Search results for "state complexity"
showing 7 items of 7 documents
The Average State Complexity of the Star of a Finite Set of Words Is Linear
2008
We prove that, for the uniform distribution over all sets Xof m(that is a fixed integer) non-empty words whose sum of lengths is n, $\mathcal{D}_X$, one of the usual deterministic automata recognizing X*, has on average $\mathcal{O}(n)$ states and that the average state complexity of X*is i¾?(n). We also show that the average time complexity of the computation of the automaton $\mathcal{D}_X$ is $\mathcal{O}(n\log n)$, when the alphabet is of size at least three.
Error-Free Affine, Unitary, and Probabilistic OBDDs
2021
We introduce the affine OBDD model and show that zero-error affine OBDDs can be exponentially narrower than bounded-error unitary and probabilistic OBDDs on certain problems. Moreover, we show that Las-Vegas unitary and probabilistic OBDDs can be quadratically narrower than deterministic OBDDs. We also obtain the same results for the automata counterparts of these models.
The average state complexity of rational operations on finite languages is linear
2010
Considering the uniform distribution on sets of m non-empty words whose sum of lengths is n, we establish that the average state complexities of the rational operations are asymptotically linear.
Counting with Probabilistic and Ultrametric Finite Automata
2014
We investigate the state complexity of probabilistic and ultrametric finite automata for the problem of counting, i.e. recognizing the one-word unary language \(C_n=\left\{ 1^n \right\} \). We also review the known results for other types of automata.
Jauni ieskati kvantu automātu stāvokļu skaita efektivitātē
2022
Kvantu galīgi automāti var sasniegt eksponenciālu stāvokļu skaitu efektivitāti, salīdzinot ar determinētiem galīgiem automātiem. Viena problēma, kurā ir zināms, ka kvantu galīgiem automātiem ir eksponenciālas priekšrocības, ir MODn problēma, taču nav zināma metode, kā uzkonstruēt tādu kvantu automātu. Šajā darbā eksponenciāli efektīvie MODn algoritmi tiek vispārināti jaunā algoritmā, kas samazina vajadzīgo stāvokļu skaitu. Jaunā algoritma saaistības ar esošiem virzieniem literatūrā tiek aprakstītas, un tiek piedāvātas divas jaunas skaitļu virknes, kuras varētu izmantot, lai uzkonstruētu tādus kvantu automātus.
Transition Function Complexity of Finite Automata
2019
State complexity of finite automata in some cases gives the same complexity value for automata which intuitively seem to have completely different complexities. In this paper we consider a new measure of descriptional complexity of finite automata -- BC-complexity. Comparison of it with the state complexity is carried out here as well as some interesting minimization properties are discussed. It is shown that minimization of the number of states can lead to a superpolynomial increase of BC-complexity.
Complexity of operations on cofinite languages
2010
International audience; We study the worst case complexity of regular operation on cofinite languages (i.e., languages whose complement is finite) and provide algorithms to compute efficiently the resulting minimal automata.