From Finite Automata to Regular Expressions and Back--A Summary on Descriptional Complexity

The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the present paper we tour a fragment of the literature and summarize results on upper and lower bounds on the conversion of finite automata to regular expressions and vice versa. We also briefly recall the known bounds for the removal of spontaneous transitions (epsilon-transitions) on non-epsilon-free nondeterministic devices. Moreover, we report on recent results on the average case descriptional complexity bounds for the conversion of regular expressions to finite automata and brand new developments on the state elimination algorithm that converts finite automata to regular expressions.Comment: In Proceedings AFL 2014, arXiv:1405.527

Digraph Complexity Measures and Applications in Formal Language Theory

We investigate structural complexity measures on digraphs, in particular the cycle rank. This concept is intimately related to a classical topic in formal language theory, namely the star height of regular languages. We explore this connection, and obtain several new algorithmic insights regarding both cycle rank and star height. Among other results, we show that computing the cycle rank is NP-complete, even for sparse digraphs of maximum outdegree 2. Notwithstanding, we provide both a polynomial-time approximation algorithm and an exponential-time exact algorithm for this problem. The former algorithm yields an O((log n)^(3/2))- approximation in polynomial time, whereas the latter yields the optimum solution, and runs in time and space O*(1.9129^n) on digraphs of maximum outdegree at most two. Regarding the star height problem, we identify a subclass of the regular languages for which we can precisely determine the computational complexity of the star height problem. Namely, the star height problem for bideterministic languages is NP-complete, and this holds already for binary alphabets. Then we translate the algorithmic results concerning cycle rank to the bideterministic star height problem, thus giving a polynomial-time approximation as well as a reasonably fast exact exponential algorithm for bideterministic star height.Comment: 19 pages, 1 figur

On Knot Polynomials of Annular Surfaces and their Boundary Links

Stoimenow and Kidwell asked the following question: Let $K$ be a non-trivial knot, and let $W(K)$ be a Whitehead double of $K$. Let $F(a,z)$ be the Kauffman polynomial and $P(v,z)$ the skein polynomial. Is then always $\max\deg_z P_{W(K)} - 1 = 2 \max\deg_z F_K$? Here this question is rephrased in more general terms as a conjectured relation between the maximum $z$-degrees of the Kauffman polynomial of an annular surface $A$ on the one hand, and the Rudolph polynomial on the other hand, the latter being defined as a certain M\"obius transform of the skein polynomial of the boundary link $\partial A$. That relation is shown to hold for algebraic alternating links, thus simultaneously solving the conjecture by Kidwell and Stoimenow and a related conjecture by Tripp for this class of links. Also, in spite of the heavyweight definition of the Rudolph polynomial $\{K\}$ of a link $K$, the remarkably simple formula \{\bigcirc\}\{L#M\}=\{L\}\{M\} for link composition is established. This last result can be used to reduce the conjecture in question to the case of prime links.Comment: Version 4: revision as of October 10, 2008. Fixed several errors and inaccuracies. 11 pages, 1 figure. To appear in Mathematical Proceedings of the Cambridge Philosophical Societ

Inflammatory bowel disease-specific autoantibodies in HLA-B27-associated spondyloarthropathies: Increased prevalence of ASCA and pANCA

Aims: An association between inflammatory bowel disease (IBD) and spondyloarthropathies (SpA) has repeatedly been reported. The aim of the present study was to investigate whether serologic markers of IBD, e. g. antibodies against Saccharomyces cerevisiae (ASCA), antibodies against exocrine pancreas (PAB) and perinuclear antineutrophil cytoplasmic antibodies (pANCA) are present in HLA-B27-associated SpA. Methods: 87 patients with HLA-B27-positive SpA and 145 controls were tested for ASCA, PAB and pANCA employing ELISA or indirect immunofluorescence, respectively. Antibody-positive patients were interviewed regarding IBD-related symptoms using a standardized questionnaire. Results/Conclusion: When compared to the controls, ASCA IgA but not ASCA IgG levels were significantly increased in patients with SpA, in particular in ankylosing spondylitis (AS) and undifferentiated SpA (uSpA). pANCA were found in increased frequency in patients with SpA whereas PAB were not detected. The existence of autoantibodies was not associated with gastrointestinal symptoms but sustains the presence of a pathophysiological link between bowel inflammation and SpA. Copyright (C) 2004 S. Karger AG, Basel

Predicting the influence of a p2-symmetric substrate on molecular self-organization with an interaction-site model

An interaction-site model can a priori predict molecular selforganisation on a new substrate in Monte Carlo simulations. This is experimentally confirmed with scanning tunnelling microscopy on Fre´chet dendrons of a pentacontane template. Local and global ordering motifs, inclusion molecules and a rotated unit cell are correctly predicted

Imaging morphological details and pathological differences of red blood cells using tapping-mode AFM

The surface topography of red blood cells (RBCs) was investigated under nearphysiological conditions using atomic force microscopy (AFM). An immobilization protocol was established where RBCs are coupled via molecular bonds of the membrane glycoproteins to wheat germ agglutinin (WGA), which is covalently and flexibly tethered to the support. This results in a tight but noninvasive attachment of the cells. Using tappingmode AFM, which is known as gentle imaging mode and therefore most appropriate for soft biological samples like erythrocytes, it was possible to resolve membrane skeleton structures without major distortions or deformations of the cell surface. Significant differences in the morphology of RBCs from healthy humans and patients with systemic lupus erythematosus (SLE) were observed on topographical images. The surface of RBCs from SLE patients showed characteristic circularshaped holes with approx. 200 nm in diameter under physiological conditions, a possible morphological correlate to previously published changes in the SLE erythrocyte membrane