Related papers: The Complexity of Poor Man's Logic
The computational complexity of polynomial ideals and Gr\"obner bases has been studied since the 1980s. In recent years, the related notions of polynomial subalgebras and SAGBI bases have gained more and more attention in computational…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
In a \emph{separability problem}, we are given two sets $K$ and $L$ from a class $\mathcal{C}$, and we want to decide whether there exists a set $S$ from a class $\mathcal{S}$ such that $K\subseteq S$ and $S\cap L=\emptyset$. In this case,…
For every class $\mathscr{C}$ of word languages, one may associate a decision problem called $\mathscr{C}$-separation. Given two regular languages, it asks whether there exists a third language in $\mathscr{C}$ containing the first…
It is known that the satisfiability problems of the product logics K4xS5 and S4xS5 are NEXPTIME-hard and that the satisfiability problem of the logic SSL of subset spaces is PSPACE-hard. We improve these lower bounds for the complexity of…
Modal dependence logic (MDL) was introduced recently by V\"a\"an\"anen. It enhances the basic modal language by an operator =(). For propositional variables p_1,...,p_n the atomic formula =(p_1,...,p_(n-1),p_n) intuitively states that the…
The computational properties of modal and propositional dependence logics have been extensively studied over the past few years, starting from a result by Sevenster showing NEXPTIME-completeness of the satisfiability problem for modal…
Complexity theory can be viewed as the study of the relationship between computation and applications, understood the former as complexity classes and the latter as problems. Completeness results are clearly central to that view. Many…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
We show that for every fixed $k\geq 3$, the problem whether the termination/counter complexity of a given demonic VASS is $\mathcal{O}(n^k)$, $\Omega(n^{k})$, and $\Theta(n^{k})$ is coNP-complete, NP-complete, and DP-complete, respectively.…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
The expressive power of interval temporal logics (ITLs) makes them one of the most natural choices in a number of application domains, ranging from the specification and verification of complex reactive systems to automated planning.…
Polymodal provability logic GLP is incomplete w.r.t. Kripke frames. It is known to be complete w.r.t. topological semantics, where the diamond modalities correspond to topological derivative operations. However, the topologies needed for…
Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a knowledge representation that is useful in mechanizing decision theoretic planning in relational domains. GFODDs generalize function-free first order logic and…
We study linear-time temporal logics interpreted over data words with multiple attributes. We restrict the atomic formulas to equalities of attribute values in successive positions and to repetitions of attribute values in the future or…
We consider the general problem of blocking all solutions of some given combinatorial problem with only few elements. For example, the problem of destroying all maximum cliques of a given graph by forbidding only few vertices. Problems of…
We present a PSPACE algorithm that decides satisfiability of the graded modal logic Gr(K_R)---a natural extension of propositional modal logic K_R by counting expressions---which plays an important role in the area of knowledge…
The methods used to establish PSPACE-bounds for modal logics can roughly be grouped into two classes: syntax driven methods establish that exhaustive proof search can be performed in polynomial space whereas semantic approaches directly…
We consider well-known provability logic GLP. We prove that the GLP-provability problem for variable-free polymodal formulas is PSPACE-complete. For a number n, let L^n_0 denote the class of all polymodal variable-free formulas without…
The constraint satisfaction probem (CSP) is a well-acknowledged framework in which many combinatorial search problems can be naturally formulated. The CSP may be viewed as the problem of deciding the truth of a logical sentence consisting…