Related papers: Automatic Groups and Knuth-Bendix with Infinitely …
This text, Chapter 23 in the "AutoMathA" handbook, is devoted to the study of rational subsets of groups, with particular emphasis on the automata-theoretic approach to finitely generated subgroups of free groups. Indeed, Stallings'…
Symbolic automata are finite state automata that support potentially infinite alphabets, such as the set of rational numbers, generally applied to regular expressions/languages over finite words. In symbolic automata (or automata modulo…
In the classic problem of sequence prediction, a predictor receives a sequence of values from an emitter and tries to guess the next value before it appears. The predictor masters the emitter if there is a point after which all of the…
This paper introduces two mechanisms for computing over-approximations of sets of reachable states, with the aim of ensuring termination of state-space exploration. The first mechanism consists in over-approximating the automata…
We consider multi-task learning, which simultaneously learns related prediction tasks, to improve generalization performance. We factorize a coefficient matrix as the product of two matrices based on a low-rank assumption. These matrices…
We present algorithms to perform modular polynomial multiplication or modular dot product efficiently in a single machine word. We pack polynomials into integers and perform several modular operations with machine integer or floating point…
In this article, we introduce and investigate a class of finite deterministic automata that all recognize the language of reduced words of a finitely generated Coxeter system (W,S). The definition of these automata is straightforward as it…
The purpose of this survey is to serve both as a gentle introduction and a coherent overview of state-of-the-art Frank--Wolfe algorithms, also called conditional gradient algorithms, for function minimization. These algorithms are…
Dialogical argumentation is an important cognitive activity by which agents exchange arguments and counterarguments as part of some process such as discussion, debate, persuasion and negotiation. Whilst numerous formal systems have been…
Due to the high energy consumption and scalability challenges of deep learning, there is a critical need to shift research focus towards dealing with energy consumption constraints. Tsetlin Machines (TMs) are a recent approach to machine…
Recently, a new paradigm was introduced in automata theory. The main idea is to classify regular languages according to their propensity to be sorted, establishing a deep connection between automata theory and data compression [J. ACM…
This paper introduces a general approach for synthesizing procedural models of the state-transitions of a given discrete system. The approach is general in that it accepts different target languages for modeling the state-transitions of a…
Donald Knuth introduced in The Art of Computer Programming (Vol 4a) a fast approximation to the addition of integers (given in binary) in terms of bit-wise operations by $a + b \; \approx \; a \oplus b \oplus ((a\land b) \ll 1).$…
In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…
In this paper, we identify a fragment of second-order logic with restricted quantification that is expressive enough to capture numerous static analysis problems (e.g. safety proving, bug finding, termination and non-termination proving,…
We present several infinite series of synchronizing automata for which the minimum length of reset words is close to the square of the number of states. These automata are closely related to primitive digraphs with large exponent.
Alternating automata have been widely used to model and verify systems that handle data from finite domains, such as communication protocols or hardware. The main advantage of the alternating model of computation is that complementation is…
We show how to efficiently enumerate a class of finite-memory stochastic processes using the causal representation of epsilon-machines. We characterize epsilon-machines in the language of automata theory and adapt a recent algorithm for…
In this paper, we study algorithmic problems for automaton semigroups and automaton groups related to freeness and finiteness. In the course of this study, we also exhibit some connections between the algebraic structure of automaton…
We describe a minimization procedure for nondeterministic B\"uchi automata (NBA). For an automaton A another automaton A_min with the minimal number of states is learned with the help of a SAT-solver. This is done by successively computing…