Related papers: Quotient Complexity of Regular Languages
Generalizing the notion of automatic complexity of individual strings due to Shallit and Wang, we define the automatic complexity $A(E)$ of an equivalence relation $E$ on a finite set $S$ of strings. We prove that the problem of determining…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
We introduce a flexible class of well-quasi-orderings (WQOs) on words that generalizes the ordering of (not necessarily contiguous) subwords. Each such WQO induces a class of piecewise testable languages (PTLs) as Boolean combinations of…
Although classifiers/quantifiers (CQs) expressions appear frequently in everyday communications or written documents, they are described neither in classical bilingual paper dictionaries , nor in machine-readable dictionaries. The paper…
Semiautomata form a rich class of sequence-processing algorithms with applications in natural language processing, robotics, computational biology, and data mining. We establish the first Statistical Query hardness result for semiautomata…
We solve two open problems concerning syntactic complexity: We prove that the cardinality of the syntactic semigroup of a left ideal or a suffix-closed language with $n$ left quotients (that is, with state complexity $n$) is at most…
The infimal prefix-closed, controllable and observable superlanguage plays an essential role in the relationship between controllability, observability and co-observability -- the central notions of supervisory control theory. Existing…
Language models (LMs) are often expected to generate strings in some formal language; for example, structured data, API calls, or code snippets. Although LMs can be tuned to improve their adherence to formal syntax, this does not guarantee…
Logical approaches to representing language have developed and evaluated computational models of quantifier words since the 19th century, but today's NLU models still struggle to capture their semantics. We rely on Generalized Quantifier…
The $k$'th frequency moment of a sequence of integers is defined as $F_k = \sum_j n_j^k$, where $n_j$ is the number of times that $j$ occurs in the sequence. Here we study the quantum complexity of approximately computing the frequency…
We introduce Qunity, a new quantum programming language designed to treat quantum computing as a natural generalization of classical computing. Qunity presents a unified syntax where familiar programming constructs can have both quantum and…
The avoidability, or unavoidability of patterns in words over finite alphabets has been studied extensively. A word (pattern) over a finite set is said to be unavoidable if, for all but finitely many words, there exists a morphism mapping…
We study the state complexity of binary operations on regular languages over different alphabets. It is known that if $L'_m$ and $L_n$ are languages of state complexities $m$ and $n$, respectively, and restricted to the same alphabet, the…
An automaton is unambiguous if for every input it has at most one accepting computation. An automaton is k-ambiguous (for k > 0) if for every input it has at most k accepting computations. An automaton is boundedly ambiguous if it is…
We provide an exact estimate on the maximal subword complexity for quasiperiodic infinite words. To this end we give a representation of the set of finite and of infinite words having a certain quasiperiod q via a finite language derived…
The behavior of a quantum system depends on how it is measured. How much of what is observed comes from the structure of the quantum system itself and how much from the observer's choice of measurement? We explore these questions by…
Optimization is a key task in a number of applications. When the set of feasible solutions under consideration is of combinatorial nature and described in an implicit way as a set of constraints, optimization is typically NP-hard.…
We introduce a new measure on regular languages: their nondeterministic syntactic complexity. It is the least degree of any extension of the `canonical boolean representation' of the syntactic monoid. Equivalently, it is the least number of…
The subword complexity of a finite word $w$ of length $N$ is a function which associates to each $n\le N$ the number of all distinct subwords of $w$ having the length $n$. We define the \emph{maximal complexity} C(w) as the maximum of the…
Nonterminal complexity of a context-free language is the smallest possible number of nonterminals in its generating grammar. While in general case nonterminal complexity computation problem is unsolvable, it can be computed for different…