Related papers: The Complexity of Modified Instances
Complexity theory is a useful tool to study computational issues surrounding the elicitation of preferences, as well as the strategic manipulation of elections aggregating together preferences of multiple agents. We study here the…
Query complexity measures the amount of information an algorithm needs about a problem to compute a solution. On a quantum computer there are different realizations of a query and we will show that these are not always equivalent. Our…
Abduction is one of the most important forms of reasoning; it has been successfully applied to several practical problems such as diagnosis. In this paper we investigate whether the computational complexity of abduction can be reduced by an…
A given subset $A$ of natural numbers is said to be complete if every element of $\mathbb{N}$ is the sum of distinct terms taken from $A$. This topic is strongly connected to the knapsack problem which is known to be NP complete.…
In the well-known complexity class NP are combinatorial problems, whose optimization counterparts are important for many practical settings. These problems typically consider full knowledge about the input. In practical settings, however,…
We introduce and analyze the problem of the compilation of decision models from a decision-theoretic perspective. The techniques described allow us to evaluate various configurations of compiled knowledge given the nature of evidential…
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…
Modal logics are widely used in computer science. The complexity of modal satisfiability problems has been investigated since the 1970s, usually proving results on a case-by-case basis. We prove a very general classification for a wide…
We investigate the impact of modifying the constraining relations of a Constraint Satisfaction Problem (CSP) instance, with a fixed template, on the set of solutions of the instance. More precisely we investigate sensitive instances: an…
Larrauri and \v{Z}ivn\'y [ICALP'25/ACM ToCL'24] recently established a complete complexity classification of the problem of solving a system of equations over a monoid $N$ assuming that a solution exists over a monoid $M$, where both…
Efforts to apply transformer-based language models (TLMs) to the problem of reasoning in natural language have enjoyed ever-increasing success in recent years. The most fundamental task in this area to which nearly all others can be reduced…
Machine learning (ML) in its current form implies that an answer to any problem can be well approximated by a function of a very peculiar form: a specially adjusted iteration of Heavyside theta-functions. It is natural to ask if the answers…
I shall describe a general model-theoretic task to construct expansions of pseudofinite structures and discuss several examples of particular relevance to computational complexity. Then I will present one specific situation where finding a…
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…
Today's propositional satisfiability (SAT) solvers are extremely powerful and can be used as an efficient back-end for solving NP-complete problems. However, many fundamental problems in knowledge representation and reasoning are located at…
The class of problems complete for NP via first-order reductions is known to be characterized by existential second-order sentences of a fixed form. All such sentences are built around the so-called generalized IS-form of the sentence that…
The computational complexity of a Delta 2 set will be calibrated by the amount of changes needed for any of its computable approximations. Firstly, we study Martin-Loef random sets, where we quantify the changes of initial segments.…
In this paper we present a novel tool to evaluate problem solving systems. Instead of using a system to solve a problem, we suggest using the problem to evaluate the system. By finding a numerical representation of a problem's complexity,…
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and…
A probabilistic database with attribute-level uncertainty consists of relations where cells of some attributes may hold probability distributions rather than deterministic content. Such databases arise, implicitly or explicitly, in the…