Canonical Algebraic Generators in Automata Learning

Many methods for the verification of complex computer systems require the existence of a tractable mathematical abstraction of the system, often in the form of an automaton. In reality, however, such a model is hard to come up with, in particular manually. Automata learning is a technique that can automatically infer an automaton model from a system -- by observing its behaviour. The majority of automata learning algorithms is based on the so-called L* algorithm. The acceptor learned by L* has an important property: it is canonical, in the sense that, it is, up to isomorphism, the unique deterministic finite automaton of minimal size accepting a given regular language. Establishing a similar result for other classes of acceptors, often with side-effects, is of great practical importance. Non-deterministic finite automata, for instance, can be exponentially more succinct than deterministic ones, allowing verification to scale. Unfortunately, identifying a canonical size-minimal non-deterministic acceptor of a given regular language is in general not possible: it can happen that a regular language is accepted by two non-isomorphic non-deterministic finite automata of minimal size. In particular, it thus is unclear which one of the automata should be targeted by a learning algorithm. In this thesis, we further explore the issue and identify (sub-)classes of acceptors that admit canonical size-minimal representatives.Comment: PhD thesi

Canonical Algebraic Generators in Automata Learning

Many methods for the verification of complex computer systems require the existence of a tractable mathematical abstraction of the system, often in the form of an automaton. In reality, however, such a model is hard to come up with, in particular manually. Automata learning is a technique that can automatically infer an automaton model from a system -- by observing its behaviour. The majority of automata learning algorithms is based on the so-called L* algorithm. The acceptor learned by L* has an important property: it is canonical, in the sense that, it is, up to isomorphism, the unique deterministic finite automaton of minimal size accepting a given regular language. Establishing a similar result for other classes of acceptors, often with side-effects, is of great practical importance. Non-deterministic finite automata, for instance, can be exponentially more succinct than deterministic ones, allowing verification to scale. Unfortunately, identifying a canonical size-minimal non-deterministic acceptor of a given regular language is in general not possible: it can happen that a regular language is accepted by two non-isomorphic non-deterministic finite automata of minimal size. In particular, it thus is unclear which one of the automata should be targeted by a learning algorithm. In this thesis, we further explore the issue and identify (sub-)classes of acceptors that admit canonical size-minimal representatives. In more detail, the contributions of this thesis are three-fold. First, we expand the automata (learning) theory of Guarded Kleene Algebra with Tests (GKAT), an efficiently decidable logic expressive enough to model simple imperative programs. In particular, we present GL*, an algorithm that learns the unique size-minimal GKAT automaton for a given deterministic language, and prove that GL* is more efficient than an existing variation of L*. We implement both algorithms in OCaml, and compare them on example programs. Second, we present a category-theoretical framework based on generators, bialgebras, and distributive laws, which identifies, for a wide class of automata with side-effects in a monad, canonical target models for automata learning. Apart from recovering examples from the literature, we discover a new canonical acceptor of regular languages, and present a unifying minimality result. Finally, we show that the construction underlying our framework is an instance of a more general theory. First, we see that deriving a minimal bialgebra from a minimal coalgebra can be realized by applying a monad on a category of subobjects with respect to an epi-mono factorisation system. Second, we explore the abstract theory of generators and bases for algebras over a monad: we discuss bases for bialgebras, the product of bases, generalise the representation theory of linear maps, and compare our ideas to a coalgebra-based approach

Generators and Bases for Monadic Closures

It is well-known that every regular language admits a unique minimal deterministic acceptor. Establishing an analogous result for non-deterministic acceptors is significantly more difficult, but nonetheless of great practical importance. To tackle this issue, a number of sub-classes of non-deterministic automata have been identified, all admitting canonical minimal representatives. In previous work, we have shown that such representatives can be recovered categorically in two steps. First, one constructs the minimal bialgebra accepting a given regular language, by closing the minimal coalgebra with additional algebraic structure over a monad. Second, one identifies canonical generators for the algebraic part of the bialgebra, to derive an equivalent coalgebra with side effects in a monad. In this paper, we further develop the general theory underlying these two steps. On the one hand, we show that deriving a minimal bialgebra from a minimal coalgebra can be realized by applying a monad on an appropriate category of subobjects. On the other hand, we explore the abstract theory of generators and bases for algebras over a monad

Canonical automata via distributive law homomorphisms

The classical powerset construction is a standard method converting a nondeterministic automaton into a deterministic one recognising the same language. Recently, the powerset construction has been lifted to a more general framework that converts an automaton with side-effects, given by a monad, into a deterministic automaton accepting the same language. The resulting automaton has additional algebraic properties, both in the state space and transition structure, inherited from the monad. In this paper, we study the reverse construction and present a framework in which a deterministic automaton with additional algebraic structure over a given monad can be converted into an equivalent succinct automaton with side-effects. Apart from recovering examples from the literature, such as the canonical residual finite-state automaton and the \'atomaton, we discover a new canonical automaton for a regular language by relating the free vector space monad over the two element field to the neighbourhood monad. Finally, we show that every regular language satisfying a suitable property parametric in two monads admits a size-minimal succinct acceptor

Enoxaparin for outpatients with COVID-19: 90-day results from the randomised, open-label, parallel-group, multinational, phase III OVID trial.

INTRODUCTION The benefits of early thromboprophylaxis in symptomatic COVID-19 outpatients remain unclear. We present the 90-day results from the randomised, open-label, parallel-group, investigator-initiated, multinational OVID phase III trial. METHODS Outpatients aged 50 years or older with acute symptomatic COVID-19 were randomised to receive enoxaparin 40 mg for 14 days once daily vs. standard of care (no thromboprophylaxis). The primary outcome was the composite of untoward hospitalisation and all-cause death within 30 days from randomisation. Secondary outcomes included arterial and venous major cardiovascular events, as well as the primary outcome within 90 days from randomisation. The study was prematurely terminated based on statistical criteria after the predefined interim analysis of 30-day data, which has been previously published. In the present analysis, we present the final, 90-day data from OVID and we additionally investigate the impact of thromboprophylaxis on the resolution of symptoms. RESULTS Of the 472 patients included in the intention-to-treat population, 234 were randomised to receive enoxaparin and 238 no thromboprophylaxis. The median age was 57 (Q1-Q3: 53-62) years and 217 (46 %) were women. The 90-day primary outcome occurred in 11 (4.7 %) patients of the enoxaparin arm and in 11 (4.6 %) controls (adjusted relative risk 1.00; 95 % CI: 0.44-2.25): 3 events per group occurred after day 30. The 90-day incidence of cardiovascular events was 0.9 % in the enoxaparin arm vs. 1.7 % in controls (relative risk 0.51; 95 % CI: 0.09-2.75). Individual symptoms improved progressively within 90 days with no difference between groups. At 90 days, 42 (17.9 %) patients in the enoxaparin arm and 40 (16.8 %) controls had persistent respiratory symptoms. CONCLUSIONS In adult community patients with COVID-19, early thromboprophylaxis with enoxaparin did not improve the course of COVID-19 neither in terms of hospitalisation and death nor considering COVID-19-related symptoms

Enoxaparin for outpatients with COVID-19: 90-day results from the randomised, open-label, parallel-group, multinational, phase III OVID trial

INTRODUCTION The benefits of early thromboprophylaxis in symptomatic COVID-19 outpatients remain unclear. We present the 90-day results from the randomised, open-label, parallel-group, investigator-initiated, multinational OVID phase III trial. METHODS Outpatients aged 50 years or older with acute symptomatic COVID-19 were randomised to receive enoxaparin 40 mg for 14 days once daily vs. standard of care (no thromboprophylaxis). The primary outcome was the composite of untoward hospitalisation and all-cause death within 30 days from randomisation. Secondary outcomes included arterial and venous major cardiovascular events, as well as the primary outcome within 90 days from randomisation. The study was prematurely terminated based on statistical criteria after the predefined interim analysis of 30-day data, which has been previously published. In the present analysis, we present the final, 90-day data from OVID and we additionally investigate the impact of thromboprophylaxis on the resolution of symptoms. RESULTS Of the 472 patients included in the intention-to-treat population, 234 were randomised to receive enoxaparin and 238 no thromboprophylaxis. The median age was 57 (Q1-Q3: 53-62) years and 217 (46 %) were women. The 90-day primary outcome occurred in 11 (4.7 %) patients of the enoxaparin arm and in 11 (4.6 %) controls (adjusted relative risk 1.00; 95 % CI: 0.44-2.25): 3 events per group occurred after day 30. The 90-day incidence of cardiovascular events was 0.9 % in the enoxaparin arm vs. 1.7 % in controls (relative risk 0.51; 95 % CI: 0.09-2.75). Individual symptoms improved progressively within 90 days with no difference between groups. At 90 days, 42 (17.9 %) patients in the enoxaparin arm and 40 (16.8 %) controls had persistent respiratory symptoms. CONCLUSIONS In adult community patients with COVID-19, early thromboprophylaxis with enoxaparin did not improve the course of COVID-19 neither in terms of hospitalisation and death nor considering COVID-19-related symptoms

Knowledge-based scene analysis with saccadic eye-movements

The perception of an image by a human observer is usually modeled as a parallel process in which all parts of the image are treated more or less equivalently, but in reality the analysis of scenes is a highly selective procedure, in which only a small subset of image locations is processed by the precise and efficient neural machinery of foveal vision. To understand the principles behind this selection of the "informative" regions of images, we have developed a hybrid system that consists of a combination of a knowledge-based reasoning system with a low-level preprocessing by linear and nonlinear neural operators. This hybrid system is intended as a first step towards a complete model of the sensorimotor system of saccadic scene analysis. In the analysis of a scene, the system calculates in each step which eye movement has to be made to reach a maximum of information about the scene. The possible information gain is calculated by means of a parallel strategy which is suitable for adaptive reasoning. The output of the system is a fixation sequence, and finally, a hypothesis about the scene

Mesiotemporal Volume Loss Associated with Disorder Severity: A VBM Study in Borderline Personality Disorder

<div><p>Results of MRI volumetry in Borderline Personality Disorder (BPD) are inconsistent. Some, but not all, studies reported decreased hippocampus, amygdala, and/or prefrontal volumes. In the current study, we used rater-independent voxel-based morphometry (VBM) in 33 female BPD patients and 33 healthy women. We measured gray matter (GM) volumes of the whole brain and of three volumes of interest (VOI), i.e., the hippocampus/parahippocampal gyrus, the amygdala and the anterior cingulate gyrus (ACC). Analyses were conducted using lifetime diagnoses of posttraumatic stress disorder (PTSD) and major depression (MD) as covariates. We used adversive childhood experiences and the numbers of BPD criteria (as an indicator of disorder severity) to investigate associations with GM volumes. We did not find volume differences between BPD patients and healthy subject, neither of the whole brain nor of the three VOIs, independent of presence or absence of comorbid PTSD and MD. We also did not find a relationship between childhood maltreatment and the patients’ brain volumes. However, within the patient group, the number of BPD criteria fulfilled was inversely correlated with left hippocampal/parahippocampal volume (x=-32, y=-23, z=-18, k=496, t=5.08, p=.007). Consequently, mesiotemporal GM volumes do not seem to differentiate patients from healthy subjects, but might be associated with symptom severity within the BPD group.</p> </div