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The knapsack problem is a classic optimisation problem that has been recently extended in the setting of groups. Its study reveals to be interesting since it provides many different behaviours, depending on the considered class of groups.…
The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful…
We consider the growth, order, and finiteness problems for automaton (semi)groups. We propose new implementations and compare them with the existing ones. As a result of extensive experimentations, we propose some conjectures on the order…
Systems now exist which are able to compile unification grammars into language models that can be included in a speech recognizer, but it is so far unclear whether non-trivial linguistically principled grammars can be used for this purpose.…
An attractive mechanism to specify global constraints in rostering and other domains is via formal languages. For instance, the Regular and Grammar constraints specify constraints in terms of the languages accepted by an automaton and a…
One of the major open problems in automata and logic is the following: is there an algorithm which inputs a regular tree language and decides if the language can be defined in first-order logic? The goal of this paper is to present this…
As Large Language Models (LLMs) have shown significant intelligence, the progress to leverage LLMs as planning modules of autonomous agents has attracted more attention. This survey provides the first systematic view of LLM-based agents…
We describe the development of the theory of automatic groups. We begin with a historical introduction, define the concepts of automatic, biautomatic and combable groups, derive basic properties, then explain how hyperbolic groups and the…
An equivalence relation in the symmetric group, where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described.
There is a subset of computational problems that are computable in polynomial time for which an existing algorithm may not complete due to a lack of high performance technology on a mission field. We define a subclass of deterministic…
Tree automata based algorithms are essential in many fields in computer science such as verification, specification, program analysis. They become also essential for databases with the development of standards such as XML. In this paper, we…
This paper contains results related to synthesis and presentation of abstract automata by fragments of behaviour and investigates the structure of the classes of finite connected initial output-less automata specified by systems of defining…
Human languages use a wide range of grammatical categories to constrain which words or phrases can fill certain slots in grammatical patterns and to express additional meanings, such as tense or aspect, through morpho-syntactic means. These…
Originally proposed for handling time series data, Auto-regressive Decision Trees (ARDTs) have not yet been explored for language modeling. This paper delves into both the theoretical and practical applications of ARDTs in this new context.…
This paper contains a survey of recent developments in investigation of word equations in simple matrix groups and polynomial equations in simple (associative and Lie) matrix algebras along with some new results on the image of word maps on…
Languages based on the theory of timed automata are a well established approach for modelling and analysing real-time systems, with many applications both in industrial and academic context. Model checking for timed automata has been…
The spin--network quantum simulator model, which essentially encodes the (quantum deformed) SU(2) Racah--Wigner tensor algebra, is particularly suitable to address problems arising in low dimensional topology and group theory. In this…
We consider some questions about formal languages that arise when inverses of letters, words and languages are defined. The reduced representation of a language over the free monoid is its unique equivalent representation in the free group.…
The planning ability of Large Language Models (LLMs) has garnered increasing attention in recent years due to their remarkable capacity for multi-step reasoning and their ability to generalize across a wide range of domains. While some…
A fundamental theme in automata theory is regular languages of words and trees, and their many equivalent definitions. Salvati has proposed a generalization to regular languages of simply typed $\lambda$-terms, defined using denotational…