally bounded clique-width only little is currently known about FO model checking of den...

We study the parameterized complexity of several positional games. Our main result is that Short Generalized Hex is W[1]-complete parameterized by the number of moves. This solves an open problem from Downey and Fellows’ influential list of open problems from 1999. Previously, the problem was thought of as a natural candidate for AW[*]-completeness. Our main tool is a new fragment of first-orde...

We study the parameterized space complexity of model-checking first-order logic with a bounded number of variables. By restricting the number of the quantifier alternations we obtain problems complete for a natural hierarchy between parameterized logarithmic space and FPT. We call this hierarchy the tree hierarchy, provide a machine characterization, and link it to the recently introduced class...

The elimination distance to some target graph property P is a general modification parameter introduced by Bulian and Dawar. We initiate the study of distances properties expressible in first-order logic. delimit problem’s fixed-parameter tractability identifying sufficient necessary conditions on structure prefixes logic formulas. Our main result following meta-theorem: For every first order-l...