The Parikh counting functions of sparse context-free languages are quasi-polynomials

  • Authors:

  • Flavio DAlessandro;Benedetto Intrigila;Stefano Varricchio

  • Affiliations:

  • Dipartimento di Matematica, Università di Roma La Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy;Dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 00133 Roma, Italy;Dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 00133 Roma, Italy

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2009

Quantified Score

Hi-index 5.23

Visualization

Abstract

Let L be a sparse context-free language over an alphabet of t letters and let f"L:N^t-N be its Parikh counting function. We prove the following two results: 1.There exists a partition of N^t into a finite family of polyhedra such that the function f"L is a quasi-polynomial on each polyhedron of the partition. 2.There exists a partition of N^t into a finite family of rational subsets such that the function f"L is a polynomial on each set of the partition.