Related papers: A Casual Tour Around a Circuit Complexity Bound
We show that the genus problem for alternating knots with $n$ crossings has linear time complexity and is in Logspace$(n)$. Almost all alternating knots of given genus possess additional combinatorial structure, we call them standard. We…
Temporal graphs are graphs with time-stamped edges. We study the problem of finding a small vertex set (the separator) with respect to two designated terminal vertices such that the removal of the set eliminates all temporal paths…
This version is similar to math.CO/0210113. We've changed Conjectures 1.1 and 1.2 so that they cover arbitrary graphs(digraphs). Let G be an arbitrary graph(digraph). Then - in polynomial time - either an algorithm obtains a hamilton…
This paper introduces a class of linear programming examples which cause the simplex method to cycle indefinitely and which are the simplest possible examples showing this behaviour. The structure of examples from this class repeats after…
The class of loop spaces whose mod p cohomology is Noetherian is much larger than the class of p-compact groups (for which the mod p cohomology is required to be finite). It contains Eilenberg-Mac Lane spaces such as the infinite complex…
The objective of this article is to formalize the definition of NP problems. We construct a mathematical model of discrete problems as independence systems with weighted elements. We introduce two auxiliary sets that characterize the…
We study limit cycles in piecewise complex systems with switching manifold $\mathbb{S}^1$. Using M\"obius transformations we establish an equivalence between circular and straight-line discontinuities that preserves periods, stability, and…
A multi-species generalization of the Asymmetric Simple Exclusion Process (ASEP) has been considered in the presence of a single impurity on a ring. The model describes particles hopping in one direction with stochastic dynamics and hard…
Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics…
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…
Random instances of feedforward Boolean circuits are studied both analytically and numerically. Evaluating these circuits is known to be a P-complete problem and thus, in the worst case, believed to be impossible to perform, even given a…
The cohomology of the degree-$n$ general linear group over a finite field of characteristic $p$, with coefficients also in characteristic $p$, remains poorly understood. For example, the lowest degree previously known to contain nontrivial…
We present the finite first-order theory (FFOT) machine, which provides an atemporal description of computation. We then develop a concept of complexity for the FFOT machine, and prove that the class of problems decidable by a FFOT machine…
The product homomorphism problem (PHP) takes as input a finite collection of relational structures A1, ..., An and another relational structure B, all over the same schema, and asks whether there is a homomorphism from the direct product A1…
We connect the study of pseudodeterministic algorithms to two major open problems about the structural complexity of $\mathsf{BPTIME}$: proving hierarchy theorems and showing the existence of complete problems. Our main contributions can be…
This work is devoted to study of a class of elliptic singular perturbed systems and their singular limit to a phase segregating system. We prove existence and uniqueness and study the asymptotic behaviour with convergence to a limiting…
This paper analyzes infinitary nondeterministic computability theory. The main result is D $\ne$ ND $\cap$ coND where D is the class of sets decidable by infinite time Turing machines and ND is the class of sets recognizable by a…
In this article we study the existence of limit cycles in families of piecewise smooth differential equations having the unit circle as discontinuity region. We consider families presenting singularities of center or saddle type, visible or…
The causal graph of a planning instance is an important tool for planning both in practice and in theory. The theoretical studies of causal graphs have largely analysed the computational complexity of planning for instances where the causal…
We study the higher (or sequential) topological complexity $\mathrm{TC}_s$ of manifolds with abelian fundamental group. We give sufficient conditions for $\mathrm{TC}_s$ to be non-maximal in both the orientable and non-orientable cases. In…