Information Content in Formal Languages

On Languages with Very High Information Content

The main result of this paper is the following: Any language in ESPACE that is bounded truthtable reducible in polynomial time to a set with very high space-bounded Kolmogorov complexity must be bounded truth-table reducible in polynomial time to a sparse set.

Factorization in Formal Languages

We consider several novel aspects of unique factorization in formal languages. We reprove the familiar fact that the set uf(L) of words having unique factorization into elements of L is regular if L is regular, and from this deduce an quadratic upper and lower bound on the length of the shortest word not in uf(L). We observe that uf(L) need not be context-free if L is context-free. Next, we con...

Formal Languages

Learning Families of Formal Languages from Positive and Negative Information

For 50 years, research in the area of inductive inference aims at investigating the learning of formal languages and is influenced by computability theory, complexity theory, cognitive science, machine learning, and more generally artificial intelligence. Being one of the pioneers, Gold [1967] investigated the most common formalization, learning in the limit both from solely positive examples a...

Formal Languages in Dynamical Systems

We treat here the interrelation between formal languages and those dynamical systems that can be described by cellular automata (CA). There is a well-known injective map which identifies any CA-invariant subshift with a central formal language. However, in the special case of a symbolic dynamics, i.e. where the CA is just the shift map, one gets a stronger result: the identification map can be ...