Descriptional Complexity of the Languages KaL: Automata, Monoids and Varieties

Descriptional Complexity of the Languages KaL: Automata, Monoids and Varieties

The first step when forming the polynomial hierarchies of languages is to consider languages of the form KaL where K and L are over a finite alphabet A and from a given variety V of languages, a ∈ A being a letter. All such KaL’s generate the variety of languages BPol1(V ). We estimate the numerical parameters of the language KaL in terms of their values for K and L. These parameters include th...

Descriptional complexity measures of context-free languages

In [2], [3] and [4] several measures of descriptional complexity of context-free grammars (cfg's) and context-free languages (cfl's) have been investigated, most of them having the following properties: 1. The corresponding hierarchy of complexity classes of languages over two-letter alphabets is infinite. 2. The basic algorithmic problems are undecidable. (For example, the problems to determin...

Nondeterministic Descriptional Complexity Of Regular Languages

1 . 3 Varieties of languages and varieties of finite monoids

In 1980, Janusz A. Brzozowski presented a selection of six open problems about regular languages and mentioned two other problems in the conclusion of his article. These problems have been the source of some of the greatest breakthroughs in automata theory over the past 35 years. This survey article summarizes the state of the art on these questions and the hopes for the next 35 years. Thirty-f...

Descriptional Complexity of Bounded Context-Free Languages

Finite-turn pushdown automata (PDA) are investigated concerning their descriptional complexity. It is known that they accept exactly the class of ultralinear contextfree languages. Furthermore, the increase in size when converting arbitrary PDAs accepting ultralinear languages to finite-turn PDAs cannot be bounded by any recursive function. The latter phenomenon is known as non-recursive trade-...