The Accepting Power of Finite Automata over Groups
نویسندگان
چکیده
Some results from [2], [5], [6] are generalized for nite automata over arbitrary groups. The accepting power is smaller when abelian groups are considered, in comparison with the non-abelian groups. We prove that this is due to the commutativity. Each language accepted by a nite automaton over an abelian group is actually a unordered vector language. Finally, deterministic nite automata over groups are investigated. TUCS Research Group Mathematical Structures of Computer Science
منابع مشابه
Three-Way Two-Dimensional Deterministic Finite Automata with Rotated Inputs
Inoue et al. introduced an automaton on a twodimensional tape, which decides acceptance or rejection of an input tape by scanning the tape from various sides by various automata which move one way, and investigated the accepting power of such an automaton. This paper continues the investigation of this type of automata, especially, ∨-type automata (obtained by combining four three-way two-dimen...
متن کاملOn the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata
We investigate the succinctness of several kinds of unary automata by studying their state complexity in accepting the family {Lm} of cyclic languages, where Lm = {a | k ∈ N}. In particular, we show that, for any m, the number of states necessary and sufficient for accepting the unary language Lm with isolated cut point on one-way probabilistic finite automata is p1 1 +p α2 2 + · · ·+ps s , wit...
متن کاملOn the power of parallel communicating Watson-Crick automata systems
Parallel communicating Watson-Crick automata systems were introduced in [2] as possible models of DNA computations. This combination of Watson-Crick automata and parallel communicating systems comes as a natural extension due to the new developments in DNA manipulation techniques. It is already known, see [5], that for Watson-Crick finite automata, the complementarity relation plays no active r...
متن کاملExtended finite automata over groups
Some results from Dassow and Mitrana (Internat. J. Comput. Algebra (2000)), Griebach (Theoret. Comput. Sci. 7 (1978) 311) and Ibarra et al. (Theoret. Comput. Sci. 2 (1976) 271) are generalized for finite autómata over arbitrary groups. The closure properties of these autómata are poorer and the accepting power is smaller when abelian groups are considered. We prove that the addition of any abel...
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 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 1997