Related papers: On counting functions and slenderness of languages
Automata admitting at most one accepting run per structure, known as unambiguous automata, find applications in verification of reactive systems as they extend the class of deterministic automata whilst maintaining some of their desirable…
The {\em diagonalization technique} was invented by Georg Cantor to show that there are more real numbers than algebraic numbers and is very crucial in {\em theoretical computer science}. In this work, we enumerate all of the…
Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages $L$ that assign to each word $w$ a real number $L(w)$. In the case of infinite words, the value of a run is…
Large language models can perform new tasks in a zero-shot fashion, given natural language prompts that specify the desired behavior. Such prompts are typically hand engineered, but can also be learned with gradient-based methods from…
In this paper, we study arbitrary regular factorial languages over a finite alphabet $\Sigma$. For the set of words $L(n)$ of the length $n$ belonging to a regular factorial language $L$, we investigate the depth of decision trees solving…
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
In this work, we study the problems of counting and sampling Mazurkiewicz traces that a regular language touches. Fix an alphabet $\Sigma$ and an independence relation $\mathbb{I} \subseteq \Sigma \times \Sigma$. The input consists of a…
It is well known that for a regular tree language it is decidable whether or not it can be recognized by a deterministic top-down tree automaton (DTA). However, the computational complexity of this problem has not been studied. We show that…
1-way quantum finite state automata are reversible in nature, which greatly reduces its accepting property. In fact, the set of languages accepted by 1-way quantum finite automata is a proper subset of regular languages. We introduce 2-tape…
We study the capabilities of probabilistic finite-state machines that act as verifiers for certificates of language membership for input strings, in the regime where the verifiers are restricted to toss some fixed nonzero number of coins…
Language is typically modelled with discrete sequences. However, the most successful approaches to language modelling, namely neural networks, are continuous and smooth function approximators. In this work, we show that Transformer-based…
In this article, we evaluate computational models of natural language with respect to the universal statistical behaviors of natural language. Statistical mechanical analyses have revealed that natural language text is characterized by…
This work attempts to explain the types of computation that neural networks can perform by relating them to automata. We first define what it means for a real-time network with bounded precision to accept a language. A measure of network…
We consider two natural problems about nondeterministic finite automata. First, given such an automaton M of n states, and a length l, does M accept a word of length l? We show that the classic problem of triangle-free graph recognition…
In this paper we develop little further the theory of quantum finite automata (QFA). There are already few properties of QFA known, that deterministic and probabilistic finite automata do not have e.g. they cannot recognize all regular…
A Wheeler automaton is a finite state automaton whose states admit a total Wheeler order, reflecting the co-lexicographic order of the strings labeling source-to-node paths. A Wheeler language is a regular language admitting an accepting…
Transformers have supplanted recurrent models in a large number of NLP tasks. However, the differences in their abilities to model different syntactic properties remain largely unknown. Past works suggest that LSTMs generalize very well on…
Sequential Constraint Grammar (SCG) (Karlsson, 1990) and its extensions have lacked clear connections to formal language theory. The purpose of this article is to lay a foundation for these connections by simplifying the definition of…
We show that autoregressive decoding of a transformer-based language model can realize universal computation, without external intervention or modification of the model's weights. Establishing this result requires understanding how a…
A regular tree language L is locally testable if membership of a tree in L depends only on the presence or absence of some fix set of neighborhoods in the tree. In this paper we show that it is decidable whether a regular tree language is…