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This is Chapter 24 in the "AutoMathA" handbook. Finite automata have been used effectively in recent years to define infinite groups. The two main lines of research have as their most representative objects the class of automatic groups…
A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA $N$, there exists a process algebraic term $p$ such that its semantics is…
Combining ideas from distributed algorithms and alternating automata, we introduce a new class of finite graph automata that recognize precisely the languages of finite graphs definable in monadic second-order logic. By restricting…
Existing efforts are dedicated to designing many topologies and graph-aware strategies for the graph Transformer, which greatly improve the model's representation capabilities. However, manually determining the suitable Transformer…
We give algorithms to accelerate the computation of deterministic finite automata (DFA) by calculating the state of a DFA n positions ahead utilizing a reverse scan of the next n characters. Often this requires scanning fewer than n…
Complementation of finite automata is a basic operation used in numerous applications. The standard way to complement a nondeterministic finite automaton (NFA) is to transform it into an equivalent deterministic finite automaton (DFA) and…
Graph-Rewriting Automata (GRA) are an extension of Cellular Automata to a dynamic structure using local graph-rewriting rules. This work introduces linear algebra based tools that allow for a practical investigation of their behavior in…
Memory safety is an essential correctness property of software systems. For programs operating on linked heap-allocated data structures, the problem of proving memory safety boils down to analyzing the possible shapes of data structures,…
We have developed a methodology for the systematic generation of a large image dataset of macerated wood references, which we used to generate image data for nine hardwood genera. This is the basis for a substantial approach to automate,…
Many natural language processing systems operate over tokenizations of text to address the open-vocabulary problem. In this paper, we give and analyze an algorithm for the efficient construction of deterministic finite automata (DFA)…
Formal Concept Analysis (FCA) is a mathematical theory based on the formalization of the notions of concept and concept hierarchies. It has been successfully applied to several Computer Science fields such as data mining,software…
Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice. In this work we focus on a generalised version of typical CA, called graph…
An index for a finite automaton is a powerful data structure that supports locating paths labeled with a query pattern, thus solving pattern matching on the underlying regular language. In this paper, we solve the long-standing problem of…
Many dynamic processes such as telecommunication and transport networks can be described through discrete time series of graphs. Modelling the dynamics of such time series enables prediction of graph structure at future time steps, which…
Tree ensembles have demonstrated state-of-the-art predictive performance across a wide range of problems involving tabular data. Nevertheless, the black-box nature of tree ensembles is a strong limitation, especially for applications with…
Vector space models for symbolic processing that encode symbols by random vectors have been proposed in cognitive science and connectionist communities under the names Vector Symbolic Architecture (VSA), and, synonymously, Hyperdimensional…
A new method for the Automated Protein Structure Analysis (APSA) is derived, which simplifies the protein backbone to a smooth curve in 3-dimensional space. For the purpose of obtaining this smooth line each amino acid is represented by its…
We introduce heap automata, a formalism for automatic reasoning about robustness properties of the symbolic heap fragment of separation logic with user-defined inductive predicates. Robustness properties, such as satisfiability,…
Fault Tree Analysis (FTA) is a well-established method in failure analysis and is widely used in safety and reliability assessments. While FTA tools enable users to manage complex analyses effectively, they can sometimes obscure the…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…