On the Expression of Graph Properties in some Fragments of Monadic Second-Order Logic

Graph equivalences and decompositions definable in Monadic Second-Order Logic. The case of Circle Graphs

Many graph properties and graph transformations can be formalized inMonadic Second-Order logic. This language is the extension of First-Order logic allowing variables denoting sets of elements. In the case of graphs, these elements can be vertices, and in some cases edges. Monadic second-order graph properties can be checked in linear time on the class of graphs of tree-width at most k for any ...

On the complexity of fragments of second-order logic

Existential second order logic (ESO) is an extension of first-order logic (FO) that allows the existential quantification of relation and function symbols. The seminal result due to Fagin states that the properties expressible in ESO coincide with the decision problems in the complexity class NP. On the other hand, the monadic fragment of ESO is considerably weaker as it corresponds to the clas...

The Expression of Graph Properties and Graph Transformations in Monadic Second-Order Logic

The succinctness of first-order logic on linear orders (Full Version)

Succinctness is a natural measure for comparing the strength of different logics. Intuitively, a logic L1 is more succinct than another logic L2 if all properties that can be expressed in L2 can be expressed in L1 by formulas of (approximately) the same size, but some properties can be expressed in L1 by (significantly) smaller formulas. We study the succinctness of logics on linear orders that...

A modal perspective on monadic second-order alternation hierarchies

We establish that the quantifier alternation hierarchy of formulae of Second-Order Propositional Modal Logic (SOPML) induces an infinite corresponding semantic hierarchy over the class of finite directed graphs. This is a response to an open problem posed in [4] and [8]. We also provide modal characterizations of the expressive power of Monadic Second-Order Logic (MSO) and address a number of p...