相关论文: Quotient Complexities of Atoms in Regular Ideal La…

This paper deals with the size complexity of minimal {\it two-way quantum finite automata} (2qfa's) necessary for operations to perform on all inputs of each fixed length. Such a complexity measure, known as state complexity of operations,…

We investigate the expressive power of first-order quantifications in the context of monadic second-order logic over pictures. We show that k+1 set quantifier alternations allow to define a picture language that cannot be defined using k…

In this paper we explore a new hierarchy of classes of languages and infinite words and its connection with complexity classes. Namely, we say that a language belongs to the class $L_k$ if it is a subset of the catenation of $k$ languages…

In a recent thread of papers, we have introduced FQL, a precise specification language for test coverage, and developed the test case generation engine FShell for ANSI C. In essence, an FQL test specification amounts to a set of regular…

This work is concerned with regular languages defined over large alphabets, either infinite or just too large to be expressed enumeratively. We define a generic model where transitions are labeled by elements of a finite partition of the…

As is the case of many signals produced by complex systems, language presents a statistical structure that is balanced between order and disorder. Here we review and extend recent results from quantitative characterisations of the degree of…

Though English sentences are typically inflexible vis-\`a-vis word order, constituents often show far more variability in ordering. One prominent theory presents the notion that constituent ordering is directly correlated with constituent…

A quantitative method is suggested, where meanings of words, and grammatic rules about these, of a vocabulary are represented by real numbers. People meet randomly, and average their vocabularies if they are equal; otherwise they either…

Infinite words, also known as streams, hold significant interest in computer science and mathematics, raising the natural question of how their complexity should be measured. We introduce cellular automaton reducibility as a measure of…

In the constrained synchronization problem we ask if a given automaton admits a synchronizing word coming from a fixed regular constraint language. We show that intersecting a given constraint language with an ideal language decreases the…

We present a language $L_n$ which is recognizable by a probabilistic finite automaton (PFA) with probability $1 - \epsilon$ for all $\epsilon > 0$ with $O(log^2n)$ states, with a deterministic finite automaton (DFA) with O(n) states, but a…

Perfect Gabriel filters of right ideals and their corresponding right rings of quotients have the desirable feature that every module of quotients is determined solely by the right ring of quotients. On the other hand, symmetric rings of…

Language interpretation is a compositional process, in which the meaning of more complex linguistic structures is inferred from the meaning of their parts. Large language models possess remarkable language interpretation capabilities and…

The complexity function of an infinite word $w$ on a finite alphabet $A$ is the sequence counting, for each non-negative $n$, the number of words of length $n$ on the alphabet $A$ that are factors of the infinite word $w$. For any given…

The Chapter starts with introductory information about quantitative linguistics notions, like rank--frequency dependence, Zipf's law, frequency spectra, etc. Similarities in distributions of words in texts with level occupation in quantum…

A generalization of numeration system in which the set N of the natural numbers is recognizable by finite automata can be obtained by describing a lexicographically ordered infinite regular language. Here we show that if P belonging to Q[x]…

Partial words are sequences over a finite alphabet that may contain wildcard symbols, called holes, which match or are compatible with all letters; partial words without holes are said to be full words (or simply words). Given an infinite…

The creation complexity of a quantum state is the minimum number of elementary gates required to create it from a basic initial state. The creation complexity of quantum states is closely related to the complexity of quantum circuits, which…

Let $S$ be a finite alphabet. An injective word over $S$ is a word over $S$ such that each letter in $S$ appears at most once in the word. We study Boolean cell complexes of injective words over $S$ and their commutation classes. This…

We prove lower bounds on the length of regular expressions for finite languages by methods from arithmetic circuit complexity. First, we show a reduction: the length of a regular expression for a language $L\subseteq \{0,1\}^n$ is bounded…