Martin Kutrib

NONDETERMINISTIC DESCRIPTIONAL COMPLEXITY OF REGULAR LANGUAGES

We investigate the descriptional complexity of operations on finite and infinite regular languages over unary and arbitrary alphabets. The languages are represented by nondeterministic finite automata (NFA). In particular, we consider Boolean operations, catenation operations – concatenation, iteration, λ-free iteration – and the reversal. Most of the shown bounds are tight in the exact number of states, i.e. the number is sufficient and necessary in the worst case. Otherwise tight bounds in the order of magnitude are shown.

State complexity of basic operations on nondeterministic finite automata

The state complexities of basic operations on nondeterministic finite automata (NFA) are investigated. In particular, we consider Boolean operations, catenation operations - concatenation, iteration, λ-free iteration - and the reversal on NFAs that accept finite and infinite languages over arbitrary alphabets. Most of the shown bounds are tight in the exact number of states, i.e. the number is sufficient and necessary in the worst case. For the complementation tight bounds in the order of magnitude are proved. It turns out that the state complexities of operations on NFAs and deterministic finite automata (DFA) are quite different. For example, the reversal and concatenation have exponential state complexity on DFAs but linear complexity on NFAs. Conversely, the complementation can be done with linear complexity on DFAs but needs exponentially many states on NFAs.

On Stateless Two-Pushdown Automata and Restarting Automata

Restarting automata and two-pushdown automata are investigated that have a single internal state only. As such an automaton must always stay in the same state, this state is of no importance for the behaviour of the automaton. Accordingly, these automata are called stateless. We consider various types of stateless two-pushdown automata and restarting automata. We investigate their expressive power, comparing them in particular to each other and to the corresponding types of automata with states.

On time computability of functions in one-way cellular automata

Abstract. The capability of one-way (space-bounded) cellular automata (OCA) to time-compute functions is investigated. That means given a constant input of length

Determination of finite automata accepting subregular languages

n

NONDETERMINISTIC FINITE AUTOMATA — RECENT RESULTS ON THE DESCRIPTIONAL AND COMPUTATIONAL COMPLEXITY

a distinguished cell has to enter a distinguished state exactly after

Unary language operations and their nondeterministic state complexity

f(n)

Complexity of multi-head finite automata: Origins and directions

time steps. The family of such functions (

THE PHENOMENON OF NON-RECURSIVE TRADE-OFFS

{\cal C}

Flip-pushdown automata: k + 1 pushdown reversals are better than k

(OCA)) is characterized in terms of formal language recognition. Several functions are proved to be time-computable and properties of