Received by the editors on July 11, 2012. Accepted for publication on May 26, 2013. Handling Editor: Michael Tsatsomeros. Department of Mathematics, University of Ljubljana, Slovenia ([email protected], [email protected]). Supported by Research Programs P1-0222 and L1-069 of the Slovenian Research Agency. Department of Computer and Information Science, University of Ljubl...

For an integer n≥ 2, let p(z)=nk=1(z−αk) and q(z)= ∏n k=1(z−βk), where αk,βk are real. We find the number of connected components of the real algebraic curve {(x,y)∈R2 : |p(x+iy)|−|q(x+iy)| = 0} for some αk and βk. Moreover, in these cases, we show that each connected component contains zeros of p(z)+q(z), and we investigate the locus of zeros of p(z)+q(z). 2000 Mathematics Subject Classificati...

In this paper we present a CTL-like logic which is interpreted over the state spaces of Coloured Petri Nets. The logic has been designed to express properties of both state and transition information. This is possible because the state spaces are labelled transition systems. We compare the expressiveness of our logic with CTL’s. Then, we present a model checking algorithm which for efficiency r...

Finding strongly connected components (SCCs) in the state-space of discrete-state models is a critical task in formal verification of LTL and fair CTL properties, but the potentially huge number of reachable states and SCCs constitutes a formidable challenge. This paper is concerned with computing the sets of states in SCCs or terminal SCCs of asynchronous systems. Because of its advantages in ...

LetM be a compact closed non-orientable surface. We show that the space of representations of the fundamental group of M into PSL(2,R) has exactly two connected components. These two components are the preimages of a certain Stiefel-Whitney characteristic class, computed in a similar way as the Euler class in the orientable case.

We propose a novel method for Web page grouping based only on hyperlink information. Because of the explosive growth of the World Wide Web, page grouping is expected to provide a general grasp of the Web for effective information search and netsurfing. The Web can be regarded as a gigantic digraph where pages are vertices and links are arcs. Our grouping method is a generalization of decomposit...

We determine the set of connected components of closed affine Deligne-Lusztig varieties for special maximal compact subgroups of split connected reductive groups. We show that there is a transitive group action on this set. Thus such an affine Deligne-Lusztig variety has isolated points if and only if its dimension is 0. We also obtain a description of the set of these varieties that are zero-d...

We give examples of definable groups G (in a saturated model, sometimes o-minimal) such that G00 6= G000, yielding also new examples of “non G-compact” theories. We also prove that for G definable in a (saturated) o-minimal structure, G has a “bounded orbit” (i.e. there is a type of G whose stabilizer has bounded index) if and only if G is definably amenable, giving a positive answer to a conje...

Given a large graph G = (V,E) with millions of nodes and edges, how do we compute its connected components efficiently? Recent work addresses this problem in map-reduce, where a fundamental trade-off exists between the number of mapreduce rounds and the communication of each round. Denoting d the diameter of the graph, and n the number of nodes in the largest component, all prior techniques for...

We consider how to maintain the topological order of a directed acyclic graph (DAG) in the presence of edge insertions and deletions. We present a new algorithm and obtain a marginally improved complexity result over the previously known O(||δ||log||δ||). In addition, we provide an empirical comparison against three existing solutions using random DAG’s. The results show our algorithm to out pe...