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.

Algebraic aggregation of random forests: towards explainability and rapid evaluation

Random Forests are one of the most popular classifiers in machine learning. The larger they are, the more precise the outcome of their predictions. However, this comes at a cost: it is increasingly difficult to understand why a Random Forest made a specific choice, and its running time for classification grows linearly with the size (number of trees). In this paper, we propose a method to aggregate large Random Forests into a single, semantically equivalent decision diagram which has the following two effects: (1) minimal, sufficient explanations for Random Forest-based classifications can be obtained by means of a simple three step reduction, and (2) the running time is radically improved. In fact, our experiments on various popular datasets show speed-ups of several orders of magnitude, while, at the same time, also significantly reducing the size of the required data structure.

Extending a brainiac prover to lambda-free higher-order logic

Decades of work have gone into developing efficient proof calculi, data structures, algorithms, and heuristics for first-order automatic theorem proving. Higher-order provers lag behind in terms of efficiency. Instead of developing a new higher-order prover from the ground up, we propose to start with the state-of-the-art superposition prover E and gradually enrich it with higher-order features. We explain how to extend the prover’s data structures, algorithms, and heuristics to $$\lambda $$ λ -free higher-order logic, a formalism that supports partial application and applied variables. Our extension outperforms the traditional encoding and appears promising as a stepping stone toward full higher-order logic.

Using linear algebra in decomposition of Farkas interpolants

The use of propositional logic and systems of linear inequalities over reals is a common means to model software for formal verification. Craig interpolants constitute a central building block in this setting for over-approximating reachable states, e.g. as candidates for inductive loop invariants. Interpolants for a linear system can be efficiently computed from a Simplex refutation by applying the Farkas’ lemma. However, these interpolants do not always suit the verification task—in the worst case, they can even prevent the verification algorithm from converging. This work introduces the decomposed interpolants, a fundamental extension of the Farkas interpolants, obtained by identifying and separating independent components from the interpolant structure, using methods from linear algebra. We also present an efficient polynomial algorithm to compute decomposed interpolants and analyse its properties. We experimentally show that the use of decomposed interpolants in model checking results in immediate convergence on instances where state-of-the-art approaches diverge. Moreover, since being based on the efficient Simplex method, the approach is very competitive in general.

Formal testing of timed graph transformation systems using metric temporal graph logic

Embedded real-time systems generate state sequences where time elapses between state changes. Ensuring that such systems adhere to a provided specification of admissible or desired behavior is essential. Formal model-based testing is often a suitable cost-effective approach. We introduce an extended version of the formalism of symbolic graphs, which encompasses types as well as attributes, for representing states of dynamic systems. Relying on this extension of symbolic graphs, we present a novel formalism of timed graph transformation systems (TGTSs) that supports the model-based development of dynamic real-time systems at an abstract level where possible state changes and delays are specified by graph transformation rules. We then introduce an extended form of the metric temporal graph logic (MTGL) with increased expressiveness to improve the applicability of MTGL for the specification of timed graph sequences generated by a TGTS. Based on the metric temporal operators of MTGL and its built-in graph binding mechanics, we express properties on the structure and attributes of graphs as well as on the occurrence of graphs over time that are related by their inner structure. We provide formal support for checking whether a single generated timed graph sequence adheres to a provided MTGL specification. Relying on this logical foundation, we develop a testing framework for TGTSs that are specified using MTGL. Lastly, we apply this testing framework to a running example by using our prototypical implementation in the tool AutoGraph.