Probabilistic Deterministic Finite Automata and Recurrent Networks, Revisited

Reservoir computers (RCs) and recurrent neural networks (RNNs) can mimic any finite-state automaton in theory, and some workers demonstrated that this can hold in practice. We test the capability of generalized linear models, RCs, and Long Short-Term Memory (LSTM) RNN architectures to predict the stochastic processes generated by a large suite of probabilistic deterministic finite-state automata (PDFA) in the small-data limit according to two metrics: predictive accuracy and distance to a predictive rate-distortion curve. The latter provides a sense of whether or not the RNN is a lossy predictive feature extractor in the information-theoretic sense. PDFAs provide an excellent performance benchmark in that they can be systematically enumerated, the randomness and correlation structure of their generated processes are exactly known, and their optimal memory-limited predictors are easily computed. With less data than is needed to make a good prediction, LSTMs surprisingly lose at predictive accuracy, but win at lossy predictive feature extraction. These results highlight the utility of causal states in understanding the capabilities of RNNs to predict.

Chordality in Matroids: In Search of the Converse to Hliněný's Theorem

<p>Bodlaender et al. [7] proved a converse to Courcelle's Theorem for graphs [15] for the class of chordal graphs of bounded treewidth. Hliněný [25] generalised Courcelle's Theorem for graphs to classes of matroids represented over finite fields and of bounded branchwidth. This thesis has investigated the possibility of obtaining a generalisation of chordality to matroids that would enable us to prove a converse of Hliněný's Theorem [25]. There is a variety of equivalent characterisations for chordality in graphs. We have investigated the relationship between their generalisations to matroids. We prove that they are equivalent for binary matroids but typically inequivalent for more general classes of matroids. Supersolvability is a well studied property of matroids and, indeed, a graphic matroid is supersolvable if and only if its underlying graph is chordal. This is among the stronger ways of generalising chordality to matroids. However, to obtain the structural results that we need we require a stronger property that we call supersolvably saturated. Chordal graphs are well known to induce canonical tree decompositions. We show that supersolvably saturated matroids have the same property. These tree decompositions of supersolvably saturated matroids can be processed by a finite state automaton. However, they can not be completely described in monadic second-order logic. In order to express the matroids and their tree decompositions in monadic second-order logic we need to extend the logic over an extension field for each matroid represented over a finite field. We then use the fact that each maximal round modular flat of the tree decomposition for every matroid represented over a finite field, and in the specified class, spans a point in the vector space over the extension field. This enables us to derive a partial converse to Hliněný's Theorem.</p>

Chordality in Matroids: In Search of the Converse to Hliněný's Theorem

<p>Bodlaender et al. [7] proved a converse to Courcelle's Theorem for graphs [15] for the class of chordal graphs of bounded treewidth. Hliněný [25] generalised Courcelle's Theorem for graphs to classes of matroids represented over finite fields and of bounded branchwidth. This thesis has investigated the possibility of obtaining a generalisation of chordality to matroids that would enable us to prove a converse of Hliněný's Theorem [25]. There is a variety of equivalent characterisations for chordality in graphs. We have investigated the relationship between their generalisations to matroids. We prove that they are equivalent for binary matroids but typically inequivalent for more general classes of matroids. Supersolvability is a well studied property of matroids and, indeed, a graphic matroid is supersolvable if and only if its underlying graph is chordal. This is among the stronger ways of generalising chordality to matroids. However, to obtain the structural results that we need we require a stronger property that we call supersolvably saturated. Chordal graphs are well known to induce canonical tree decompositions. We show that supersolvably saturated matroids have the same property. These tree decompositions of supersolvably saturated matroids can be processed by a finite state automaton. However, they can not be completely described in monadic second-order logic. In order to express the matroids and their tree decompositions in monadic second-order logic we need to extend the logic over an extension field for each matroid represented over a finite field. We then use the fact that each maximal round modular flat of the tree decomposition for every matroid represented over a finite field, and in the specified class, spans a point in the vector space over the extension field. This enables us to derive a partial converse to Hliněný's Theorem.</p>

Formally proving whether the software implementation of models applied in instrumentation and control systems conform to the specified requirements

Research objective is to study the possibility to formally validate whether the model’s software implementation meets all the specified requirements of the systems, the model of which can be represented in the form of finite-state automata. Research relevance. At one of the first stages, the development of software for instrumentation and control systems provides for the creation of the system model. The model is based on the terms of reference, specification, and various a priori information. Most of the models for engineering systems in the modern mining industry (conveyor systems, ventilation systems, etc.) can be described in terms of the finite state automaton model. Such a model can be applied to solve diverse tasks. The next step is to implement the model in whole or in part. In this context, the task arises to determine the model’s software implementation conformity to its initial description. Results. One way to solve the task is to formally prove that the software model possesses the properties which are provided in the specification (description) of the initial model. By the example of the mine conveyor system, the paper illustrates the application of the method which consists in the software implementation of the corresponding finite-state automaton model, forecasting whether the model possesses the properties through theorems and their subsequent proof by applying special software. Conclusions. Formal methods of specification, development, and verification of system models’ software implementation together with other methods make it possible to improve the quality and reliability of solutions under development.

A New Approach to Automatic Detection and Correction of Derivational Errors in L2 Russian

Learner corpora serve as one of the most valuable sources of statistical data on learners' errors. For instance, data from foreign-language learners’ corpora can be used for the Second Language Acquisition research. However, corpora representativity strongly depends on the quality of its error markup, which is most frequently carried out manually and thus presents a time-consuming and painstaking routine for the annotators. To make annotation process easier, additional tools, such as spellcheckers, are usually used. This paper focuses on developing a program for automatic correction of derivational errors made by learners of Russian as a foreign language. Derivational errors, which are not common for adult Russian native speakers (L1), but occur quite often in written texts or speech of Russian as foreign language learners (L2) [Chernigovskaya, Gor, 2000], were chosen as scope of our research because correction of such mistakes presents a formidable challenge for existing spellcheckers. Using the data from the Russian Learner Corpus (http://www.web-corpora.net/RLC/), we tested two already existing approaches to solve such kind of problems. The first one is based on a finite state automaton principle developed by Dickinson and Herring 2008, and it was test-ed as algorithm for derivational errors detection. The second one which relies on the Noisy Channel model by Brill and Moore, 2000, was used for studying errors correction. After we analyzed effectiveness of these tests, we developed our own system for autocorrection of derivational errors. In our program the algorithm of Dickinson and Herring was used as word-formation error detection module. The Noisy Channel model has been rejected, and we decided to use instead the Continuous Bag of Words FastText model, based on Harris distributional semantics theory [1954]. In addition, filtering rules have been developed for correcting frequent errors that the model is unable to handle. To restore automatically the correct grammatical word form, dictionary of word paradigms is used. Model results were validated on the data of Russian Learner Corpus.

Soundness Verification of Data-Aware Process Models with Variable-to-Variable Conditions

Traditionally Business Process Modeling has only focused on the control-flow perspective, thus allowing process designers to specify the constraints on the activities of the process: the order and potential concurrency of their execution, their mutual exclusivity, the possibility of being repeated, etc. However, activities are executed by different resources, manipulate data objects and are constrained by the state of such objects. This requires that the traditional notion of soundness, typically introduced for control-flow-only models, is extended so as to consider data. Intuitively, a (data-aware) process model is sound if (1) it does not contain deadlocks, (2) no more activities are enabled when the process instance is marked as completed and finally (3) there are no parts of the model that cannot be executed. Although several data-aware notations have been introduced in the literature, not all of these are given a formal semantics. In this paper, we propose a technique for checking the data-aware soundness for a specific class of such integrated models, with a simple syntax and semantics, building on Data Petri Nets (DPNs). These are Petri nets enriched with case variables, where transitions are guarded by formulas that inspect and update such variables, and are of the form variable-operator-variable or variable-operator-constant. Even though DPNs are less expressive than Petri nets where data are carried by tokens, they elegantly capture business processes operating over simple case data, allowing to model complex data-aware decisions. We show that, if a DPN is data-aware sound, the Constraint Graph is a finite-state automaton; however, a finite-state Constraint Graph does not guarantee data-aware soundness, but provides a finite structure through which this property can be checked. Finally, we investigate further properties beyond data-aware soundness, such as the problem of verifying that an actor participating in the business process can unilaterally enforce data-aware soundness by restricting the possible executions of a bounded DPN, assuming this actor to be able to control the firing of some transitions and decide the value of some of the case variables whenever these are updated.

Receding Horizon Control Using Graph Search for Multi-Agent Trajectory Planning

<pre>It is hard to find the global optimum to general nonlinear, nonconvex optimization problems in reasonable time. This paper presents a method to transfer the receding horizon control approach, where nonlinear, nonconvex optimization problems are considered, into graph-search problems. Specifically, systems with symmetries are considered to transfer system dynamics into a finite state automaton. In contrast to traditional graph-search approaches where the search continues until the goal vertex is found, the transfer of a receding horizon control approach to graph-search problems presented in this paper allows to solve them in real-time. We proof that the solutions are recursively feasible by restricting the graph search to end in accepting states of the underlying finite state automaton. The approach is applied to trajectory planning for multiple networked and autonomous vehicles. We evaluate its effectiveness in simulation as well as in experiments in the Cyber-Physical Mobility Lab, an open source platform for networked and autonomous vehicles. We show real-time capable trajectory planning with collision avoidance in experiments on off-the-shelf hardware and code in MATLAB for two vehicles.</pre>

Receding Horizon Control Using Graph Search for Multi-Agent Trajectory Planning

<pre>It is hard to find the global optimum to general nonlinear, nonconvex optimization problems in reasonable time. This paper presents a method to transfer the receding horizon control approach, where nonlinear, nonconvex optimization problems are considered, into graph-search problems. Specifically, systems with symmetries are considered to transfer system dynamics into a finite state automaton. In contrast to traditional graph-search approaches where the search continues until the goal vertex is found, the transfer of a receding horizon control approach to graph-search problems presented in this paper allows to solve them in real-time. We proof that the solutions are recursively feasible by restricting the graph search to end in accepting states of the underlying finite state automaton. The approach is applied to trajectory planning for multiple networked and autonomous vehicles. We evaluate its effectiveness in simulation as well as in experiments in the Cyber-Physical Mobility Lab, an open source platform for networked and autonomous vehicles. We show real-time capable trajectory planning with collision avoidance in experiments on off-the-shelf hardware and code in MATLAB for two vehicles.</pre>