Related papers: Quotient Complexity of Regular Languages
An open problem in communication complexity proposed by several authors is to prove that for every Boolean function f, the task of computing f(x AND y) has polynomially related classical and quantum bounded-error complexities. We solve a…
Generalizations of numeration systems in which N is recognizable by a finite automaton are obtained by describing a lexicographically ordered infinite regular language L over a finite alphabet A. For these systems, we obtain a…
A quantum finite-state automaton (QFA) is a theoretical model designed to simulate the evolution of a quantum system with finite memory in response to sequential input strings. We define the language of a QFA as the set of strings that lead…
We examine deterministic and nondeterministic state complexities of regular operations on prefix-free languages. We strengthen several results by providing witness languages over smaller alphabets, usually as small as possible. We next…
In this paper we examine how the notion of algebra of quotients for Lie algebras ties up with the corresponding well-known concept in the associative case. Specifically, we completely characterize when a Lie algebra $Q$ is an algebra of…
This article contains ideas and their elaboration for quantifiers, which appeared after checking in practice the experimental language of the formal knowledge representation YAFOLL [1]: - looking at for_all and exists quantifiers as…
It is generally well agreed that developing a unifying theory is one of the most important issues in Data Mining research. In the last two decades, a great deal of work has been devoted to the algorithmic aspects of the Frequent Itemset…
Some of the most interesting and important results concerning quantum finite automata are those showing that they can recognize certain languages with (much) less resources than corresponding classical finite automata…
We show that classical and quantum Kolmogorov complexity of binary strings agree up to an additive constant. Both complexities are defined as the minimal length of any (classical resp. quantum) computer program that outputs the…
We resolve an open question by determining matching (asymptotic) upper and lower bounds on the state complexity of the operation that sends a language L to (c(L*))*, where c() denotes complement.
We study regular expressions that use variables, or parameters, which are interpreted as alphabet letters. We consider two classes of languages denoted by such expressions: under the possibility semantics, a word belongs to the language if…
The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of the class of regular languages is the maximal syntactic complexity of languages in that class, taken as…
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…
The automatic complexity of a finite word (string) is an analogue for finite automata of Sipser's distinguishing complexity (1983) and was introduced by Shallit and Wang (2001). For a finite alphabet $\Sigma$ of at least two elements, we…
Classically, the time complexity of a first-order method is estimated by its number of gradient computations. In this paper, we study a more refined complexity by taking into account the `lingering' of gradients: once a gradient is computed…
The height of a piecewise-testable language $L$ is the maximum length of the words needed to define $L$ by excluding and requiring given subwords. The height of $L$ is an important descriptive complexity measure that has not yet been…
Finite-state tree automata are a well studied formalism for representing term languages. This paper studies the problem of determining the regularity of the set of instances of a finite set of terms with variables, where each variable is…
This paper proposes an extension to classical regular expressions by the addition of two operators allowing the inclusion of boolean formulae from the zeroth order logic. These expressions are called constrained expressions. The associated…
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…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…