Corpus ID: 54159

Finding the growth rate of a regular language in polynomial time

  title={Finding the growth rate of a regular language in polynomial time},
  author={D. Krieger and N. Rampersad and J. Shallit},
AbstractWe give an O(n 3 +n 2 t) time algorithm to determine whether an NFA with n statesand t transitions accepts a language of polynomial or exponential growth. We alsoshow that given a DFA accepting a language of polynomial growth, we can determinethe order of polynomial growth in quadratic time. 1 Introduction Let L ⊆ Σ ∗ be a language. If there exists a polynomial p(x) such that |L ∩ Σ m | ≤ p(m) forall m ≥ 0, then L has polynomial growth . Languages of polynomial growth are also called… Expand


Characterizing Regular Languages with Polynomial Densities
It is shown that the function p R(n) of a regular language R is O(n k ), for some k≥0, if and only if R can be represented as a finite union of the regular expressions of the form xy 1 * z1 ...y t * zt with a nonnegative integer t≤k+1. Expand
On Sparseness, Ambiguity and other Decision Problems for Acceptors and Transducers
This work considers some decision problems on sparseness, degrees of ambiguity and multiple valuedness concerning finite-state and pushdown acceptors and transducers and shows that they are decidable for finite- state devices. Expand
Length Considerations in Context-Free Languages
  • D. Raz
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 1997
A length characterization for bounded context-free languages and a proof that thinness and slenderness are decidable, based upon a novel characterization of languages in terms of the structure of the infinite paths in their prefix closure. Expand
A characterization of poly-slender context-free languages
It is given that a language L is k -poly-slender if the number of words of length n in L is of order ${\cal O}. Expand
Context-Free Languages of Sub-exponential Growth
Context-free languages of sub-exponential growth were studied and it was shown that context- free languages of intermediate growth were nonexistent. Expand
On the complexity of computing determinants
New baby steps/giant steps algorithms of asymptotically fast running time for dense matrix problems that deterministically compute the determinant, characteristic polynomial and adjoint of A with n3.2+o(1) and O(n2.697263) ring additions, subtractions and multiplications are presented. Expand
A gap result for the norms of semigroups of matrices
Let �·� be a matrix norm on Md (C) and let A be a finite set of matrices in Md (C). We define mn(A) to be the maximum norm of a product of n elements of A. We show that there is a gap in the possibleExpand
Almost tight recursion tree bounds for the Descartes method
A unified ("basis free") framework is given for the Descartes method for real root isolation of square-free real polynomials and a new bound on the size of the recursion tree is given. Expand
The growth function of context-free languages
  • R. Incitti
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 2001
It is shown that the growth of a context-free language is either polynomial or exponential, which means it can be assumed that the specification of a language is a function of the input language. Expand
Abstract : Two characterizations of bounded regular sets are given. In addition, certain bounded regular sets are related to their commutative closure. (Author)