There has been a great deal of progress in the fifteen years that have elapsed since Wigderson published his survey on the complexity of the graph connectivity problem [Wig92]. Most significantly, Reingold solved the longstanding question of the complexity of the s-t connectivity problem in undirected graphs, showing that this is complete for logspace (L) [Rei05]. This survey talk will focus on...

The undecidability of basic decision problems for general FIFO machines such as reachability and unboundedness is well-known. In this paper, we provide an underapproximation the model by considering only runs that are input-bounded (i.e. sequence messages sent through a particular channel belongs to given bounded language). We prove, reducing counter machine with restricted zero tests, rational...

Abstract Consider an agent traversing a graph of “gadgets”, where each gadget has local state that changes with traversal by the according to specified rules. Prior work studied computational complexity deciding whether can reach location, problem we call reachability . This paper introduces new goals for agent, aiming characterize when these problems is same or differs from reachability. First...

We formally show that the directed graph reachability problem can be reduced to several problems using a linear number of processors; hence an eecient parallel algorithm to solve any of these problems would imply an eecient parallel algorithm for the directed graph reachability problem. This formally establishes that all these problems are at least as hard as the s ? t reachability problem.

The primary function of a BGP speaking system is to exchange network reachability information with other BGP systems. This network reachability information includes information on the list of Autonomous Systems (ASs) that reachability information traverses. This information is sufficient to construct a graph of AS connectivity from which routing loops may be pruned and some policy decisions at ...

The reachability problem in component systems is PSPACEcomplete. We show here that even the reachability problem in the subclass of component systems with “tree-like” communication is PSPACEcomplete. For this purpose we reduce the question if a Quantified Boolean Formula (QBF) is true to the reachability problem in “tree-like” component systems.

Constrained path problems have to do with finding paths in graphs subject to constraints. One way of constraining the graph is by enforcing reachability on nodes. For instance, it may be required that a node reaches a particular set of nodes by respecting some restrictions like visiting a particular set of nodes or edges and using less than a certain amount of resources. The reachability constr...

Context-free language reachability (CFL-reachability) is a fundamental framework for program analysis. A large variety of static analyses can be formulated as CFL-reachability problems, which determines whether specific source-sink pairs in an edge-labeled graph are connected by reachable path, i.e., path whose edge labels form string accepted the given CFL. Computing expensive. The fastest alg...