Compositional learning of mutually recursive procedural systems

This paper presents a compositional approach to active automata learning of Systems of Procedural Automata (SPAs), an extension of Deterministic Finite Automata (DFAs) to systems of DFAs that can mutually call each other. SPAs are of high practical relevance, as they allow one to efficiently learn intuitive recursive models of recursive programs after an easy instrumentation that makes calls and returns observable. Key to our approach is the simultaneous inference of individual DFAs for each of the involved procedures via expansion and projection: membership queries for the individual DFAs are expanded to membership queries of the entire SPA, and global counterexample traces are transformed into counterexamples for the DFAs of concerned procedures. This reduces the inference of SPAs to a simultaneous inference of the DFAs for the involved procedures for which we can utilize various existing regular learning algorithms. The inferred models are easy to understand and allow for an intuitive display of the procedural system under learning that reveals its recursive structure. We implemented the algorithm within the LearnLib framework in order to provide a ready-to-use tool for practical application which is publicly available on GitHub for experimentation.

Forecasting in Small Business Management

This work aims to verify an authorial forecasting method from a system of interdependent equations, which is based on empirical equations of the structural form and is mainly intended for econometric micromodels. The prediction procedure will be analogous to the so-called chain prediction that is used for recursive models. The difference—compared with the prediction from a recursive model—entails the necessity of using one of the reduced-form empirical equations to begin the procedure of constructing a sequence of forecasts from successive structural-form empirical equations. The research results presented above indicate that the above-proposed iterative forecasting method from structural-form equations of a system of interdependent equations guarantees synchronization of forecasts as part of a closed cycle of relations. A different number of iterations is required to obtain convergent forecasts. It can be noticed that the further ahead the forecasted period is, the more iterations should be carried out to obtain convergent forecasts. Small business management with the use of forecasting can be done remotely. Rapid updates of statistical information will require cloud-based communication. Completion of data in a cloud will allow, on one hand, accurate assessment of expired forecasts and, on the other, to update the predictor equations. This can be carried out at any place with Internet access.