The natural adaptation of the cops-and-robber game to directed graphs is considered and it is shown that monotone strategies in the game yield a measure with an associated notion of graph decomposition that can be seen to describe how close a directed graph is to a directed acyclic graph (DAG).Expand

It is shown that the problem of determining the winner of a parity game is solvable in polynomial time on graphs of bounded dag-width, a consequence of which is that certain NP-complete problems such as Hamiltonicity and disjoint paths arePolynomial-time computable on graph of bounded dagger-width.Expand

We introduce a restricted version of second order logic SOω in which the second order quantifiers range over relations that are closed under the equivalence relation ≡k of k variable equivalence, for… Expand

It is found that monadic second-order logic is no more expressive than first-order as far as bisimulation invariant properties are concerned — though both are more expressive here than basic modal logic.Expand

The present investigation primarily concerns ramifications for specific classes of structures defined through conditions on the underlying frames, with a focus on frame classes that play a major role in modal correspondence theory and often correspond to typical application domains of modal logics.Expand

It is shown that if C is a class of graphs which is nowhere dense then rst-order model-checking is xed-parameter tractable on C, which essentially gives a precise characterisation of classes for which FO model- checking is tractable.Expand

The extensions of first-order logic with a least fixed point operator (FO + LFP) and with a partial fixed point operator (FO + PFP) are known to capture the complexity classes P and PSPACE… Expand

It is shown that testing the solvability of systems of equations over a finite Abelian group, a tractable CSP that was previously known not to be definable in Datalog, is not Definable in an infinitary logic with counting and hence that it is not definite in least fixed point logic or its extension with counting.Expand

It is shown that if there is any recursively enumerable set of quantifiers that can be added to FO (or LFP) to capture P, then there is one with strong uniformity conditions, and this strengthens results in [Hel92] and [KV92a].Expand