Related papers: Guarded Negation Transitive Closure Logic

We formulate the $P<NP$ hypothesis in the case of the satisfiability problem as a $\Pi ^0_2$ sentence, out of which we can construct a partial recursive function $f_{\neg A}$ so that $f_{\neg A}$ is total if and only if $P < NP$. We then…

Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…

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.…

We introduce a model of register automata over infinite trees with extrema constraints. Such an automaton can store elements of a linearly ordered domain in its registers, and can compare those values to the suprema and infima of register…

This paper explores the computational complexity of various natural one-variable fragments of first-order modal logics with the addition of counting quantifiers, over both constant and varying domains. The addition of counting quantifiers…

The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…

We study the complexity of constraint satisfaction problems for templates $\Gamma$ that are first-order definable in $(\Bbb Z; succ)$, the integers with the successor relation. Assuming a widely believed conjecture from finite domain…

We propose a modal logic in which counting modalities appear in linear inequalities. We show that each formula can be transformed into an equivalent graph neural network (GNN). We also show that a broad class of GNNs can be transformed…

In this paper, we study the complexity of the periodic temporal graph realization problem with respect to upper bounds on the fastest path durations among its vertices. This constraint with respect to upper bounds appears naturally in…

We study the satisfiability problem of symbolic finite automata and decompose it into the satisfiability problem of the theory of the input characters and the monadic second-order theory of the indices of accepted words. We use our…

A complete classification of the complexity of the local and global satisfiability problems for graded modal language over traditional classes of frames have already been established. By "traditional" classes of frames, we mean those…

Although the CSP (constraint satisfaction problem) is NP-complete, even in the case when all constraints are binary, certain classes of instances are tractable. We study classes of instances defined by excluding subproblems. This approach…

We prove a complexity dichotomy theorem for all non-negative weighted counting Constraint Satisfaction Problems (CSP). This caps a long series of important results on counting problems including unweighted and weighted graph homomorphisms…

The Number Partitioning Problem (NPP) is one of the NP-complete computational problems. Its definite exact solution generally requires a check of all $N$ solution candidates, which is exponentially large. Here we describe a path to the fast…

We study the two-variable fragments D^2 and IF^2 of dependence logic and independence-friendly logic. We consider the satisfiability and finite satisfiability problems of these logics and show that for D^2, both problems are…

Tree containment problem is a fundamental problem in phylogenetic study, as it is used to verify a network model. It asks whether a given network contain a subtree that resembles a binary tree. The problem is NP-complete in general, even in…

Second-order transitive-closure logic, SO(TC), is an expressive declarative language that captures the complexity class PSPACE. Already its monadic fragment, MSO(TC), allows the expression of various NP-hard and even PSPACE-hard problems in…

An important class of decidable first-order logic fragments are those satisfying a guardedness condition, such as the guarded fragment (GF). Usually, decidability for these logics is closely linked to the tree-like model property - the fact…

Inquiries such as whether a task A depends on a task B, whether an author A has been influenced by a paper B, whether a certain protein is associated with a specific biological process or molecular function, or whether class A inherits from…

We initiate the study of the complexity-theoretic properties of convex logics in team semantics. We focus on the extension of classical propositional logic with the nonemptiness atom NE, a logic known to be both convex and union closed. We…