Related papers: New tools for state complexity
A language L is prefix-free if, whenever words u and v are in L and u is a prefix of v, then u=v. Suffix-, factor-, and subword-free languages are defined similarly, where "subword" means "subsequence". A language is bifix-free if it is…
Inflection graphs are highly complex networks representing relationships between inflectional forms of words in human languages. For so-called synthetic languages, such as Latin or Polish, they have particularly interesting structure due to…
Dictionary learning is a branch of signal processing and machine learning that aims at finding a frame (called dictionary) in which some training data admits a sparse representation. The sparser the representation, the better the…
Optics, aka functional references, are classes of tools that allow composable access into compound data structures. Usually defined as programming language libraries, they provide combinators to manipulate different shapes of data such as…
Document Summarization is the procedure of generating a meaningful and concise summary of a given document with the inclusion of relevant and topic-important points. There are two approaches: one is picking up the most relevant statements…
In this work a collective of interacting stateless automata in a discrete geometric $n$-dimenstional environment is considered as an integral automaton-like computational dynamic object. For such distributed on the environment object…
We introduce a new formalisation of languages, called keyboards. We consider a set of elementary operations (writing/erasing a letter, going to the right or to the left,...) and we define a keyboard as a set of finite sequences of such…
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…
This paper presents an efficient method for LR parsing of permutation phrases. In practical cases, the proposed algorithm constructs an LR(0) automaton that requires significantly fewer states to process a permutation phrase compared to the…
We treat here the interrelation between formal languages and those dynamical systems that can be described by cellular automata (CA). There is a well-known injective map which identifies any CA-invariant subshift with a central formal…
Transformers play a central role in the inner workings of large language models. We develop a mathematical framework for analyzing Transformers based on their interpretation as interacting particle systems, which reveals that clusters…
This paper proposes a new approach to animacy detection, the task of determining whether an entity is represented as animate in a text. In particular, this work is focused on atypical animacy and examines the scenario in which typically…
State conversion generalizes query complexity to the problem of converting between two input-dependent quantum states by making queries to the input. We characterize the complexity of this problem by introducing a natural…
We describe witness languages meeting the upper bound on the state complexity of the multiple concatenation of $k$ regular languages over an alphabet of size $k+1$ with a significantly simpler proof than that in the literature. We also…
We present a vision-language model whose parameters are jointly trained on all tasks and fully shared among multiple heterogeneous tasks which may interfere with each other, resulting in a single model which we named Musketeer. The…
We study the state complexity of boolean operations and product (concatenation, catenation) combined with star. We derive tight upper bounds for the symmetric differences and differences of two languages, one or both of which are starred,…
Artificial intelligence systems exhibit many useful capabilities, but they appear to lack understanding. This essay describes how we could go about constructing a machine capable of understanding. As John Locke (1689) pointed out words are…
Quantum state tomography is an elementary tool to fully characterize an unknown quantum state. As the quantum hardware scales up in size, the standard quantum state tomography becomes increasingly challenging due to its exponentially…
A regular language $L$ is union-free if it can be represented by a regular expression without the union operation. A union-free language is deterministic if it can be accepted by a deterministic one-cycle-free-path finite automaton; this is…
In a jumping finite automaton, the input head can jump to an arbitrary position within the remaining input after reading and consuming a symbol. We characterize the corresponding class of languages in terms of special shuffle expressions…