Conjugacy and Equivalence of Weighted Automata and Functional Transducers

International audienceWe show that two equivalent K-automata are conjugate to a third one, when K is equal to B, N, Z, or any (skew) ¯eld and that the same holds true for functional tranducers as well

Minimal Synthesis of String To String Functions From Examples

We study the problem of synthesizing string to string transformations from a set of input/output examples. The transformations we consider are expressed using deterministic finite automata (DFA) that read pairs of letters, one letter from the input and one from the output. The DFA corresponding to these transformations have additional constraints, ensuring that each input string is mapped to exactly one output string. We suggest that, given a set of input/output examples, the smallest DFA consistent with the examples is a good candidate for the transformation the user was expecting. We therefore study the problem of, given a set of examples, finding a minimal DFA consistent with the examples and satisfying the functionality and totality constraints mentioned above. We prove that, in general, this problem (the corresponding decision problem) is NP-complete. This is unlike the standard DFA minimization problem which can be solved in polynomial time. We provide several NP-hardness proofs that show the hardness of multiple (independent) variants of the problem. Finally, we propose an algorithm for finding the minimal DFA consistent with input/output examples, that uses a reduction to SMT solvers. We implemented the algorithm, and used it to evaluate the likelihood that the minimal DFA indeed corresponds to the DFA expected by the user.Comment: SYNT 201

Languages ordered by the subword order

We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the language, the used predicates, and the fragment of the logic, we determine four new combinations that yield decidable theories. These results extend earlier ones where only the language of all words without the cover relation and fragments of first-order logic were considered

Long‐term surveillance biopsy: Is it necessary after pediatric heart transplant?

Due to limited and conflicting data in pediatric patients, long‐term routine surveillance endomyocardial biopsy (RSB) in pediatric heart transplant (HT) remains controversial. We sought to characterize the rate of positive RSB and determine factors associated with RSB‐detected rejection. Records of patients transplanted at a single institution from 1995 to 2015 with >2 year of post‐HT biopsy data were reviewed for RSB‐detected rejections occurring >2 year post‐HT. We illustrated the trajectory of significant rejections (ISHLT Grade ≥3A/2R) among total RSB performed over time and used multivariable logistic regression to model the association between time and risk of rejection. We estimated Kaplan‐Meier freedom from rejection rates by patient characteristics and used the log‐rank test to assess differences in rejection probabilities. We identified the best‐fitting Cox proportional hazards regression model. In 140 patients, 86% did not have any episodes of significant RSB‐detected rejection >2 year post‐HT. The overall empirical rate of RSB‐detected rejection >2 year post‐HT was 2.9/100 patient‐years. The percentage of rejection among 815 RSB was 2.6% and remained stable over time. Years since transplant remained unassociated with rejection risk after adjusting for patient characteristics (OR = 0.98; 95% CI 0.78‐1.23; P = 0.86). Older age at HT was the only factor that remained significantly associated with risk of RSB‐detected rejection under multivariable Cox analysis (P = 0.008). Most pediatric patients did not have RSB‐detected rejection beyond 2 years post‐HT, and the majority of those who did were older at time of HT. Indiscriminate long‐term RSB in pediatric heart transplant should be reconsidered given the low rate of detected rejection.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147767/1/petr13330_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/147767/2/petr13330.pd

Implementation of Code Properties via Transducers

The FAdo system is a symbolic manipulator of formal language objects, implemented in Python. In this work, we extend its capabilities by implementing methods to manipulate transducers and we go one level higher than existing formal language systems and implement methods to manipulate objects representing classes of independent languages (widely known as code properties). Our methods allow users to define their own code properties and combine them between themselves or with fixed properties such as prefix codes, suffix codes, error detecting codes, etc. The satisfaction and maximality decision questions are solvable for any of the definable properties. The new online system LaSer allows one to query about a code property and obtain the answer in a batch mode. Our work is founded on independence theory as well as the theory of rational relations and transducers, and contributes with improved algorithms on these objects

Regular Expressions and Transducers over Alphabet-invariant and User-defined Labels

We are interested in regular expressions and transducers that represent word relations in an alphabet-invariant way---for example, the set of all word pairs u,v where v is a prefix of u independently of what the alphabet is. Current software systems of formal language objects do not have a mechanism to define such objects. We define transducers in which transition labels involve what we call set specifications, some of which are alphabet invariant. In fact, we give a more broad definition of automata-type objects, called labelled graphs, where each transition label can be any string, as long as that string represents a subset of a certain monoid. Then, the behaviour of the labelled graph is a subset of that monoid. We do the same for regular expressions. We obtain extensions of a few classic algorithmic constructions on ordinary regular expressions and transducers at the broad level of labelled graphs and in such a way that the computational efficiency of the extended constructions is not sacrificed. For regular expressions with set specs we obtain the corresponding partial derivative automata. For transducers with set specs we obtain further algorithms that can be applied to questions about independent regular languages, in particular the witness version of the independent property satisfaction question

Pepsinogen A, pepsinogen C, and gastrin as markers of atrophic chronic gastritis in European dyspeptics

Serum levels of pepsinogen and gastrin are parameters that can be used as biomarkers for gastric mucosa. The aim of this study was to validate these serum biomarkers, that is pepsinogen A (PGA), pepsinogen C (PGC), PGA/PGC ratio, and gastrin, as screening tests for precancerous lesions: atrophic chronic gastritis (ACG) or Helicobacter pylori-related corpus-predominant or multifocal atrophy. The study population was comprised of a subsample of 284 patients from the 451 included in the Eurohepygast cohort, between 1995 and 1997. The concentrations of PGA, PGC, and gastrin were measured by radioimmunoassays. Histological diagnosis was the gold standard. Cut-off points were calculated using receiving operator characteristics (ROC) curves. Factors linked to variation of biomarkers were identified using multivariate linear regression. The mean of each biomarker in the sample was: PGA, 77.4 μg l−1; PGC, 13.2 μg l−1; PGA/PGC, 6.7; and gastrin, 62.4 ng l−1. For ACG patients, the areas under the PGA, PGC, PGA/PGC, and gastrin ROC curves were 0.55, 0.62, 0.73, and 0.58, respectively. The best cut-off point for PGA/PGC was 5.6, with sensitivity 65% and specificity 77.9%. For H. pylori-related corpus-predominant or multifocal atrophy, the areas under the respective ROC curves were 0.57, 0.67, 0.84, and 0.69. The best cut-off point for PGA/PGC was 4.7, with sensitivity 77.1% and specificity 87.4%. The results suggested that only the PGA/PGC ratio can be considered as a biomarker for precancerous lesions of the stomach, and may be useful as a screening test

Dual Testing Algorithm of BED-CEIA and AxSYM Avidity Index Assays Performs Best in Identifying Recent HIV Infection in a Sample of Rwandan Sex Workers

To assess the performance of BED-CEIA (BED) and AxSYM Avidity Index (Ax-AI) assays in estimating HIV incidence among female sex workers (FSW) in Kigali, Rwanda. Eight hundred FSW of unknown HIV status were HIV tested; HIV-positive women had BED and Ax-AI testing at baseline and ≥12 months later to estimate assay false-recent rates (FRR). STARHS-based HIV incidence was estimated using the McWalter/Welte formula, and adjusted with locally derived FRR and CD4 results. HIV incidence and local assay window periods were estimated from a prospective cohort of FSW. At baseline, 190 HIV-positive women were BED and Ax-AI tested; 23 were classified as recent infection (RI). Assay FRR with 95% confidence intervals were: 3.6% (1.2-8.1) (BED); 10.6% (6.1-17.0) (Ax-AI); and 2.1% (0.4-6.1) (BED/Ax-AI combined). After FRR-adjustment, incidence estimates by BED, Ax-AI, and BED/Ax-AI were: 5.5/100 person-years (95% CI 2.2-8.7); 7.7 (3.2-12.3); and 4.4 (1.4-7.3). After CD4-adjustment, BED, Ax-AI, and BED/Ax-AI incidence estimates were: 5.6 (2.6-8.6); 9.7 (5.0-14.4); and 4.7 (2.0-7.5). HIV incidence rates in the first and second 6 months of the cohort were 4.6 (1.6-7.7) and 2.2 (0.1-4.4). Adjusted incidence estimates by BED/Ax-AI combined were similar to incidence in the first 6 months of the cohort. Furthermore, false-recent rate on the combined BED/Ax-AI algorithm was low and substantially lower than for either assay alone. Improved assay specificity with time since seroconversion suggests that specificity would be higher in population-based testing where more individuals have long-term infectio