Related papers: Rice-like complexity lower bounds for Boolean and …
This paper considers the problem of minimal control inputs to affect the system states such that the resulting system is structurally controllable. This problem and the dual problem of minimal observability are claimed to have no…
We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches, for an alphabet with an arbitrary number of letters. The analytic expression…
Sofic shifts are symbolic dynamical systems defined by the set of bi-infinite sequences on an edge-labeled directed graph, called a presentation. We study the computational complexity of an array of natural decision problems about…
Modularity is a very widely used measure of the level of clustering or community structure in networks. Here we consider a recent generalisation of the definition of modularity to temporal graphs, whose edge-sets change over discrete…
The website reductions.network serves as a comprehensive database for exploring problems and reductions between them. It presents several complexity classes in the form of an interconnected graph where problems are represented as vertices,…
We survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language -- which is the number of its (left) quotients, and…
The automatic complexity of a finite word (string) is an analogue for finite automata of Sipser's distinguishing complexity (1983) and was introduced by Shallit and Wang (2001). For a finite alphabet $\Sigma$ of at least two elements, we…
We investigate the computational complexity of various problems for simple recurrent neural networks (RNNs) as formal models for recognizing weighted languages. We focus on the single-layer, ReLU-activation, rational-weight RNNs with…
We study the classical and parameterized complexity of computing the positive non-clashing teaching dimension of a set of concepts, that is, the smallest number of examples per concept required to successfully teach an intelligent learner…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
We study the satisfiability problem of symbolic finite automata and decompose it into the satisfiability problem of the theory of the input characters and the monadic second-order theory of the indices of accepted words. We use our…
Maximum entropy null models of networks come in different flavors that depend on the type of constraints under which entropy is maximized. If the constraints are on degree sequences or distributions, we are dealing with configuration…
In this paper we consider a nondeterministic computation by deterministic multi-head 2-way automata having a read-only access to an auxiliary memory. The memory contains additional data (a guess) and computation is successful iff it is…
In the present work, we lay out a new theory showing that all automata can always be co-lexicographically partially ordered, and an intrinsic measure of their complexity can be defined and effectively determined, namely, the minimum width…
It is already shown that a Boolean function for a NP-complete problem can be computed by a polynomial-sized circuit if its variables have enough number of automorphisms. Looking at this previous study from the different perspective gives us…
Modern computer networks support interesting new routing models in which traffic flows from a source s to a destination t can be flexibly steered through a sequence of waypoints, such as (hardware) middleboxes or (virtualized) network…
We give a new upper bound on the quantum query complexity of deciding $st$-connectivity on certain classes of planar graphs, and show the bound is sometimes exponentially better than previous results. We then show Boolean formula evaluation…
We give lower bounds on the communication complexity of graph problems in the multi-party blackboard model. In this model, the edges of an $n$-vertex input graph are partitioned among $k$ parties, who communicate solely by writing messages…
We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend…
We prove complexity dichotomies for \#CSP problems (not necessarily symmetric) with Boolean domain and complex range on several typical minor-closed graph classes. These dichotomies give a complete characterization of the complexity of…