Results 1 
6 of
6
MultiHead Finite Automata: Characterizations, Concepts and Open Problems
 EPTCS 1
, 2009
"... Multihead finite automata were introduced in [36] and [38]. Since that time, a vast literature on computational and descriptional complexity issues on multihead finite automata documenting the importance of these devices has been developed. Although multihead finite automata are a simple concept, ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
(Show Context)
Multihead finite automata were introduced in [36] and [38]. Since that time, a vast literature on computational and descriptional complexity issues on multihead finite automata documenting the importance of these devices has been developed. Although multihead finite automata are a simple concept, their computational behavior can be already very complex and leads to undecidable or even nonsemidecidable problems on these devices such as, for example, emptiness, finiteness, universality, equivalence, etc. These strong negative results trigger the study of subclasses and alternative characterizations of multihead finite automata for a better understanding of the nature of nonrecursive tradeoffs and, thus, the borderline between decidable and undecidable problems. In the present paper, we tour a fragment of this literature.
Communication Gap for Finite Memory Devices ⋆
"... Abstract. So far, not much is known on communication issues for computations on distributed systems, where the components are weak and simultaneously the communication bandwidth is severely limited. We consider synchronous systems consisting of finite automata which communicate by sending messages w ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. So far, not much is known on communication issues for computations on distributed systems, where the components are weak and simultaneously the communication bandwidth is severely limited. We consider synchronous systems consisting of finite automata which communicate by sending messages while working on a shared readonly data. We consider the number of messages necessary to recognize a language as a its complexity measure. We present an interesting phenomenon that the systems described require either a constant number of messages or at least Ω((logloglogn) c) of them (in the worst case) for input data of length n and some constant c. Thus, in the hierarchy of message complexity classes there is a gap between the languages requiring only O(1) messages and those that need a nonconstant number of messages. We show a similar result for systems of oneway automata. In this case, there is no language that requires ω(1) and o(logn) messages (in the worst case). These results hold for any fixed number of automata in the system. The lower bound arguments presented in this paper depend very much on results concerning solving systems of diophantine equations and inequalities.
Aspekty Komunikacyjne Oblicze N Systemw Automatw Sko Nczonych
, 1999
"... port I would never be able to finish this thesis. I also thank my parents; they were always enthusiastic about my work. Contents 1 Introduction 1 1.1 Modes of Cooperation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Complexity Issues for Multiautomata Systems . . . . . . . ..."
Abstract
 Add to MetaCart
port I would never be able to finish this thesis. I also thank my parents; they were always enthusiastic about my work. Contents 1 Introduction 1 1.1 Modes of Cooperation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Complexity Issues for Multiautomata Systems . . . . . . . . . . . . . . . . . . 2 1.3 Notions and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3.1 Multiautomata and Multiprocessors Systems . . . . . . . . . . . . . . . 4 1.3.2 Alternative Notion: Multihead and Multiprocessor Finite Automata. . 5 1.3.3 Communication Complexity . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.4 Communication Measure for Multiautomata Systems . . . . . . . . . . 6 1.3.5 Kolmogorov Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.6 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Previous Results . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Power of Cooperation and Multihead Finite Systems ⋆
"... Abstract. We consider systems of finite automata performing together computation on an input string. Each automaton has its own read head that moves independently of the other heads, but the automata cooperate in making state transitions. Computational power of such devices depends on the number of ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We consider systems of finite automata performing together computation on an input string. Each automaton has its own read head that moves independently of the other heads, but the automata cooperate in making state transitions. Computational power of such devices depends on the number of states of automata, the number of automata, and the way they cooperate. We concentrate our attention on the last issue. The first situation that we consider is that each automaton has a full knowledge on the states of all automata (multihead automata). The other extreme is that each automaton (called also a processor) has no knowledge of the states of other automata; merely, there is a central processing unit that may “freeze ” any automaton or let it proceed its work (so called multiprocessor automata). The second model seems to be severely restricted, but we show that multihead and multiprocessor automata have similar computational power. Nevertheless, we show a separation result. 1
A SIMULATION OF OBLIVIOUS MULTIHEAD ONEWAY FINITE AUTOMATA BY REALTIME CELLULAR AUTOMATA
"... ar ..."
(Show Context)