Related papers: Automata theory in nominal sets
Krebs et al. (2007) gave a characterization of the complexity class TC0 as the class of languages recognized by a certain class of typed monoids. The notion of typed monoid was introduced to extend methods of algebraic automata theory to…
We develop formal theories of conversion for Church-style lambda-terms with Pi-types in first-order syntax using one-sorted variables names and Stoughton's multiple substitutions. We then formalize the Pure Type Systems along some…
Linear temporal logic was introduced in order to reason about reactive systems. It is often considered with respect to infinite words, to specify the behaviour of long-running systems. One can consider more general models for linear time,…
Finite automata (FA) are a fundamental computational abstraction that is widely used in practice for various tasks in computer science, linguistics, biology, electrical engineering, and artificial intelligence. Given an input word, an FA…
We use the notion of a partial action of a monoid to introduce a generalization of automata, which we call "a preautomaton". We study properties of preautomata and of languages recognized by preautomata.
This article is an introduction to formal languages from the point of view of combinatorial group theory. Group theoretic applications are included and language classes are defined algebraically.
We prove that for a suitably nice class of random substitutions, their corresponding subshifts have automorphism groups that contain an infinite simple subgroup and a copy of the automorphism group of a full shift. Hence, they are…
We present a passive automata learning algorithm that can extract automata from recurrent networks with very large or even infinite alphabets. Our method combines overapproximations from the field of Abstract Interpretation and passive…
We study automaton structures, i.e. groups, monoids and semigroups generated by an automaton, which, in this context, means a deterministic finite-state letter-to-letter transducer. Instead of considering only complete automata, we…
We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…
We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the…
B\"uchi Automata on infinite words present many interesting problems and are used frequently in program verification and model checking. A lot of these problems on B\"uchi automata are computationally hard, raising the question if a…
We survey facts mostly emerging from the seminal results of Alan Cobham obtained in the late sixties and early seventies. We do not attempt to be exhaustive but try instead to give some personal interpretations and some research directions.…
During the last decades, classical models in language theory have been extended by control mechanisms defined by monoids. We study which monoids cause the extensions of context-free grammars, finite automata, or finite state transducers to…
A group is combable if it can be represented by a language of words satisfying a fellow traveller property; an automatic group has a synchronous combing which is a regular language. This paper gives a systematic analysis of the properties…
Automaton models are often seen as interpretable models. Interpretability itself is not well defined: it remains unclear what interpretability means without first explicitly specifying objectives or desired attributes. In this paper, we…
Traditionally, finite automata theory has been used as a framework for the representation of possibly infinite sets of strings. In this work, we introduce the notion of second-order finite automata, a formalism that combines finite automata…
Let $G$ be a finite $p$-group and let Aut$(G)$ denote the full automorphism group of $G$. In the recent past, there has been interest in finding necessary and sufficient conditions on $G$ such that certain subgroups of Aut$(G)$ are equal.…
Let $A$ be an infinitely generated free abelian group. We prove that the automorphism group $\aut A$ first-order interprets the full second-order theory of the set $|A|$ with no structure. In particular, this implies that the automorphism…
The Naming Game has been studied to explore the role of self-organization in the development and negotiation of linguistic conventions. In this paper, we define an automata networks approach to the Naming Game. Two problems are faced: (1)…