Related papers: An O(m log n) Algorithm for Stuttering Equivalence…
Groote and Wijs recently described an algorithm for deciding stuttering equivalence and branching bisimulation equivalence, acclaimed to run in $\mathcal{O}(m \log n)$ time. Unfortunately, the algorithm does not always meet the acclaimed…
Branching bisimilarity is a behavioural equivalence relation on labelled transition systems that takes internal actions into account. It has the traditional advantage that algorithms for branching bisimilarity are more efficient than all…
A number of algorithms for computing the simulation preorder (and equivalence) on Kripke structures are available. Let Sigma denote the state space, -> the transition relation and Psim the partition of Sigma induced by simulation…
The well known Hopcroft's algorithm to minimize deterministic complete automata runs in $O(kn\log n)$-time, where $k$ is the size of the alphabet and $n$ the number of states. The main part of this algorithm corresponds to the computation…
We introduce a bisimulation learning algorithm for non-deterministic transition systems. We generalise bisimulation learning to systems with bounded branching and extend its applicability to model checking branching-time temporal logic,…
The most efficient way to calculate strong bisimilarity is by calculation the relational coarsest partition on a transition system. We provide the first linear time algorithm to calculate strong bisimulation using parallel random access…
Computing the simulation preorder of a given Kripke structure (i.e., a directed graph with $n$ labeled vertices) has crucial applications in model checking of temporal logic. It amounts to solving a specific two-players reachability game,…
Stuttering bisimulation is a well-known behavioral equivalence that preserves CTL-X, namely CTL without the next-time operator X. Correspondingly, the stuttering simulation preorder induces a coarser behavioral equivalence that preserves…
We introduce an algorithm for the minimization of deterministic Kripke structures with O(kn log2 n) time complexity. We prove the correctness and complexity properties of this algorithm.
Algorithms which compute the coarsest simulation preorder are generally designed on Kripke structures. Only in a second time they are extended to labelled transition systems. By doing this, the size of the alphabet appears in general as a…
We consider the problem of finding \textit{semi-matching} in bipartite graphs which is also extensively studied under various names in the scheduling literature. We give faster algorithms for both weighted and unweighted case. For the…
We study space and time efficient quantum algorithms for two graph problems -- deciding whether an $n$-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms…
We present a novel self-stabilizing algorithm for minimum spanning tree (MST) construction. The space complexity of our solution is $O(\log^2n)$ bits and it converges in $O(n^2)$ rounds. Thus, this algorithm improves the convergence time of…
We give an O(sqrt n log n)-query quantum algorithm for evaluating size-n AND-OR formulas. Its running time is poly-logarithmically greater after efficient preprocessing. Unlike previous approaches, the algorithm is based on a quantum walk…
A number of algorithms for computing the simulation preorder are available. Let Sigma denote the state space, -> the transition relation and Psim the partition of Sigma induced by simulation equivalence. The algorithms by Henzinger,…
In the k-mappability problem, we are given a string x of length n and integers m and k, and we are asked to count, for each length-m factor y of x, the number of other factors of length m of x that are at Hamming distance at most k from y.…
We study the Multiple Cluster Scheduling problem and the Multiple Strip Packing problem. For both problems, there is no algorithm with approximation ratio better than $2$ unless $P = NP$. In this paper, we present an algorithm with…
The famous Padberg-Rao separation algorithm for b-matching polyhedra can be implemented to run in O(n^2m log(n^2/m)) time in the uncapacitated case, and in O(nm^2 log(n^2/m)) time in the capacitated case (where n is the number of vertices…
The {\em maximum cardinality} and {\em maximum weight matching} problems can be solved in time $\tilde{O}(m\sqrt{n})$, a bound that has resisted improvement despite decades of research. (Here $m$ and $n$ are the number of edges and…
We present a novel self-stabilizing algorithm for minimum spanning tree (MST) construction. The space complexity of our solution is $O(\log^2n)$ bits and it converges in $O(n^2)$ rounds. Thus, this algorithm improves the convergence time of…