Related papers: Complexity of correctness for pomset logic proof n…
We point out that the computation of true \emph{proof} and \emph{disproof} numbers for proof number search in arbitrary directed acyclic graphs is NP-hard, an important theoretical result for proof number search. The proof requires a…
Verifying graph algorithms has long been considered challenging in separation logic, mainly due to structural sharing between graph subcomponents. We show that these challenges can be effectively addressed by representing graphs as a…
We show that the problem of deciding whether the vertex set of a graph can be covered with at most two bicliques is in NP$\cap$coNP. We thus almost determine the computational complexity of a problem whose status has remained open for quite…
We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…
Geometric embedding of graphs in a point set in the plane is a well known problem. In this paper, the complexity of a variant of this problem, where the point set is bounded by a simple polygon, is considered. Given a point set in the plane…
A secure set $S$ in a graph is defined as a set of vertices such that for any $X\subseteq S$ the majority of vertices in the neighborhood of $X$ belongs to $S$. It is known that deciding whether a set $S$ is secure in a graph is…
We show the functional completeness for the connectives of the non-trivial negation inconsistent logic C by using a well-established method implementing purely proof-theoretic notions only. Firstly, given that C contains a strong negation,…
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…
On example of tasks of class NP the questions concerning accuracy of work of already existing and possible in the future algorithms for the solution of tasks on discrete structures are considered.
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
Probabilistic justification logic is a modal logic with two kind of modalities: probability measures and explicit justification terms. We present a tableau procedure that can be used to decide the satisfiability problem for this logic in…
Recent advances in reading comprehension have resulted in models that surpass human performance when the answer is contained in a single, continuous passage of text. However, complex Question Answering (QA) typically requires multi-hop…
Coding theory is very useful for real world applications. A notable example is digital television. Basically, coding theory is to study a way of detecting and/or correcting data that may be true or false. Moreover coding theory is an area…
This article is a supplementary document for the CoPPar Tree paper, providing a detailed correctness proof for the CoPPar architecture.
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…
The simple greedy algorithm to find a maximal independent set of a graph can be viewed as a sequential update of a Boolean network, where the update function at each vertex is the conjunction of all the negated variables in its…
We document a connection between constraint reasoning and probabilistic reasoning. We present an algorithm, called {em probabilistic arc consistency}, which is both a generalization of a well known algorithm for arc consistency used in…
In this paper, we study a hypothesis test to determine the underlying directed graph structure of nodes in a network, where the nodes represent random processes and the direction of the links indicate a causal relationship between said…
Mining for trees in a graph is shown to be NP-complete.
This article describes a formal strategy of geometric complexity theory (GCT) to resolve the {\em self referential paradox} in the $P$ vs. $NP$ and related problems. The strategy, called the {\em flip}, is to go for {\em explicit proofs} of…