Algorithms to Compute the Lyndon Array

We first describe three algorithms for computing the Lyndon array that have been suggested in the literature, but for which no structured exposition has been given. Two of these algorithms execute in quadratic time in the worst case, the third achieves linear time, but at the expense of prior computation of both the suffix array and the inverse suffix array of x. We then go on to describe two variants of a new algorithm that avoids prior computation of global data structures and executes in worst-case n log n time. Experimental evidence suggests that all but one of these five algorithms require only linear execution time in practice, with the two new algorithms faster by a small factor. We conjecture that there exists a fast and worst-case linear-time algorithm to compute the Lyndon array that is also elementary (making no use of global data structures such as the suffix array)

Ground-state energy of biquadratic spin systems (S=3/2) in the (1/z)1-approximation

Corrections to the molecular-field ground- state energies of the Heisenberg model with isotropic biquadrati c interactions (spin S = 3= 2) are calculated in the ( 1= z ) 1 -approximation using the diagrammatic technique based on the Wick reduction theorem (z is the numb er of spins interacting with any given spin) . The present results for the antiferri- and antiferromagnetic phases complete the previously obtained data for the antiquadrupolar, ferriand ferromagnetic phases. From among the boundaries between different ground states only that b etw een the antiferri- and antiferromagnetic phases is shifted with respect to its molecular-field value

k-Dirac operator and parabolic geometries

The principal group of a Klein geometry has canonical left action on the homogeneous space of the geometry and this action induces action on the spaces of sections of vector bundles over the homogeneous space. This paper is about construction of differential operators invariant with respect to the induced action of the principal group of a particular type of parabolic geometry. These operators form sequences which are related to the minimal resolutions of the k-Dirac operators studied in Clifford analysis

The BaBar Event Building and Level-3 Trigger Farm Upgrade

The BaBar experiment is the particle detector at the PEP-II B-factory facility at the Stanford Linear Accelerator Center. During the summer shutdown 2002 the BaBar Event Building and Level-3 trigger farm were upgraded from 60 Sun Ultra-5 machines and 100MBit/s Ethernet to 50 Dual-CPU 1.4GHz Pentium-III systems with Gigabit Ethernet. Combined with an upgrade to Gigabit Ethernet on the source side and a major feature extraction software speedup, this pushes the performance of the BaBar event builder and L3 filter to 5.5kHz at current background levels, almost three times the original design rate of 2kHz. For our specific application the new farm provides 8.5 times the CPU power of the old system.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics (CHEP03), La Jolla, Ca, USA, March 2003, 4 pages, 1 eps figure, PSN MOGT00

Model Checking a C++ Software Framework, a Case Study

This paper presents a case study on applying two model checkers, SPIN and DIVINE, to verify key properties of a C++ software framework, known as ADAPRO, originally developed at CERN. SPIN was used for verifying properties on the design level. DIVINE was used for verifying simple test applications that interacted with the implementation. Both model checkers were found to have their own respective sets of pros and cons, but the overall experience was positive. Because both model checkers were used in a complementary manner, they provided valuable new insights into the framework, which would arguably have been hard to gain by traditional testing and analysis tools only. Translating the C++ source code into the modeling language of the SPIN model checker helped to find flaws in the original design. With DIVINE, defects were found in parts of the code base that had already been subject to hundreds of hours of unit tests, integration tests, and acceptance tests. Most importantly, model checking was found to be easy to integrate into the workflow of the software project and bring added value, not only as verification, but also validation methodology. Therefore, using model checking for developing library-level code seems realistic and worth the effort.Comment: In Proceedings of the 27th ACM Joint European Software Engineering Conference and Symposium on the Foundations of Software Engineering (ESEC/FSE '19), August 26-30, 2019, Tallinn, Estonia. ACM, New York, NY, USA, 11 page

Efficient Online Timed Pattern Matching by Automata-Based Skipping

The timed pattern matching problem is an actively studied topic because of its relevance in monitoring of real-time systems. There one is given a log $w$ and a specification $\mathcal{A}$ (given by a timed word and a timed automaton in this paper), and one wishes to return the set of intervals for which the log $w$, when restricted to the interval, satisfies the specification $\mathcal{A}$. In our previous work we presented an efficient timed pattern matching algorithm: it adopts a skipping mechanism inspired by the classic Boyer--Moore (BM) string matching algorithm. In this work we tackle the problem of online timed pattern matching, towards embedded applications where it is vital to process a vast amount of incoming data in a timely manner. Specifically, we start with the Franek-Jennings-Smyth (FJS) string matching algorithm---a recent variant of the BM algorithm---and extend it to timed pattern matching. Our experiments indicate the efficiency of our FJS-type algorithm in online and offline timed pattern matching

Generalised median of a set of correspondences based on the hamming distance.

A correspondence is a set of mappings that establishes a relation between the elements of two data structures (i.e. sets of points, strings, trees or graphs). If we consider several correspondences between the same two structures, one option to define a representative of them is through the generalised median correspondence. In general, the computation of the generalised median is an NP-complete task. In this paper, we present two methods to calculate the generalised median correspondence of multiple correspondences. The first one obtains the optimal solution in cubic time, but it is restricted to the Hamming distance. The second one obtains a sub-optimal solution through an iterative approach, but does not have any restrictions with respect to the used distance. We compare both proposals in terms of the distance to the true generalised median and runtime