Related papers: Technical Notes on Complexity of the Satisfiabilit…
Replicability, introduced by (Impagliazzo et al. STOC '22), is the notion that algorithms should remain stable under a resampling of their inputs (given access to shared randomness). While a strong and interesting notion of stability, the…
In this survey, we address the worst-case, average-case, and generic-case time complexity of the word problem and some other algorithmic problems in several classes of groups and show that it is often the case that the average-case…
Evaluating conjunctive queries and solving constraint satisfaction problems are fundamental problems in database theory and artificial intelligence, respectively. These problems are NP-hard, so that several research efforts have been made…
What factors impact the comprehensibility of code? Previous research suggests that expectation-congruent programs should take less time to understand and be less prone to errors. We present an experiment in which participants with…
Motivated by an application where we try to make proofs for Description Logic inferences smaller by rewriting, we consider the following decision problem, which we call the small term reachability problem: given a term rewriting system $R$,…
Fixed-parameter tractable (FPT) algorithms have been successfully applied to many intractable problems -- with a focus on decision and optimization problems. Their aim is to confine the exponential explosion to some parameter, while the…
Motivated by certain applications from physics, biochemistry, economics, and computer science, in which the objects under investigation are not accessible because of various limitations, we propose a trial-and-error model to examine…
In this work, we are interested in the detailed analysis of complexity aspects of both time and space that arises from the implementation of a quantum algorithm on a quantum based hardware. In particular, some steps of the implementation,…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
The classical approach to solvability of a mathematical problem is to define a method which includes certain rules of operation or algorithms. Then using the defined method, one can show that some problems are solvable or not solvable or…
A large deviation analysis of the solving complexity of random 3-Satisfiability instances slightly below threshold is presented. While finding a solution for such instances demands an exponential effort with high probability, we show that…
This paper is a study of weighted counting of the solutions of acyclic conjunctive queries ($\ACQ$). The unweighted quantifier free version of this problem is known to be tractable (for combined complexity), but it is also known that…
Tasks are central in machine learning, as they are the most natural objects to assess the capabilities of current models. The trend is to build general models able to address any task. Even though transfer learning and multitask learning…
We study the computational complexity of fundamental problems over the $p$-adic numbers ${\mathbb Q}_p$ and the $p$-adic integers ${\mathbb Z}_p$. Gu\'epin, Haase, and Worrell proved that checking satisfiability of systems of linear…
Constraint propagation is one of the techniques central to the success of constraint programming. To reduce search, fast algorithms associated with each constraint prune the domains of variables. With global (or non-binary) constraints, the…
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…
By considering probability distributions over the set of assignments the expected truth values assignment to propositional variables are extended through linear operators, and the expected truth values of the clauses at any given…
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…
We give an overview of certain aspects of tractability analysis of multivariate problems. This paper is not intended to give a complete account of the subject, but provides an insight into how the theory works for particular types of…