Combinatorial Characterization of Formal Languages

Lovász-Schrijver SDP-operator, near-perfect graphs and near-bipartite graphs

We study the Lovász-Schrijver lift-and-project operator (LS+) based on the cone of symmetric, positive semidefinite matrices, applied to the fractional stable set polytope of graphs. The problem of obtaining a combinatorial characterization of graphs for which the LS+-operator generates the stable set polytope in one step has been open since 1990. We call these graphs LS+-perfect. In the curren...

Formal Languages and Their Application to Combinatorial Group Theory

TOPOLOGICAL CHARACTERIZATION FOR FUZZY REGULAR LANGUAGES

We present a topological characterization for fuzzy regular languages: we show that there is a bijective correspondence between fuzzy regular languages and the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular...

Formal languages and infinite groups

This article is an introduction to formal languages from the point of view of combinatorial group theory.

Modular and Threshold Subword Counting and Matrix Representations of Finite Monoids

The subword relation reveals interesting combinatorial properties and plays a prominent role in formal language theory. For instance, recall that languages consisting of all words over Σ having a given word u ∈ Σ∗ as a subword serve as a generating system for the Boolean algebra of so-called piecewise testable languages. It was a deep study of combinatorics of the subword relation that led Simo...

Block Sorting: A Characterization and some Heuristics

Given a permutation π, the   problem is to find a shortest series of block moves which, when applied in succession, sorts π. Here a block is a maximal substring of successive integers in order, and a block move is the displacement of a block to a location where it merges with another block.   is an NP-hard optimization problem [3] and has a factor 2 approximation algorit...