Related papers: SAT Has No Wizards
This paper gives a novel approach to analyze SAT problem more deeply. First, I define new elements of Boolean formula such as dominant variable, decision chain, and chain coupler. Through the analysis of the SAT problem using the elements,…
In recent research on non-monotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P union R and Q union R have the same answer sets for any other program R. This…
This paper solves a long standing open problem of whether NP-complete problems could be solved in polynomial time on a deterministic Turing machine by showing that the indistinguishable binomial decision tree can be formed in a 3-SAT…
We prove a number of results around kernelization of problems parameterized by the size of a given vertex cover of the input graph. We provide three sets of simple general conditions characterizing problems admitting kernels of polynomial…
Constraint Logic Programming (CLP) is a logic programming formalism used to solve problems requiring the consideration of constraints, like resource allocation and automated planning and scheduling. It has previously been extended in…
This paper describes diff-SAT, an Answer Set and SAT solver which combines regular solving with the capability to use probabilistic clauses, facts and rules, and to sample an optimal world-view (multiset of satisfying Boolean variable…
In the last two decades, modal and description logics have been applied to numerous areas of computer science, including knowledge representation, formal verification, database theory, distributed computing and, more recently, semantic web…
In this paper, we investigate problems which are dual to the unification problem, namely the Fixed Point (FP) problem, Common Term (CT) problem and the Common Equation (CE) problem for string rewriting systems. Our main motivation is…
During the last years, several algorithmic meta-theorems have appeared (Bodlaender et al. [FOCS 2009], Fomin et al. [SODA 2010], Kim et al. [ICALP 2013]) guaranteeing the existence of linear kernels on sparse graphs for problems satisfying…
We provide a positive answer to a long-standing open question of the decidability of the not-contains string predicate. Not-contains is practically relevant, for instance in symbolic execution of string manipulating programs. Particularly,…
Here we study the complexity of string problems as a function of the size of a program that generates input. We consider straight-line programs (SLP), since all algorithms on SLP-generated strings could be applied to processing…
Earlier we introduced the notion of a stable set of points (SSP). We proved that a CNF formula is unsatisfiable iff there is a set of points (i.e. complete assignments) that is stable with respect to this formula. Experiments showed that…
We study the parameterized complexity of Split Contraction and Threshold Contraction. In these problems we are given a graph G and an integer k and asked whether G can be modified into a split graph or a threshold graph, respectively, by…
Answer Set Programming (ASP) is a declarative programming paradigm based on logic programming and non-monotonic reasoning. It is a tremendously powerful tool for describing and solving combinatorial problems. Like any other language, ASP…
The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g.…
Rules in logic programming encode information about mutual interdependencies between literals that is not captured by any of the commonly used semantics. This information becomes essential as soon as a program needs to be modified or…
Kernel-based learning algorithms are widely used in machine learning for problems that make use of the similarity between object pairs. Such algorithms first embed all data points into an alternative space, where the inner product between…
A strong geodetic set of a graph~$G=(V,E)$ is a vertex set~$S \subseteq V(G)$ in which it is possible to cover all the remaining vertices of~$V(G) \setminus S$ by assigning a unique shortest path between each vertex pair of~$S$. In the…
We consider the average-case complexity of some otherwise undecidable or open Diophantine problems. More precisely, consider the following: (I) Given a polynomial f in Z[v,x,y], decide the sentence \exists v \forall x \exists y f(v,x,y)=0,…
Epistemic Logic Programs (ELPs), that is, Answer Set Programming (ASP) extended with epistemic operators, have received renewed interest in recent years, which led to a flurry of new research, as well as efficient solvers. An important…