Size of Nondeterministic and Deterministic Automata for Certain Languages
نویسندگان
چکیده
In the theory of automata the question about difference between the size of deterministic and nondeterministic automata which recognize the same language is of great importance. However, this problem has been studied mainly in case when input alphabet consists of at least 2 letters. In this paper some special kind of languages in one letter alphabet will be discussed and the estimate of the number of states required for deterministic and nondeterministic automata to accept these languages will be made. For one of these languages nondeterministic automaton with ≤ ⎡ n ⎤ + 1 states can be built, but for other with
منابع مشابه
On the Recursion-Theoretic Complexity of Relative Succinctness of Representations of Languages
In Hartmanis (1980) a simple proof is given of the fact (originally proved in Valiant (1976)) that the relative succinctness of representing deterministic context-free languages by deterministic vs. nondeterministic pushdown automata is not recursively bounded, in the following sense: there is no recursive function which, for deterministic context-free languages L, can bound the size of the min...
متن کاملOn the average state and transition complexity of finite languages
We investigate the average-case state and transition complexity of deterministic and nondeterministic finite automata, when choosing a finite language of a certain “size” n uniformly at random from all finite languages of that particular size. Here size means that all words of the language are either of length n, or of length at most n. It is shown that almost all deterministic finite automata ...
متن کاملResults on the Average State and Transition Complexity of Finite Automata Accepting Finite Languages (Extended Abstract)
The study of descriptional complexity issues for finite automata dates back to the mid 1950’s. One of the earliest results is that deterministic and nondeterministic finite automata are computationally equivalent, and that nondeterministic finite automata can offer exponential state savings compared to deterministic ones, see [11]—by the powerset construction one increases the number of states ...
متن کاملA Technique for Proving Lower Bounds on the Size of Sweeping Automata
A sweeping automaton is a two-way deterministic finite automaton which makes turns only at the endmarkers. Sipser [12] has proved that one-way nondeterministic finite automata can be exponentially more succinct in sizes than sweeping automata. In this paper, we propose a technique based on the work in [6] for establishing lower bounds on the size of sweeping automata. We show that Sipser’s tech...
متن کاملSimplifying Nondeterministic Finite Cover Automata
The concept of Deterministic Finite Cover Automata (DFCA) was introduced at WIA ’98, as a more compact representation than Deterministic Finite Automata (DFA) for finite languages. In some cases representing a finite language, Nondeterministic Finite Automata (NFA) may significantly reduce the number of states used. The combined power of the succinctness of the representation of finite language...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005