Related papers: Rice-like complexity lower bounds for Boolean and …
We present a Rice-like complexity lower bound for any MSO-definable problem on binary structures succinctly encoded by circuits. This work extends the framework recently developed as a counterpoint to Courcelle's theorem for graphs encoded…
An automata network is a graph of entities, each holding a state from a finite set and evolving according to a local update rule which depends only on its neighbors in the network's graph. It is freezing if there is an order on the states…
Boolean automata networks (aka Boolean networks) are space-time discrete dynamical systems, studied as a model of computation and as a representative model of natural phenomena. A collection of simple entities (the automata) update their…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
An automata network is a network of entities, each holding a state from a finite set and evolving according to a local update rule which depends only on its neighbors in the network's graph. It is freezing if there is an order on states…
Automata networks can be seen as bare finite dynamical systems, but their growing theory has shown the importance of the underlying communication graph of such networks. This paper tackles the question of what dynamics can be realized up to…
The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of…
A new proof technique combining finite model theory and dynamical systems has recently been introduced to obtain general complexity lower bounds on any question one may formulate on the dynamics (seen as a graph) of a given automata network…
An Automata Network is a map ${f:Q^n\rightarrow Q^n}$ where $Q$ is a finite alphabet. It can be viewed as a network of $n$ entities, each holding a state from $Q$, and evolving according to a deterministic synchronous update rule in such a…
The linear space hypothesis is a practical working hypothesis, which originally states the insolvability of a restricted 2CNF Boolean formula satisfiability problem parameterized by the number of Boolean variables. From this hypothesis, it…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
A Boolean network (BN) is a discrete dynamical system defined by a Boolean function that maps to the domain itself. A trap space of a BN is a generalization of a fixed point, which is defined as the sub-hypercubes closed by the function of…
We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone input. The nodes may have either a discrete or continuous set…
We apply a Bethe-Peierls approach to statistical-mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices. Using the NP-hard optimization problem of…
Parameterized complexity seeks to use input structure to obtain faster algorithms for NP-hard problems. This has been most successful for graphs of low treewidth: Many problems admit fast algorithms relative to treewidth and many of them…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even…
We analyse the power of graph neural networks (GNNs) in terms of Boolean circuit complexity and descriptive complexity. We prove that the graph queries that can be computed by a polynomial-size bounded-depth family of GNNs are exactly those…
The Recognizability Theorem states that if a set of finite graphs is definable by a monadic second-order (MSO) sentence, then it is recognizable with respect to the graph algebra upon which the definition of clique-width is based.…
Technology trends will cause data movement to account for the majority of energy expenditure and execution time on emerging computers. Therefore, computational complexity will no longer be a sufficient metric for comparing algorithms, and a…