arXiv subjects

Lei Song

Publications and source records attributed to Lei Song.

84 records · Page 5Linked to original sources

arXiv2016

Verify LTL with Fairness Assumptions Efficiently

This paper deals with model checking problems with respect to LTL properties under fairness assumptions. We first present an efficient algorithm to deal with a fragment of fairness assumptions and then extend the algorithm to handle arbitrary %fairness assumptions ones. Notably, by making use of some syntactic transformations, our algorithm avoids to construct corresponding Büchi automata for the whole fairness assumptions, which can be very large in practice. We implement our algorithm in NuSMV and consider a large selection of formulas. Our experiments show that in many cases our approach exceeds the automata-theoretic approach up to several orders of magnitude, in both time and memory.

cs.LO↗

arXiv2015

Distribution-based Bisimulation and Bisimulation Metric in Probabilistic Automata

Probabilistic automata were introduced by Rabin in 1963 as language acceptors. Two automata are equivalent if and only if they accept each word with the same probability. On the other side, in the process algebra community, probabilistic automata were re-proposed by Segala in 1995 which are more general than Rabin's automata. Bisimulations have been proposed for Segala's automata to characterize the equivalence between them. So far the two notions of equivalences and their characteristics have been studied mostly independently. In this paper, we consider Segala's automata, and propose a novel notion of distribution-based bisimulation by joining the existing equivalence and bisimilarities. We demonstrate the utility of our definition by studying distribution-based bisimulation metrics, which gives rise to a robust notion of equivalence for Rabin's automata. We compare our notions of bisimulation to some existing distribution-based bisimulations and discuss their compositionality and relations to trace equivalence. Finally, we show the decidability and complexity of all relations.

cs.FL↗

arXiv2015

On the universal family of Hilbert schemes of points on a surface

For a smooth quasi-projective surface $X$ and an integer $n\ge 3$, we show that the universal family $Z^n$ over the Hilbert scheme $\text{Hilb}^{n}(X)$ of $n$ points has non $\mathbb{Q}$-Gorenstein, rational singularities, and that the Samuel multiplicity $μ$ at a closed point on $Z^n$ can be computed in terms of the dimension of the socle. We also show that $μ\le n$.

math.AG↗

arXiv2015

Design and optimization of DBSCAN Algorithm based on CUDA

DBSCAN is a very classic algorithm for data clus- tering, which is widely used in many fields. However, with the data scale growing much more bigger than before, the traditional serial algorithm can not meet the performance requirement. Recently, parallel computing based on CUDA has developed very fast and has great advantage on big data. This paper summarizes the algorithms proposed before and improves the performance of the old DBSCAN algorithm by using CUDA and parallel computing. The algorithm uses shared memory as much as possible compared with other algorithms and it has very good scalability. A data set is tested on the new version of DBSCAN. Finally, we analyze the results and give a conclusion that our algorithm is approximately 97 times faster than the serial version.

cs.DC↗

arXiv2015

A Simple Probabilistic Extension of Modal Mu-calculus

Probabilistic systems are an important theme in AI domain. As the specification language, the logic PCTL is now the default logic for reasoning about probabilistic properties. In this paper, we present a natural and succinct probabilistic extension of mu-calculus, another prominent logic in the concurrency theory. We study the relationship with PCTL. Interestingly, the expressiveness is highly orthogonal with PCTL. The proposed logic captures some useful properties which cannot be expressed in PCTL. We investigate the model checking and satisfiability problem, and show that the model checking problem is in UP and co-UP, and the satisfiability checking can be decided via reducing into solving parity games. This is in contrast to PCTL as well, whose satisfiability checking is still an open problem.

cs.LO↗

arXiv2014

On the singularities of effective loci of line bundles

We prove that every irreducible component of semi-regular loci of effective line bundles in the Picard scheme of a smooth projective variety has at worst rational singularities. This generalizes Kempf's result on rational singularities of $W^0_d$ for smooth curves. We also work out an example of such loci for a ruled surface.

math.AG↗

arXiv2014

Probably Safe or Live

This paper presents a formal characterisation of safety and liveness properties à la Alpern and Schneider for fully probabilistic systems. As for the classical setting, it is established that any (probabilistic tree) property is equivalent to a conjunction of a safety and liveness property. A simple algorithm is provided to obtain such property decomposition for flat probabilistic CTL (PCTL). A safe fragment of PCTL is identified that provides a sound and complete characterisation of safety properties. For liveness properties, we provide two PCTL fragments, a sound and a complete one. We show that safety properties only have finite counterexamples, whereas liveness properties have none. We compare our characterisation for qualitative properties with the one for branching time properties by Manolios and Trefler, and present sound and complete PCTL fragments for characterising the notions of strong safety and absolute liveness coined by Sistla.

cs.LO↗

arXiv2014

Late Weak Bisimulation for Markov Automata

Weak bisimilarity is a distribution-based equivalence notion for Markov automata. It has gained some popularity as the coarsest reasonable behavioural equivalence on Markov automata. This paper studies a strictly coarser notion: Late weak bisimilarity enjoys valuable properties if restricting to important subclasses of schedulers: Trace distribution equivalence is implied for partial information schedulers, and compositionality is preserved by distributed schedulers. The intersection of the two scheduler classes thus spans a coarser and still reasonable compositional theory of Markov automata.

cs.FL↗

arXiv2013

Locating Multiple Ultrasound Targets in Chorus

Ranging by Time of Arrival (TOA) of Narrow-band ultrasound (NBU) has been widely used by many locating systems for its characteristics of low cost and high accuracy. However, because it is hard to support code division multiple access in narrowband signal, to track multiple targets, existing NBU-based locating systems generally need to assign exclusive time slot to each target to avoid the signal conflicts. Because the propagation speed of ultrasound is slow in air, dividing exclusive time slots on a single channel causes the location updating rate for each target rather low, leading to unsatisfied tracking performances as the number of targets increases. In this paper, we investigated a new multiple target locating method using NBU, called UltraChorus, which is to locate multiple targets while allowing them sending NBU signals simultaneously, i.e., in chorus mode. It can dramatically increase the location updating rate. In particular, we investigated by both experiments and theoretical analysis on the necessary and sufficient conditions for resolving the conflicts of multiple NBU signals on a single channel, which is referred as the conditions for chorus ranging and chorus locating. To tackle the difficulty caused by the anonymity of the measured distances, we further developed consistent position generation algorithm and probabilistic particle filter algorithm}to label the distances by sources, to generate reasonable location estimations, and to disambiguate the motion trajectories of the multiple concurrent targets based on the anonymous distance measurements. Extensive evaluations by both simulation and testbed were carried out, which verified the effectiveness of our proposed theories and algorithms.

cs.IT↗

arXiv2013

Bisimulations and Logical Characterizations on Continuous-time Markov Decision Processes

In this paper we study strong and weak bisimulation equivalences for continuous-time Markov decision processes (CTMDPs) and the logical characterizations of these relations with respect to the continuous-time stochastic logic (CSL). For strong bisimulation, it is well known that it is strictly finer than CSL equivalence. In this paper we propose strong and weak bisimulations for CTMDPs and show that for a subclass of CTMDPs, strong and weak bisimulations are both sound and complete with respect to the equivalences induced by CSL and the sub-logic of CSL without next operator respectively. We then consider a standard extension of CSL, and show that it and its sub-logic without X can be fully characterized by strong and weak bisimulations respectively over arbitrary CTMDPs.

cs.LO↗

arXiv2013

Bisimulations Meet PCTL Equivalences for Probabilistic Automata

Probabilistic automata (PAs) have been successfully applied in formal verification of concurrent and stochastic systems. Efficient model checking algorithms have been studied, where the most often used logics for expressing properties are based on probabilistic computation tree logic (PCTL) and its extension PCTL^*. Various behavioral equivalences are proposed, as a powerful tool for abstraction and compositional minimization for PAs. Unfortunately, the equivalences are well-known to be sound, but not complete with respect to the logical equivalences induced by PCTL or PCTL*. The desire of a both sound and complete behavioral equivalence has been pointed out by Segala in 1995, but remains open throughout the years. In this paper we introduce novel notions of strong bisimulation relations, which characterize PCTL and PCTL* exactly. We extend weak bisimulations that characterize PCTL and PCTL* without next operator, respectively. Further, we also extend the framework to simulation preorders. Thus, our paper bridges the gap between logical and behavioral equivalences and preorders in this setting.

cs.LO↗

arXiv2011

A Stochastic Broadcast Pi-Calculus

In this paper we propose a stochastic broadcast PI-calculus which can be used to model server-client based systems where synchronization is always governed by only one participant. Therefore, there is no need to determine the joint synchronization rates. We also take immediate transitions into account which is useful to model behaviors with no impact on the temporal properties of a system. Since immediate transitions may introduce non-determinism, we will show how these non-determinism can be resolved, and as result a valid CTMC will be obtained finally. Also some practical examples are given to show the application of this calculus.

cs.PF↗