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We introduce techniques for proving superlinear conditional lower bounds for polynomial time problems. In particular, we show that CircuitSAT for circuits with m gates and log(m) inputs (denoted by log-CircuitSAT) is not decidable in…
To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an…
We propose a new approach to compute an interval over-approximation of the finite time reachable set for a large class of nonlinear systems. This approach relies on the notions of sensitivity matrices, which are the partial derivatives…
We study computational complexity of the class of distance-constrained graph labeling problems from the fixed parameter tractability point of view. The parameters studied are neighborhood diversity and clique width. We rephrase the distance…
We extend Berge's Maximum Theorem to allow for incomplete preferences. We first provide a simple version of the Maximum Theorem for convex feasible sets and a fixed preference. Then, we show that if, in addition to the traditional…
Time-Basic Petri nets, is a powerful formalism for model- ing real-time systems where time constraints are expressed through time functions of marking's time description associated with transition, representing possible firing times. We…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…
We study timed systems in which some timing features are unknown parameters. Parametric timed automata (PTAs) are a classical formalism for such systems but for which most interesting problems are undecidable. Notably, the parametric…
Parameter testing algorithms are using constant number of queries to estimate the value of a certain parameter of a very large finite graph. It is well-known that graph parameters such as the independence ratio or the edit-distance from…
The problem of minimizing a polynomial over the standard simplex is one of the basic NP-hard nonlinear optimization problems --- it contains the maximum clique problem in graphs as a special case. It is known that the problem allows a…
We classify the complexity of the LTL satisfiability and model checking problems for several standard parameterisations. The investigated parameters are temporal depth, number of propositional variables and formula treewidth, resp.,…
This paper considers pairs of optimization problems that are defined from a single input and for which it is desired to find a good approximation to either one of the problems. In many instances, it is possible to efficiently find an…
Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
We show the first unconditional pseudo-determinism result for all of search-BPP. Specifically, we show that every BPP search problem can be computed pseudo-deterministically on average for infinitely many input lengths. In other words, for…
In this paper, we derive an explicit formula for constructing the confidence interval of binomial parameter with guaranteed coverage probability. The formula overcomes the limitation of normal approximation which is asymptotic in nature and…
The C-Planarity problem asks for a drawing of a $\textit{clustered graph}$, i.e., a graph whose vertices belong to properly nested clusters, in which each cluster is represented by a simple closed region with no edge-edge crossings, no…
Under a regularity assumption we prove that reachability in fixed time for nonlinear control systems is robust under control sampling.
We study the problem of opportunistic approachability: a generalization of Blackwell approachability where the learner would like to obtain stronger guarantees (i.e., approach a smaller set) when their adversary limits themselves to a…