Topic
ω-automaton
About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.
Papers published on a yearly basis
Papers
More filters
TL;DR: The study of the characteristic properties of abstract finite computer automata and their growing sequences leading to infiniteComputer automata will clarify the deep and crucial differences between traditional computation theory based on an infi'n~te concept Ce and a computation theory for computers which are strictly finite devices.
Abstract: The study of the characteristic properties of abstract finite computer automata and their growing sequences leading to infinite computer automata will clarify the deep and crucial differences between traditional computation theory based on an infi'n~te concept Ce.g., a Turing machine) and a computation theory for computers which are, and always will be, strictly finite devices. THe study of concrete arithmetic automata and programming languages accepted by ~m ~ will provide insight rinto the essential properties of finite computer arithmetics and their axiomatic-systems with respect to proving the correctness of programs an~ will lead to a knowledge which could ~nfluence the design of a new computer arithmetics and new architectures. The programming language accepted ~y a finite concrete computer automaton is an advanced defini'tion as it reflects the most important property of programs, i.e., teat-they are algorithms which should be executed. A domain and function are associated wit~ each program.-Further, the execution sequence and computat¢on are clearly differentiated. A computer automaton differs from a classical automat6n by viewing input symbols as instructions, and states as states of memory. Thus, each computer automaton controlled by a sequence of in$~u ctions may define a function from states to states. 22 I. Abstract Finite Computer Automaton A__n abstract finite computer automaton., (process) on A ~_Z Alg with s~. The programming (algorithmic) language, ALA, accepted by A is the set of all programs Alg such that there exists at least one st~ and CActiv(A,Alg,st~). The function, FA,A~ (st&)=StK, for each st~eDomaigAlg is called evaluatable on A b~ Alg. Both Alg and Alg* from A1A are function equivalent if FA,A~ =FA,i~. If ProcessA, i~ is the set of all completed execution sequences, Alg and Alg* are process equivalent if ProcessA,~ =Process Aj~t~e. 23 function and process equivalencies are decidable, the former is much less efficient than the latter. A finite abstract computer automaton can be represented in plane as its transition graph, TGA=, where • is a labelling of edges, (st,st*)&T~StxSt, by sets of instructions defined as follows: r=(st,st*)={in~ In;tra___D_~(in,st)=st*]. edges, (in,in~)~C~PxP, by sets of states defined as follows: ~(in,in*)={st~St;co~(in,st)=in*}. Graph theoretical terminology may then be used. Each completed computation is a finite path in a transition graph while each completed execution sequence (process) is a finite path in a control graph starting with inK, etc. If contr~ in Alg=. is independent of states, Alg is called sequen%i@! and the multiset, P, may be ordered in …
01 Jan 2005
TL;DR: Limits of DFAs in one letter input alphabet are discussed and it is shown that approximately 1/4 of all subsets are unreachable and for every fixed k∈{2,...,number-of-states-2} at least one subset of size k is unreachable.
Abstract: NFA usually requires significantly less states than DFA to recognize the same language. NFAs in one letter input alphabet are more restricted and the gap between NFAs and DFAs decreases, because the power of NFA is in its ability to reach many subsets of its state set. We discuss limitations of DFAs in one letter input alphabet and show that approximately 1/4 of all subsets are unreachable and for every fixed k∈{2,...,number_of_states-2} at least one subset of size k is unreachable.
TL;DR: Criteria of finiteness of the class of automata indistinguishable by simple experiments of infinite and finite length under the condition that, instead of the input-output sequence generated by an automaton, an experimenter observes this sequence coded by some function (observation medium).
Abstract: We consider criteria of finiteness of the class of automata indistinguishable by simple experiments of infinite and finite length under the condition that, instead of the input-output sequence generated by an automaton, an experimenter observes this sequence coded by some function (observation medium). Under the same conditions we obtain a criteria of break of the chain of classes of automata indistinguishable by experiments of finite length as the length of the experiments increases.
TL;DR: It is proved the universality of the proposed representation of abstract automata by finite groups is proved and its properties are studied.
Abstract: We consider the problem of representing abstract automata by finite groups. We prove the universality of the proposed representation and study its properties.
22 Apr 2007
TL;DR: A new class of one-dimensional cellular automata is presented that shows better pseudo-randomness properties based on Knuth's empirical tests than linear hybrid cellular Automata and linear feedback shift register.
Abstract: In this paper, we present a new class of one-dimensional cellular automata (which can be considered as a special case of a two dimensional cellular automata) that shows better pseudo-randomness properties based on Knuth's empirical tests than linear hybrid cellular automata and linear feedback shift register. A theorem is given to calculate the number of distinct transitions and the effectiveness of our proposed cellular automata is investigated by using them as test pattern generators for built-in self-test of the ISCAS 89 benchmark circuits. Our experimental results show that our cellular automata produce better sequential fault coverage than linear feedback shift register and linear hybrid cellular automata.