Related papers: On the Problem of Undirected st-connectivity
A celebrated theorem of Savitch states that NSPACE(S) is contained in DSPACE(S^2). In particular, Savitch gave a deterministic algorithm to solve ST-CONNECTIVITY (an NL-complete problem) using O(log^2{n}) space, implying NL is in…
We give a deterministic $\tilde{O}(\log n)$-space algorithm for approximately solving linear systems given by Laplacians of undirected graphs, and consequently also approximating hitting times, commute times, and escape probabilities for…
We formalize the proof of Reingold's Theorem that SL=L [Rei05] in the theory of bounded arithmetic VL, which corresponds to ``logspace reasoning''. As a consequence, we get that VL=VSL, where VSL is the theory of bounded arithmetic for…
Directed $st$-connectivity (DSTCON) is the problem of deciding if there exists a directed path between a pair of distinguished vertices $s$ and $t$ in an input directed graph. This problem appears in many algorithmic applications, and is…
L (Logarithmic space) versus NL (Non-deterministic logarithmic space) is one of the great open problems in computational complexity theory. In the paper "Bounds on monotone switching networks for directed connectivity", we separated…
In this paper, we consider the structural stabilizability problem of undirected networks. More specifically, we are tasked to infer the stabilizability of an undirected network from its underlying topology, where the undirected networks are…
This paper resolves a famous and longstanding open question in automata theory, i.e., the {\it linear-bounded automata question} (or shortly, LBA question), which can also be phrased succinctly in the language of computational complexity…
We prove that the homeomorphism problem for 2-manifolds can be decided in logspace. The proof relies on Reingold's logspace solution to the undirected $s,t$-connectivity problem in graphs.
Recurrent Neural Networks (RNNs) can learn to predict Signal Temporal Logic (STL) verdicts online from partial trajectories, but deploying them as runtime monitors in safety-critical systems demands more than predictive accuracy. Standard…
We report progress on the \NL vs \UL problem. [-] We show unconditionally that the complexity class $\ReachFewL\subseteq\UL$. This improves on the earlier known upper bound $\ReachFewL \subseteq \FewL$. [-] We investigate the complexity of…
Undirected $st$-connectivity is important both for its applications in network problems, and for its theoretical connections with logspace complexity. Classically, a long line of work led to a time-space tradeoff of $T=\tilde{O}(n^2/S)$ for…
We address the open problem of determining which classes of time-dependent linear Schr\"odinger equations and focusing and defocusing cubic and quintic non-linear Schr\"odinger equations (NLS) on unbounded domains that can be computed by an…
Reachability and shortest path problems are NL-complete for general graphs. They are known to be in L for graphs of tree-width 2 [JT07]. However, for graphs of tree-width larger than 2, no bound better than NL is known. In this paper, we…
In the Directed Steiner Network problem we are given an arc-weighted digraph $G$, a set of terminals $T \subseteq V(G)$, and an (unweighted) directed request graph $R$ with $V(R)=T$. Our task is to output a subgraph $G' \subseteq G$ of the…
We extend first-order logic with counting by a new operator that allows it to formalise a limited form of recursion which can be evaluated in logarithmic space. The resulting logic LREC has a data complexity in LOGSPACE, and it defines…
Standpoint linear temporal logic SLTL is a recent formalism able to model possibly conflicting commitments made by distinct agents, taking into account aspects of temporal reasoning. In this paper, we analyse the computational properties of…
Deep learning (DL) has had unprecedented success and is now entering scientific computing with full force. However, current DL methods typically suffer from instability, even when universal approximation properties guarantee the existence…
We prove a space-space trade-off for directed $st$-connectivity in the catalytic space model. For any integer $k \leq n$, we give an algorithm that decides directed $st$-connectivity using $O(\log n \cdot \log k+\log n)$ regular workspace…
We consider network design problems with deadline or delay. All previous results for these models are based on randomized embedding of the graph into a tree (HST) and then solving the problem on this tree. We show that this is not…
A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Inspired by sequential complexity theory, we focus on a complexity theory for distributed decision problems. In the context of…