The Parametric Ordinal-Recursive Complexity of Post Embedding Problems

Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove parametric lower bounds depending on the size of the alphabet.Comment: 16 + vii page

On the Commutative Equivalence of Context-Free Languages

The problem of the commutative equivalence of context-free and regular languages is studied. In particular conditions ensuring that a context-free language of exponential growth is commutatively equivalent with a regular language are investigated

Context-Sensitive String Languages and Recognizable Picture Languages

... In this article, we prove a similar result: the family of frontiers of recognizable picture languages is exactly the family of context-sensitive languages

Commutative One-counter languages are regular

AbstractA new characterization of commutative regular languages is given. Using it, it is proved that every commutative one-counter language is regular

On commutative context-free languages

AbstractLet Σ = {a1, a2, …, an} be an alphabet and let L ⊂ Σ∗ be the commutative image of FP∗ where F and P are finite subsets of Σ∗. If, for any permutation σ of {1, 2, …, n }, L ∩ ασ∗(n) … aσ∗(n) is context-free, then L is context-free. This theorem provides a solution to the Fliess conjecture in a restricted case. If the result could be extended to finite unions of the FP∗ above, the Fliess conjecture could be solved

Iterated Length-Preserving Rational Transductions

The purpose of this paper is the study of the smallest family of transductions containing length-preserving rational transductions and closed under union, composition and iteration. We give several characterizations of this class using restricted classes of length-preserving rational transductions, by showing the connections with "context-sensitive transductions" and transductions associated with recognizable picture languages. We also study the classes obtained by only using length-preserving rational functions and we show the relations with "deterministic context-sensitive transductions"